The International Symposium on Lattice Field Theory is an annual conference that attracts scientists from around the world. Originally started as a place for physicists to discuss their recent developments in lattice gauge theory, nowadays the conference is the largest of its type and has grown to include areas like algorithms and machine architectures, code development, chiral symmetry, physics beyond the standard model, and strongly interacting phenomena in low-dimensions.
The 40th Lattice conference will take place at Fermilab, Batavia, Illinois, USA, from July 31 to August 4, 2023.
Confirmed plenary speakers
Panelists for a discussion on "Exascale Computing"
Critical slowing down and topological freezing severely hinder Monte Carlo sampling of lattice field theories as the continuum limit is approached. Recently, significant progress has been made in applying a class of generative machine learning models, known as "flow-based" samplers, to combat these issues. These generative samplers also enable promising practical improvements in Monte Carlo sampling, such as fully parallelized configuration generation. In this talk, I will discuss the progress towards this goal and future prospects of the method.
Upon taking a bosonic quantum field theory in the Hamiltonian formalism and discretizing the field on a lattice, the theory becomes equivalent to a non-relativistic many-body problem. Neural networks have recently been proposed as effective wavefunction parametrizations in numerical searches for ground state solutions of quantum many-body problems using variational Monte Carlo. We introduce a novel way of enforcing Bose-symmetric neural network functions and apply them to study several non-relativistic quantum systems as well as 1+1d $\phi^4$ theory non-perturbatively.
We present a trainable framework for efficiently generating gauge configurations, and discuss ongoing work in this direction. In particular, we consider the problem of sampling configurations from a 4D $SU(3)$ lattice gauge theory, and consider a generalized leapfrog integrator in the molecular dynamics update that can be trained to improve sampling efficiency.
Effective String Theory (EST) is a non-perturbative framework used to describe confinement in Yang-Mills theory through the modeling of the interquark potential in terms of vibrating strings. An efficient numerical method to simulate such theories where analytical studies are not possible is still lacking. However, in recent years a new class of deep generative models called Normalizing Flows (NFs) has been proposed to sample lattice field theories more efficiently than traditional Monte Carlo methods. In this talk, we show a proof of concept of the application of NFs to EST regularized on the lattice. Namely, we use as case study the Nambu-Goto string in order to use the well-known analytical results of this theory as a benchmark for our methods.
Calculations of topological observables in lattice gauge theories with traditional Monte Carlo algorithms have long been known to be a difficult task, owing to the effects of long autocorrelations times. Several mitigation strategies have been put forward, including the use of open boundary conditions and methods such as parallel tempering. In this contribution we examine a new approach based on out-of-equilibrium Monte Carlo simulations. Starting from thermalized configurations with open boundary conditions on a line defect, periodic boundary conditions are gradually switched on. A sampling of topological observables is then shown to be possible with a specific reweighting-like technique inspired by Jarzynski's equality. We discuss the efficiency of this approach using results obtained for the 2-dimensional $\text{CP}^{N-1}$ model. Furthermore, we outline the implementation of our proposal in the context of Stochastic Normalizing Flows, as they share the same theoretical framework of the non-equilibrium transformations we perform, and can be thought of as their generalization.
Lattice gauge-equivariant convolutional neural networks (LGE-CNNs) can be used to form arbitrarily shaped Wilson loops and can approximate any gauge-covariant or gauge-invariant function on the lattice. Here we use LGE-CNNs to describe fixed point (FP) actions which are based on inverse renormalization group transformations. FP actions are classically perfect, i.e., they have no lattice artefacts on classical gauge-field configurations satisfying the equations of motion, and therefore possess scale invariant instanton solutions. FP actions are tree–level Symanzik–improved to all orders in the lattice spacing and can produce physical predictions with very small lattice artefacts even on coarse lattices. They may therefore provide a solution to circumvent critical slowing down towards the continuum limit.
A previous calculation of baryon-baryon scattering using CLS ensembles with nonperturbatively $O(a)$-improved Wilson fermions revealed large discretization effects in the scattering amplitude. It is natural to ask whether other systems with heavy hadrons are affected. Using the same setup and adding valence charm quarks with the same action, we study $DD^*$ scattering and the $T_{cc}$ tetraquark. With up to six lattice spacings, we examine the dependence on $a$ and focus on discretization effects beyond the ones that affect a single $D$ or $D^*$ meson.
We perform a lattice simulation to investigate the doubly charm tetraquark $T^+_{cc}$ observed by the LHCb collaboration with flavor content $cc\bar{u}\bar{d}$, isospin-$0$, and only $0.4$ MeV below the $D^{*+}D^0$ threshold. We implement two-meson interpolators, and additionally also diquark-antidiquark interpolators. This is the first extraction of the scattering amplitude from correlators based on both types of operators. The simulation is performed on $N_f=2+1$ CLS ensembles in the lattice spacing with $m_\pi \simeq 280$ MeV and $a \simeq 0.086$ fm. The main aim of this work is to determine the impact of the diquark-antidiquark operators on the eigenenergies and the scattering amplitude.
The doubly charmed tetraquark $T_{cc}^+$ recently discovered by the LHCb collaboration is studied on the basis of (2 + 1)-flavor lattice QCD simulations of $D^*D$ system with nearly physical pion mass $m_\pi = 146$ MeV. The interaction of $D^* D$ in the isoscalar and $S$-wave channel, derived from the hadronic spacetime correlation by the HAL QCD method, is attractive for all distances and leads to a near-threshold virtual state with a pole position $E_{\rm pole} = −38(73)(^{+20}_{−53})$ keV and a large scattering length $1/a_0 = −0.05(5)(^{+2}_{−2})$ fm$^{−1}$. The virtual state is shown to evolve into a loosely bound state as $m_\pi$ decreases to its physical value by using a potential modified to $m_\pi = 135$ MeV based on the pion-exchange interaction. Such a potential is found to give a semi-quantitative description of the LHCb data on the $D^0 D^0 \pi^+$ mass spectrum.
The study of doubly heavy tetraquarks has gained substantial topical interest, primarily boosted by the recent discovery of doubly charmed tetraquark $T_{cc}$ and by its phenomenological prospects. While $T_{cc}^+$ is observed to be $\sim$0.4 MeV below the $DD^*$ threshold, multiple lattice calculations point to a deep binding ($\mathcal{O}(100 MeV)$) in $T_{bb}$. However, the predictions for the binding in $T_{bc}$ are scattered. We report a lattice study of $DB^*$-$BD^*$ scattering in the isoscalar axial-vector channel with the explicitly exotic flavor $bc\bar u\bar d$. The simulation is performed on four $N_f=2+1+1$ MILC gauge ensembles with different lattice spacings and volumes. The $DB^*$ scattering amplitudes are extracted from the low-lying finite-volume spectra following the amplitude analysis {\it \'a la} L\"uscher. The light quark mass ($m_{u/d}$) dependence of the continuum extrapolated amplitudes is analyzed to determine the fate of the $bc\bar u\bar d$ at the physical $m_{u/d}$. We find strong evidence for a bound $bc\bar u\bar d$ tetraquark at physical $m_{u/d}$ in this channel. We also determine the critical $m_{u/d}$ at which such a state becomes unbound.
In this talk, we present preliminary results on $\pi\pi$ and $\rho\rho$ coupled-channel scattering with 4 degenerate light quark flavors. We focus on different scattering channels, two of which are attractive and possess the same quantum numbers as the two $X_{0,1}(2900)$ tetraquark candidates recently discovered at LHCb. Using Luscher's formalism, we investigate these resonances in the scattering amplitude. We will also discuss some ongoing study on the large $N_\mathrm{c}$ scaling of these scattering processes, which may shed light on the nature of such exotic states.
The SU(3) gauge theory with $N_f=10$ fundamental flavors is thought to be close to the sill of the conformal window. I describe a recent study of this system using the continuous $\beta$ function method based on the gradient flow. We use a Pauli-Villars improved gauge action and several gradient flow transformations. These features allow us to study the system at much stronger gauge couplings than previously possible. Prior lattice studies could not explore gauge couplings above $g^2 \approx 10$. We find strong evidence of a conformal infrared fixed point at $g^2 \approx 15$. The mass anomalous dimension at the conformal fixed point is $\gamma_m\approx 0.6$, indicating that the theory is well above the sill of the conformal window. Our results are consistent with those of prior studies where their domains overlap.
We use the continuous renormalization-group method, based on the gradient flow, to study a candidate theory of composite Higgs and a partially composite top. The model is an SU(4) gauge theory with four Dirac fermions in each of the fundamental and two-index antisymmetric representations. Our lattice action includes a set of Pauli-Villars fields, which decouple in the continuum limit while allowing us to reach much stronger renormalized coupling than otherwise possible. We find that the theory has an infrared fixed point at g^2≃15.5 in the gradient flow scheme. The mass anomalous dimensions are large at the fixed point. On the other hand, the anomalous dimensions of top-partner operators do not exceed 0.5 at the fixed point. This disfavors the theory as a model of partial compositeness.
Symmetric mass generation (SMG) is a new mechanism that leads to massive bound states without spontaneous symmetry breaking. An SMG phase could lead to a resolution of the chiral fermion problem on the lattice. Expectations from 't Hooft anomaly cancellation, combined with recent finite-size scaling results, indicate that the SU(3) gauge-fermion system with two sets of staggered fermions could support the existence of an SMG phase that is accessed by crossing a Berezinsky-Kosterlitz-Thouless (BKT)-like phase transition from weak to strong coupling. In this talk, we explore the $\beta$-function of this system. Using the gradient-flow-based "continuous $\beta$-function method'', our preliminary result for the continuum-extrapolated RG $\beta$-function shows signatures that are consistent with the development of a conformal fixed point.
The renormalization group beta function describes the running of the renormalized coupling, connects the ultraviolet and infrared regimes of quantum field theories, and characterizes the nature of gauge-fermion systems. Using the concept of the continuous beta function and renormalized couplings obtained from the gradient flow, we present results for SU(3) gauge theories with $N_f=2$, 4, 6, 8, 10 or 12 fundamental flavors. Our results are based on dynamical gauge field ensembles generated with three times stout-smeared Möbius domain-wall fermions and Symanzik gauge action.
The origin of the infinite volume based beta-function from the gradient flow is discussed with its technical implementations. Recent applications include the new beta function with ten massless fermion flavors in the SU(3) color representation and the new effort to calculate with high precision the QCD running coupling at the $Z$~pole.
Speaker: Prof. Robert Shrock
Institution: Stony Brook University
Title: Higher-Order Calculations of Anomalous Dimensions at
Infrared Fixed Points in Gauge Theories and Studies of Renormalization-Group
Behavior of Some Scalar Field Theories
Abstract
We discuss higher-order calculations of anomalous dimensions of
operators at an infrared fixed point in asymptotically free gauge
theories with various fermion contents and compare with recent results
from lattice simulations. This work is in collaboration with
T. Ryttov. If time permits, we will also report on higher-order
studies of the beta functions in O(N) $\phi^4_4$ and $\phi^6_3$
theories [R. Shrock, PRD 107, 056018 (2023); PRD 107, 096009 (2023)].
We discuss the properties of Quantum Chromodynamics at finite temperature obtained by means of lattice simulations with the overlap fermion discretization. This fermion discretization preserves chiral symmetry even at finite lattice spacing. We present the details of the formulation and discuss the properties of the chiral thermal phase transition. We compare the results obtained with the chiral fermions with predictions by other fermion discretizations.
Quantum chromodynamics (QCD) which is the theory of strong interactions describes the thermodynamics of strongly interacting matter at finite temperatures and densities. At low temperatures, chiral symmetry is broken in the QCD vacuum and as temperature increases, a transition occurs where chiral symmetry is restored, resulting in the formation of the quark gluon plasma (QGP). It is found that for the vanishing values of the light quark masses this is a
true phase transition from low to high temperatures. However, for the finite values of light quark masses, it is a smooth crossover transition from hadronic bound states to the quark gluon plasma (QGP).
In this talk, we will report our ongoing calculations of the (2+1)-flavor QCD thermodynamics with Mobius Domain Wall fermions. We consider a fifth dimension with a length of twelve, which controls the effect of the residual mass ($m_{res}$) reasonably well[1,2]. We will present chiral condensate and chiral susceptibilities calculated on several lattice spacings and lattice
volumes along the line of constant physics. Furthermore, we will also present preliminary results of quark number susceptibilities and conserved charge fluctuations.
[1] Thermodynamics with Möbius domain wall fermions near physical point (I), Y. Aoki, Lattice2022
[2] Thermodynamics with Möbius domain wall fermions near physical point (II), I. Kanamori, Lattice2022, PoS LATTICE2022 (2023) 176
We present calculations of the complex potential at non-zero temperature in 2+1 flavor QCD.
The complex potential is obtained from spectral reconstruction of the Wilson line correlators
at non-zero temperature calculated on the lattice. The calculations are performed using the HISQ
action at three lattice spacings, a=0.028 fm, a=0.04 fm and a=0.049 fm for temperatures in the range
130 MeV - 352 MeV. Quite surprisingly, we find that the real part of the potential is not
screened and is approximately equal to the zero temperature potential, while the imaginary
part of the potential increases with the temperature and distance between the static quarks.
The order of finite temperature QCD phase transition on the lower left corner of Columbia plot is yet to be determined, and the current studies show that the bound of critical mass has a strong cutoff and discretization scheme dependence. We present an update on the QCD phase transition with 3 flavors of Möbius domain wall fermions at zero chemical potential. We performed simulations on lattices of size $36^3\times12\times16$, $24^3\times12\times32$ and $36^3\times14\times16$ with a varity of quark masses at lattice spacing $a=0.1361(20)$ fm. Our previous study with one volume ( $24^3\times12\times16$) appeared to be consistent with a crossover at quark mass around 4 MeV ($\overline{\mathrm{MS}}$, 2 GeV) for temperature 121 MeV by investigating the Binder cumulant [1]. Now we add the larger volume ($36^3\times12\times16$) computation to investigate the volume dependence towards the thermodynamic limit for this temperature. In this talk, we will show the results of such analyses to discuss the nature of transition there. Besides that, with the newly generated lattices $24^3\times12\times32$, we will show the the effects of residual chiral symmetry breaking on the observables by using different $L_s$.
[1] Finite temperature QCD phase transition with 3 flavors of Möbius domain wall fermions, Yu Zhang et al., PoS LATTICE2022 (2023) 197
Based on simulations of 2+1 flavor lattice QCD with M\"obius domain wall fermions at high temperatures, we use a series of recently developed spatial correlation functions to study the screened masses for quarks in meson bound states. We compare these screened masses with the symmetries of the correlators using a pair of fitting ansatz for various quark masses and lattice sizes with temperatures above the critical point. Using these spatial correlation functions we can analyze the lattices by way of standard $SU(2)_L \times SU(2)_R$ symmetry as well as examine the behaviors of the anomalous axial $U(1)_A$ symmetry above the critical point. Additionally we explore a possible and emergent chiral-spin symmetry $SU(2)_{CS}$ which we discuss at length.
We study the $U(1)_A$ anomaly at high temperatures of $N_f=2+1$ lattice QCD with chiral fermions. Gauge ensembles are generated with M\"obius domain-wall (MDW) fermions, and in the measurements, the determinant is reweighted to that of overlap fermions. We report the results for the Dirac spectra, the $U(1)_A$ susceptibility, and the topological susceptibility at temperatures, T=136, 153, 175, and 204 MeV.
We discuss implementations of lattice gauge theories on digital quantum computers. In particular, we investigate the number of gates required to simulate the time time evolution. Using state-of-the art methods with our own augmentation, we find that the cost of simulating a single time step evolution of an elementary plaquette is prohibitive in the current era of quantum hardware. Moreover, we observe that such a cost is highly sensitive to the scheme adopted in deriving lattice gauge theories Hamiltonians, emphasizing the need for low-dimensional formulations of lattice gauge theories in the same universality class as the desired continuum theories.
In this study, we investigate the real-time dynamics in the $(1+1)$d U(1) gauge theory called the Schwinger model via variational quantum algorithms. Specifically, we simulate the quench dynamics in the presence of the external electric field.
We first prepare the ground state in the absence of the external field using variational quantum eigensolver (VQE) and then perform the real-time simulation in the presence of the external field starting from the VQE results via variational quantum simulation (VQS). We use the same ansatz in both VQE and VQS which enables us to reduce the overall circuit depth.
We test our method using a classical simulator and confirm that our simulation results agree well with the exact results.
State preparation is a crucial aspect of quantum simulation of quantum field theories. When aiming to simulate Standard Model physics, it is likely that fault-tolerant quantum computers will be required. In this regime, it is beneficial to consider algorithms that exhibit nearly optimal scaling with the problem parameters. Many of these algorithms rely on repeated calls to a block encoding of the Hamiltonian of interest. However, the construction of this block encoding is often a bottleneck in these algorithms, resulting in a large prefactor in the overall gate cost. To overcome this challenge, recent research has introduced several algorithms based on the Hamiltonian time evolution input model. In this approach, instead of querying the block encoding subroutine, one queries an exact time evolution circuit for some short period of time. In this talk, we will focus on one such algorithm called the Quantum Eigenvalue Transformation for Unitary Matrices (QETU). The physical system we consider is a particular formulation of U(1) lattice gauge theory in two spatial dimensions. In practice, we employ product formulas to approximate the time evolution circuit. By employing QETU, we are able to prepare the ground state of this system. Furthermore, we discuss how the gate count scales with the problem size, as well as discuss the effects of approximate implementation of time evolution via product formulas.
The digital quantum simulation of lattice gauge theories is expected to become a major application of quantum computers. Measurement-based quantum computation is a widely studied competitor of the standard circuit-based approach. We formulate a measurement-based scheme to perform the quantum simulation of Abelian lattice gauge theories in general dimensions. The scheme uses an entangled resource state that reflects the spacetime structure of each gauge theory. Sequential single-qubit measurements with the bases adapted according to the former measurement outcomes induce a deterministic Hamiltonian quantum simulation of the gauge theory on the boundary. Our construction includes the $(2+1)$-dimensional Abelian lattice gauge theory simulated on a 3-dimensional cluster state as an example and generalizes to the simulation of Wegner's lattice models that involve higher-form Abelian gauge fields. The resource state has a symmetry-protected topological order with respect to generalized global symmetries that are related to the symmetries of the simulated gauge theories on the boundary. We also propose a method to simulate the imaginary-time evolution with two-qubit measurements and post-selections.
We report on our on-going study of the $B_s \to K\ell\nu$ decay in $N_f=2+1$ lattice QCD. The M\"obius domain-wall action is employed for all quark flavors at a lattice cutoff of $a^{-1} \sim 2.5$ GeV. We present preliminary results for the relevant form factors extracted from correlator ratios by inspecting their ground state saturation.
Heavy-light semileptonic decays provide an important channel to perform high-energy precision tests of the standard model, determine $|V_{ub}|$, and test lepton flavour universality. In this talk, the current status of exclusive $B_s\to K\ell\nu$ semileptonic decays within the RBC-UKQCD Relativistic Heavy Quark (RHQ) project will be presented. We will present recently-published form factor results for $B_s\to K\ell\nu$ and discuss key findings. Combining our results with experimental data yields $|V_{ub}| = 3.8(6)\times 10^{-3}$, which is dominated by experimental error. The next phase of this work is the inclusion of a physical-point ensemble to more strongly constrain the chiral-continuum behaviour, which will also be particularly important for improving our analysis of $B\to\pi\ell\nu$. Additionally, a modified form factor fit ansatz will be presented, which potentially gives stronger constraints on excited-state contributions.
We compute the complete set of form factors for the $B\to \pi$, $B\to K$, and $B_s\to K$ amplitudes, which are needed to describe semileptonic $B$-meson decay rates for both the charged and neutral current cases. We use the highly improved staggered quark (HISQ) action for the sea and light valence quarks. The b quark is described by the Wilson-clover action in the Fermilab interpretation. Simulations are carried out on $N_f = 2+1+1$ MILC HISQ ensembles at approximate lattice spacings from 0.15 fm down to 0.057 fm. We present preliminary results for the form factors.
I discuss a model-independent framework for fitting hadronic
form-factor data, which is often only available at discrete
kinematical points, using parameterisations based on unitarity and
analyticity. The accompanying dispersive bound on the form factors
(unitarity constraint) is used to regulate the ill-posed fitting
problem and allow model-independent predictions over the entire
physical range. Kinematical constraints, for example for the vector
and scalar form factors in semileptonic meson decays, can be imposed
exactly. The core formulae are straight-forward to implement with
standard math libraries. I demonstrate the method for the exclusive
semileptonic decay $B_s\to K \ell \nu$, an example requiring one to use
a generalisation of the original Boyd~Grinstein~Lebed (BGL) unitarity
constraint.
We present recent progress on the lattice calculation of semileptonic form factors for $B \to D^{\ast} \ell \nu$ decay using linear fit method. We use the Oktay-Kronfeld (OK) action for the charm and bottom valence quarks. We use results of 2pt correlator fit of $B$ and $D^{\ast}$ meson as input parameters to the data analysis on the 3pt correlation functions. Here, the masses of charm and bottom quark are tuned non-perturbatively. For the light spectator quarks (up, down and strange), we use HISQ action. Lattice calculation is done on a MILC HISQ ensemble ($a=0.12 \, \text{fm}$, $m_\pi = 220 \, \text{MeV}$, and $N_f=2+1+1$ flavors).
In this talk we present a lattice determination of the hadronic susceptibilities that, as a consequence of unitarity and analyticity, constrain the form factors entering the semileptonic $b\rightarrow c$ transitions. We evaluate the longitudinal and transverse susceptibilities of the vector, axial and tensor polarization functions at zero momentum transfer from the moments of appropriate two-point correlation functions. The latter are obtained on the lattice employing gauge ensembles of the Extended Twisted Mass Collaboration (ETMC) with $N_f = 2 + 1 + 1$ flavors of Wilson-clover twisted-mass quarks with masses of all the dynamical quark flavors tuned close to their physical values. The simulations are carried out at four values of the lattice spacing, a ≃ 0.057,0.068, 0.080, 0.091 fm, with spatial lattice sizes up to L ≃ 7.6 fm. To allow for a smooth extrapolation to the physical b-quark mass, the heavy-quark mass is simulated directly on the lattice up to ≃3 times the physical charm mass.
We update our calculation of flavor diagonal nucleon axial, scalar and tensor charges on eight 2+1+1-flavor MILC HISQ ensembles using Wilson-clover fermions. We discuss the signal in the sum of the connected and disconnected contributions for the up, down and strange quarks, control over fits to remove excited state contamination, the simultaneous chiral-continuum fit used to extract the charges. We calculate the renormalization including mixing between flavors nonperturbatively using RI-sMOM. We compare two different determinations of $Z_\psi$, one from the quark propagator and the other from the nucleon vector charge and the vector Ward identity, and consider the resulting difference in the renormalized flavor diagonal charges.
The axial charge of the nucleon, $g_A$, has been computed extensively on the lattice. However, the axial charges for other octet baryons (hyperons) such as the $\Sigma$ and $\Xi$ baryons are less well known experimentally and theoretically.
Here we present results for the isovector axial, scalar and tensor charges, as well as for the second Mellin moments of isovector PDFs. This allows us to estimate SU(3) flavour symmetry breaking effects in the different channels. Moreover, the scalar charges are related to the difference between the physical up and down quark masses via the vector Ward identity and we determine this splitting.
Our calculations are performed on a large set of $N_f = 2 + 1$ CLS ensembles of non-perturbatively $O(a)$ improved Wilson fermions with tree-level Symanzik improved gauge action. For the computation of the required three-point functions we use a stochastic technique which enables us to simultaneously compute various combinations of currents and octet baryon interpolators.
We present results from the QCDSF/UKQCD/CSSM collaboration for the charges g_T, g_A and g_S of the baryon octet, obtained through the use of Feynman-Hellmann techniques. We use a flavour symmetry breaking method to systematically approach the physical quark mass using ensembles that span five lattice spacings and multiple volumes. We extend this existing flavour breaking expansion to also account for lattice spacing and finite volume effects in order to quantify all systematic uncertainties.
A lot of progress has been made in the direct determination of nucleon sigma terms. Using similar methods we consider the sigma terms of the other octet baryons as well. These are determined on CLS gauge field ensembles employing the Lüscher-Weisz gluon action and the Sheikholeslami-Wohlert fermion action with $N_\mathrm{f} = 2 + 1$. The ensembles analysed here have pion masses ranging from ${410}\,\mathrm{MeV}$ down to ${216}\,\mathrm{MeV}$ and lattice spacings covering a range between ${0.039}\,\mathrm{fm}$ and ${0.098}\,\mathrm{fm}$.
To tackle the well-known problem of excited state contamination we have studied the effect of different multi-state fits on the sigma terms. In order to investigate the systematic error arising from the varied treatment of the excited states we carry out the full analysis for different choices of multi-state fits. In the end, the sigma terms of the baryon octet are simultaneously extrapolated to the physical point taking the quark mass dependence and lattice spacing effects into account.
We report preliminary results from an analysis of the pion scalar form factor computed on a set of the $\mathrm{tr}[M]=\mathrm{const}$ CLS gauge ensembles with $N_f=2+1$ Wilson Clover-improved sea quarks. The calculations are carried out for light quarks masses corresponding to $M_\pi\approx 0.130\mathrm{MeV} \ldots 350\mathrm{MeV}$, four values of the lattic spacing $a\approx0.050\mathrm{fm}\ldots0.086\mathrm{fm}$ and a large range of physical volumes. A fine-grained momentum resolution is achieved by allowing for non-vanishing sink momenta and by including two particularly large and fine boxes close to physical quark masses (i.e. $T\times L^3 =192\times 96^3$, $M_\pi \le 172\mathrm{MeV}$, $a \le 0.064\mathrm{fm}$).
The pertinent quark disconnected contributions have been computed to high precision using a scheme combining 1.) the one-end trick on stochastic volume sources for the computation of differences between two quark flavors with 2.) the hopping parameter expansion and hierarchical probing to evaluate the loops for the heaviest, single quark flavor.
Traditionally, there has been a method to analyze the charge radius of the hadron based on the fits of its form factor with some model assumptions. Moreover, a completely different method has been proposed, which does not depend on the models. In this presentation, we explore several improvements to this model-independent method for analyzing the pion charge radius. Furthermore, we compare the results of the pion charge radius obtained from $N_{f}=2+1$ lattice QCD data at $m_{\pi}=0.51$ GeV using the three different methods: the traditional model-dependent method, the original model-independent method, and our improved model-independent method. In this comparison, we take into account systematic errors estimated in each analysis.
We present results of a study of spontaneous symmetry breaking through fermion bilinear condensation in the single flavor Thirring Model in 2+1$d$. Domain Wall Fermions are used to capture the symmetry breaking pattern U(2)$\to$U(1)$\otimes$U(1) in the limit of domain wall separation $L_s\to\infty$, with the conserved fermion current coupled to a real vector auxiliary field defined throughout the bulk. The new feature is use of both hyperbolic tangent and Zolotarev Optimal Rational Function approximations to the signum function, which enhances $L_s$-convergence, together with the use of both Shamir and Wilson kernel functions for the corresponding overlap operator. The results yield compatible equations of state, consistent with the existence of a unique continuum limit at a strongly-coupled UV fixed point.
The RBC & UKQCD collaborations have successfully employed G-parity boundary conditions in the measurement of $K\to\pi\pi$ decays to obtain a physical decay with the two-pion ground state, at the cost of a significant increase in computational expense. We report on new theoretical/algorithmic developments based upon the properties of the Dirac operator under complex conjugation that have been exploited to achieve highly significant computational cost reductions, and explain their impact on our ongoing effort to repeat the calculation on finer lattices.
When calculating hadronic matrix elements using a lattice regulator,
the presence of power divergences in the lattice spacing poses a significant challenge.
Non-perturbatively subtracting these power divergences presents
both theoretical and numerical difficulties.
The gradient flow offers a theoretically sound and numerically robust approach
for renormalizing power divergences.
We demonstrate how to establish a connection between flowed and physical (unflowed)
hadronic matrix elements, focusing specifically on the quark content of the nucleon and
CP-odd local operators as illustrative examples.
The measurements of nucleon Electric Dipole Moments (EDMs) are important to probe CP violation and physics beyond the Standard Model. In this talk, I will report our recent progress in calculating nucleon theta EMDs using background electric field. We extract neutron EMDs by measuring the energy shift of 2pt correlation function in the presence of background field. The gauge ensembles are dynamical domain wall configurations with lattice spacings of a=0.11 fm and the corresponding pion mass are 340MeV and 430MeV, respectively.
We present results from our lattice QCD study of the contribution of the isovector quark chromo-electric dipole moment (qcEDM) operator to the nucleon electric dipole moments (nEDM). The calculation was carried out on four 2+1+1-flavor of highly improved staggered quark (HISQ) ensembles using Wilson-clover quarks to construct correlation functions. We use the non-singlet axial Ward identity including corrections up to O(a) to show how to control the power-divergent mixing of the isovector qcEDM operator with the lower dimensional pseudoscalar operator. Results for the nEDM are presented after conversion to the MSbar scheme at the leading-log order.
Neutrinoless double beta decay is a hypothetical beyond the Standard Model (BSM) process that, if observed, would imply that neutrinos are Majorana particles. Interpreting the results of double beta decay experiments requires knowledge of nuclear matrix elements that are calculable with lattice QCD. This talk presents determinations of the long-distance (mediated by a light Majorana neutrino) and short-distance (mediated by heavy BSM physics) contributions to the $n^0n^0\rightarrow p^+p^+e^-e^-$ decay through lattice QCD calculations, performed on a single ensemble at heavier-than-physical quark mass where the dineutron is assumed to be bound. These results provide proof-of-concept and can be used to compute low-energy constants in effective field theory, and we present a determination of these quantities.
To conquer topological freezing in gauge systems, we develop a variant of trivializing map proposed in Luecher 2019. We in particular consider the 2D U(1) pure gauge model, which is the simplest gauge system with topology. The trivialization is divided into several stages, each of which corresponds to integrating local degrees of freedom, the decimation, which can be seen as coarse-graining. The simulation using the map has a gain in autocorrelation in wall clock time compared to conventional HMC which likely survives even in the continuum limit.
Scale separation is an important physical principle that has previously enabled algorithmic advances such as multigrid. Previous work on normalizing flows has been able to utilize scale separation in the context of scalar field theories, but mostly not in the context of gauge theories. In this talk, I will give an overview of a new method for generating gauge fields using heirarchical normalizing flow models. This method builds gauge fields from the outside in, allowing different parts of the model to focus on different scales of the problem. In addition I will present numerical results for U(1) and SU(3) gauge theories in 2, 3, and 4 spatial dimensions.
State-of-the-art simulations of discrete gauge theories are based on Markov chains with local changes in the field space, which however at very fine lattice spacings are notoriously difficult due to separated topological sectors of the gauge field resulting in very long autocorrelation times.
An approach, which can overcome long autocorrelation times, is based on trivializing maps, where a new gauge proposal is given by mapping a configuration from a trivial space to the target one, distributed via the associated Boltzmann factor. Using gauge equivariant coupling layers, the map can be approximated via machine learning techniques. However the deviations between exact distribution and approximated one scales with the volume in case of local theories, rendering a global update unfeasible for realistic box sizes.
In the talk, we will discuss the potential of localized updates in case of the 2D Schwinger Model. Using gauge-equivariant flow maps, a local update can be fine grained towards finer lattice spacing. Based on this we will present results on simulating the 2D Schwinger Model with dynamical Nf=2 Wilson fermions at fine lattice spacings with global correction steps and compare the performance to the HMC.
We show how multigrid preconditioners for the Wilson-clover Dirac operator can be constructed using gauge-equivariant neural networks. For the multigrid solve we employ parallel-transport convolution layers. For the multigrid setup we consider two versions: the standard construction based on the near-null space of the operator and a gauge-equivariant construction using pooling and subsampling layers. We show that both versions eliminate critical slowing down. We also show that transfer learning works and that our approach allows for communication-avoiding algorithms on large machines.
Tackling ever more complex problems of non-perturbative dynamics requires simulations and measurements on ever increasingly large lattices at physical quark masses. In the age of the exascale, addressing the challenges of ensemble generation and measurements at such scales requires a plethora of algorithmic advances, both in theory space and in the implementation space. In this talk we will focus on tackling these issues on the largest physical-quark ensembles in active use which feature a 192^3x384 global volume and utilize the HISQ fermion discretization. We will present results from a three-pronged approach implemented in the QUDA library for GPUs: a multigrid algorithm for HISQ fermions, a refactoring and optimization of the HISQ fermion force, and a local preconditioner to the Schur-preconditioned HISQ stencil.
We present a study of lattice quantum chromodynamics (QCD) calculations in 2+1 flavor full QCD ensembles with the stout smeared clover fermion action and Symanzik gauge action, at three lattice spacings in the range of a ∈ [0.05, 0.11] fm, three volume size and three pion masses down to the physical one. We determine lattice spacings by applying Wilson flow to all 11 ensembles, which is essential for comparing lattice results with experimental data. We conduct a joint fit of pion two-point correlation function, the partially conserved axial current (PCAC) relation, and a ratio of two two-point correlation functions for each valance quark mass in each ensemble, incorporating proper renormalization constants. Pion masses, quark masses, and decay constants are then extracted across ensembles. A global fit of squared pion masses (m2π) and pion decay constants (Fπ) across various quark masses according to next-to-leading order (NLO) partially quenched chiral perturbation theory equations is conducted, yielding the pion decay constant in the chiral limit, the chiral condensate, and a set of low-energy constants. Extrapolating to infinite volume and zero lattice spacing limits, our results show a light quark mass of mud = 3.375(79) MeV, considering the physical pion mass of 134.98 MeV. This result agrees with the FLAG 2019 average value for 2+1 flavor mud = 3.364(41) MeV. This study offers a detailed and precise determination of quark masses and will serve as the foundation of future study of these ensembles, enhancing our understanding of hadronic physics and the Standard Model.
We calculate the leading-order QED corrections to meson masses and bare quark masses. As lattice QCD calculations become more precise, these QED corrections are becoming more important. However, one of the challenges in adding QED effects to QCD calculations is avoiding power-law suppressed finite volume effects. These effects can enter calculations of many observables because QED has massless degrees of freedom. By using a recently introduced infinite-volume reconstruction method for QED, we are able to avoid this problem and perform calculations with exponentially-suppressed finite-volume effects.
We give an update on an ongoing project in which we calculate the masses of octet and decuplet baryons including isospin-breaking effects. To this end, we employ single- and two-state-fits to effective masses at leading and sub-leading order in the expansion in isospin-breaking parameters. In order to remove objective bias on asymptotic masses we furthermore compute an AIC-based model-average of our fits for which we show results on ensembles at lattice spacings of 0.064 fm and 0.076 fm with corresponding pion masses ranging from 220 MeV to 360 MeV.
The $\Lambda(1405)$ resonance is listed in PDG as a strangeness $S=-1$ baryon with quantum numbers $I(J^P)=0(\frac{1}{2}^-)$. However, most models based on chiral effective theory and unitary suggest two nearby overlapping resonance poles. This two-pole picture for the $\Lambda(1405)$ is disputed by recent phenomenological fits to experimental data which require only a single pole, and quark models which typically predict a single pole. In this presentation I will discuss the first lattice QCD computation of the coupled channel $\Sigma\pi$-$N\bar{K}$ scattering amplitude in the $\Lambda(1405)$ region. At a heavier-than-physical pion mass of $m_{\pi} = 200\,{\rm MeV}$, the amplitude clearly exhibits a virtual bound state below $\Sigma\pi$ threshold and an additional resonance pole just below $N\bar{K}$ threshold. These poles are identified from parametrizations of the two-channel $K$-matrix which are fit to the finite volume energy spectrum and analytically continued to the complex plane. Our first-principles QCD results cannot be described by a single pole and thus support the two-pole picture suggested by $SU(3)$ chiral symmetry and unitarity.
We perform a numerical study in lattice QCD on $\Lambda(1405)$, an excited $\Lambda$ baryon whose existence is not well explained by the quark model. Since the previous studies using the chiral unitary model suggest that $\Lambda(1405)$ may be explained by two poles in the octet and the singlet channels of the flavor SU(3), we calculate the HAL QCD potentials for the meson-baryon systems in both channels using gauge configurations in the flavor SU(3) limit on $32^4$ lattices with the meson mass $m_{M} \approx 670~\textrm{MeV}$.
We successfully extract a one-parameter family of potentials in the octet channel, all of which indicate an existence of one bound state. We find that the binding energy calculated from the meson-baryon potential in the octet channel is consistent with the one estimated from the octet baryon two-point function, though errors are much larger for the former. In the singlet channel, however, an existence of a zero point in the NBS wave function leads to a singular potential, which prevents a reliable extraction of the binding energy. We briefly discuss a possible solution to overcome this difficulty in a future study.
The Hamiltonian formulation of lattice QCD with staggered fermions in the strong coupling limit can be extended to 2 flavors. It has no sign problem at non-zero baryon density and isospin densities and allows for Quantum Monte Carlo simulations. We have implemented a Quantum Monte Carlo algorithm to measure the baryon and isospin densities in the $\mu_B$ - $\mu_I$ plane in the chiral limit. We also comment on the possibility to carry out corresponding simulations on a quantum computer.
We investigate QCD at large isospin density by computing correlation functions between sources with isospin charge $n=1,\ldots,6144$ on two lattice volumes at quark masses corresponding to a pion mass, $m_\pi\sim170$ MeV. By extracting the energies of the corresponding many-pion systems under the assumption of log-normality of the correlation function distributions, we determine the isospin chemical potential, the speed of sound, and related thermodynamic properties of the dense medium, extending previous work to considerably higher isospin chemical potentials, $\mu_I$. Significant deviations from perturbative QCD are seen until $\mu_I > 10 m_\pi$ and the speed of sound is seen to significantly exceed the expectation from a free gas of quarks over a large range of isospin chemical potentials.
We present a new way of computing the pion screening mass at finite isoscalar chemical potential $\mu_\ell$, starting from the Taylor expansion of the screening correlator in $\mu_\ell$. The method derives from the known exact expression for the free theory pion screening correlator at finite $\mu_\ell$. As a first check of the formalism, we compare the lattice results for the free theory screening correlator and its derivatives, obtained on an $80^3\times8$ lattice with HISQ/tree fermions, with the corresponding theoretical expressions. We find good agreement, thus verifying our approach. We then apply our formalism to calculate the $\mathcal{O}(\mu_\ell^2)$ correction to the pion screening mass for two temperatures in the range 2 GeV $
We determine the location of the critical point where the first-order deconfining transition in the heavy-quark region turns into a crossover in finite-temperature and density QCD with 2+1 flavors. Combining a hopping parameter expansion of the quark determinant with a reweighting method, we evaluate the chemical potential dependence of the critical point. By systematically calculating the coefficients of the hopping parameter expansion up to the higher order terms, it is found that the higher order terms are strongly correlated with the Polyakov loop, which is the first-order term, at each configuration. Furthermore, we find that the complex phase, which is important at finite density, is also strongly correlated with the complex phase of the Polyakov loop. Using this property, we develop a method for estimating the results incorporating high-order terms from calculations with only low-order terms. We report that the first-order phase transition region in the heavy-quark regime becomes exponentially narrower with increasing chemical potential. Since the hopping parameter at the critical point decreases exponentially with increasing density, the sign problem does not become too serious as the density increases, and the critical point can be evaluated up to a high density.
The Bielefeld Parma Collaboration has in recent years put forward a method to probe finite density QCD by the detection of Lee Yang singularities. The location of the latter is obtained by multi-point Padè approximants, which are in turn calculated matching Taylor series results obtained from Monte Carlo computations at (a variety of values of) imaginary baryonic chemical potential. The method has been successfully applied to probe the Roberge Weiss phase transition and preliminary, interesting results are showing up in the vicinity of a possible QCD critical endpoint candidate.
In this talk we will be concerned with a couple of significant aspects in view of a more powerful application of the method. First, we will discuss the possibility of detecting finite size scaling of Lee Yang/Fisher singularities in finite density (lattice) QCD. Secondly, we will discuss our attempts at detecting both singularities in the complex chemical potential plane and singularities in the complex temperature plane. The former are obtained from rational approximations which are functions of the chemical potential at given values of the temperature; the latter are obtained from rational approximations which are functions of the temperature at given values of the chemical potential.
We present an update for results on B-meson semileptonic decays using the highly improved staggered quark (HISQ) action for both valence and 2+1+1 sea quarks. The use of the highly improved action, combined with the MILC collaboration’s gauge ensembles with lattice spacings down to ~0.03 fm, allows the b quark to be treated with the same discretization as the lighter quarks. The talk will focus on updated results for $B_{(s)} \to D_{(s)}$ , $B_{(s)} \to K$ scalar and vector form factors.
I will present preliminary results of next-generation lattice-QCD calculations of the $\Lambda_b \to p$, $\Lambda_b \to \Lambda$, and $\Lambda_b \to \Lambda_c$ form factors based on RBC/UKQCD gauge-field ensembles with 2+1 flavors of domain-wall fermions. Compared to the work published in 2015 and 2016, the new calculations include three additional ensembles (one with 139 MeV pion mass, one with 0.73 fm lattice spacing, and one with another volume) and were performed with a more accurate tuning of the charm and bottom anisotropic clover action parameters. I will also discuss a novel approach for the kinematic extrapolations of the form factors with dispersive bounds.
Recent experimental progress measuring the branching fractions of the heavy-baryon semileptonic decays $\Xi_c \to \Xi \ell \nu$ have stimulated theoretical interest and motivate precise lattice calculations of the form factors. Here we present such a calculation using domain-wall fermions for the up, down, and strange quarks, and an anisotropic clover action for the charm quark. We use four ensembles generated by the RBC and UKQCD collaborations, with lattice spacings between 0.111 and 0.073 fm and pion masses ranging from 420 to 230 MeV. Our preliminary results for the form factors are larger in magnitude than previous lattice results.
We present a study on the nonperturbative calculation of observables for inclusive semileptonic decays of $B_{(s)}$-mesons using lattice QCD. We focus on the comparison of two different methods to analyse lattice data of Euclidean correlation functions and address inverse problems, specifically Chebyshev and Backus-Gilbert approaches. This type of computation may eventually provide new insight into the long-standing tension between the inclusive and exclusive determinations of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements $|V_{cb}|$ and $|V_{ub}|$.
We report the results from a pilot lattice computation for the decay $B_s \to X_c \, l \nu_{l}$, where the valence quark masses are approximately tuned to their physical values using the relativistic-heavy quark action for the $b$ quark and the domain-wall formalism for the other valence quarks. We address the computation of the total decay rate as well as leptonic and hadronic moments, discussing similarities and differences between the two analysis techniques.
We report on the progress in the analysis of the inclusive semi-leptonic decay of the $D_s$ meson. This analysis is based on a pilot simulation conducted for the $D_s \rightarrow X_s \ell\nu$ process where we employed Möbius domain-wall charm and strange quarks whose masses were tuned to be approximately physical and where we covered the whole kinematical region.
The focus of this talk is to present our progress in how the systematic error due to the presence of finite-volume effects can be estimated. Due to limitations in the available data, we construct a modelling strategy which is then used to fit to our lattice data to investigate the extrapolation to the infinite-volume limit. This procedure also includes a discussion of cut-off effects for higher energies which we encounter during the modelling stage of our data.
I give a status update for the Grid Python Toolkit software project.
The rise of exascale supercomputers has fueled competition among GPU vendors, requiring lattice QCD practitioners to write code that supports multiple GPU architectures and APIs. We present SIMULATeQCD, a simple multi-GPU lattice code for large-scale QCD calculations, mainly developed and used by the HotQCD collaboration. Our open source code is built on C++ and MPI, includes CUDA and HIP back-ends and leverages modern C++ language features to provide high level data structures, objects and algorithms that allow users to express lattice QCD calculations in an intuitive way without sacrificing performance. In this talk, we explain the design strategy, discuss implementation details, and show benchmarks of performance critical kernels on recent supercomputers, including Perlmutter and Frontier.
In the rapidly changing hardware landscape of high performance computing (HPC), binding workforce to optimize simulation software for just a single architecture becomes a sustainability issue.
In this work I explored the feasibility of using performance portable parallel code for a staggered fermion kernel. Fusing the Kokkos C++ Performance Portability EcoSystem with MPI allows to scale on massive parallel machines while still being able to target a plentitude of different architectures with the same simple code.
Benchmarking on a range of currently deployed and recently introduced systems, including AMD EPYC 7742, AMD MI250, Fujitsu A64FX, Nvidia A100 and Nvidia H100 components, produced mostly encouraging results.
In this presentation, we will discuss the application of recent and emerging C++ features, with a focus on portable parallel programming in lattice QCD. Specifically, the discussion will center around certain key features introduced in the C++17, C++20, and C++23 standards, as well as an exploration of some experimental features currently under development.
A primary emphasis will be placed on accelerator programming, aiming to highlight the potential of these modern C++ features in achieving highly efficient and portable solutions to enhance and streamline the programming of complex LQCD applications.
I will give a status update of using OpenMP target offloading in the Grid library. As part of the US Exascale Computing Project, we have been investigating the possibility of using a portable programming model in Grid to support execution on different architectures. OpenMP, a directives-based programming model, supports both CPU multithreading and different GPU architectures through appropriate compilers. After some success of using OpenMP target offloading in GridMini, a reduced version of Grid, we have implemented OpenMP target offloading in the full version of Grid. I will report recent benchmark results on NVIDIA, AMD and Intel GPUs and also discuss some issues encountered.
Hamiltonian truncation is a quantum variational method that approximates the ground state by minimizing the energy on a finite truncated basis of Hilbert space. A straightforward application of this method to quantum field theory would seem to be hopeless, since generic states in the Hilbert space have an exponentially small overlap with physical states. Nonetheless, this talk will present evidence that Hamiltonian truncation converges as a power law in the computational time on the lattice in finite volume. The talk will also explain why Hamiltonian truncation in the continuum is doomed for all but the simplest low-dimensional quantum field theories.
Qubit regularization provides a framework for studying gauge theories through finite-dimensional local Hilbert spaces, presenting opportunities for digital quantum simulations. In this talk, we investigate the IR phases of 2d QCD with the $\mathrm{SU}(N)$ gauge group via qubit regularization. In the continuum, a 2d $\mathrm{SU}(N)$ gauge theory coupled to a single flavor of fundamental massless Dirac fermions can be bosonized into an $\mathrm{SO}(2N)_1/\mathrm{SU}(N)_1$ Wess-Zumino-Witten (WZW) model or a compact boson. On the lattice, utilizing a strong-coupling expansion of the qubit-regularized Kogut-Susskind Hamiltonian with the assistance of a generalized Hubbard coupling, we demonstrate that the continuum physics can be reproduced by an XXZ spin chain, together with a gapped phase. We also show the existence of a confinement/deconfinement (screening) transition. These arguments are verified numerically in the $\mathrm{SU}(2)$ case using the tensor network approach. Our numerical results reveal that the lattice model has a central charge of 1, and its spectrum can be understood as the $\mathrm{SU}(2)_1$ WZW model perturbed by a tiny marginally irrelevant operator, which can be tuned away by the Hubbard coupling. The confinement/deconfinement transition is also verified numerically by measuring the string tensions.
Other than the commonly used Wilson’s regularization of quantum field theories (QFTs), there is a growing interest in regularizations that explore lattice models with a strictly finite local Hilbert space, in anticipation of the upcoming era of quantum simulations of QFTs. A notable example is Euclidean qubit regularization, which provides a natural way to recover continuum QFTs that emerge via infrared fixed points of lattice theories. A non-trivial question is whether such regularizations can also capture the physics of ultraviolet fixed points. Specifically, can we recover massive continuum QFTs which are free in the UV but contain a marginally relevant coupling?
In this talk, I will discuss a novel regularization of the asymptotically free massive continuum QFT that emerges at the BKT transition through a hard core loop-gas model. Our proposed model offers several advantages compared to traditional regularizations. Firstly, without the need for fine-tuning, it can reproduce the universal step-scaling function of the classical lattice XY model in the massive phase as we approach the phase transition. Secondly, our approach exhibits reduced finite size effects for certain universal quantities at the BKT transition compared to the traditional XY model. Lastly, our model serves as a prime example of Euclidean qubit regularization of an asymptotically free massive QFT and helps understand the emergence of asymptotic freedom as a relevant perturbation at a decoupled fixed point without fine-tuning.
We consider gauge theories on a four-dimensional torus, where the instanton number is restricted to an integral multiple of $p$. This theory possesses the nontrivial higher-group structure, which can be regarded as a generalization of the Green-Schwarz mechanism, between the $1$-form center and $\mathbb{Z}_p$ $3$-form symmetries. Following recent studies of the lattice construction of the $U(1)/\mathbb{Z}_q$ and $SU(N)/\mathbb{Z}_N$ principal bundles, we examine how such a structure is realized on the basis of lattice regularization.
We extend the definition of L\"uscher's lattice topological charge to the case
of $4$d $SU(N)$ gauge fields coupled with $\mathbb{Z}_N$ $2$-form gauge fields.
This result is achieved while maintaining the locality, the $SU(N)$ gauge
invariance, and $\mathbb{Z}_N$ $1$-form gauge invariance, and we find that the
manifest $1$-form gauge invariance plays the central role in our construction.
This result gives the lattice regularized derivation of the mixed 't~Hooft
anomaly in pure $SU(N)$ Yang--Mills theory between its $\mathbb{Z}_N$ $1$-form
symmetry and the $\theta$ periodicity.
TEK reduction is a well established technique that allows single-site simulations of Yang-Mills theory in the large-$N_c$ limit by exploiting volume reduction induced by twisted boundary conditions. We performed simulations for $SU(841)$ for several gauge couplings and applied standard Wilson flow techniques combined with a tree-level improvement methodology to set the lattice scale. The wide range of gauge couplings covered by our simulations allows us to explore a region in the coupling space where our data exhibits asymptotic scaling, and perturbation theory could be used to analyze the behavior of the $\beta$-function. In this talk I will review the methodology used and go thorugh the main results we obtained, including a determination of the $\Lambda$-parameter of Yang-Mills theory at large-$N_c$ in $\overline{\text{MS}}$-scheme.
We present preliminary results for the large-$N$ limit of the chiral condensate
computed from twisted reduced models. We followed a two-fold strategy, one constiting in extracting the condensate from the quark-mass dependence of the pion mass, the other consisting in extracting the condensate from the mode number of the Dirac operator.
The chiral condensate is computed from the mode number of the staggered Dirac operator. This result is compared with those obtained with other approaches, based on the quark mass dependence of the topological susceptibility and of the pion mass.
We present mechanisms to constrain fermionic condensates on the level of the path integral, which grant access to the quantum effective potential in the infinite volume limit. In the case of a spontaneously broken symmetry this potential possesses a manifestly flat region, which is usually inaccessible to the standard approach of a double limit of volume and explicit symmetry breaking. By constraining the appropriate order parameters such as the chiral condensate, one is then able to probe the flat region. We demonstrate our method of constraining fermionic condensates in low-dimensional four-fermion models, which exhibit a spontaneously broken chiral symmetry. We show how the potential flattens in the infinite volume limit and that the flat region is dominated by inhomogeneous field configurations.
Effective string theory has shown its universal power in the prediction of the spectrum of low-lying excited states of confining strings. In these works we focus on 3d Ising gauge model and vector $Z_N$ gauge theories. We have computed the low-lying confining flux tube spectrum in 3d Ising gauge model and shown that they agree with the prediction of the Nambu-Goto spectrum. Moreover, we observe a massive resonance on the string, which turns out to be the glueball mixing with flux tubes. In the vector $Z_N$ gauge theories (dual to clock spin models), we observe a continuous phase transition for $N \geq 4$, while for $N >5$ it is governed by O(2) universality class. Also for these cases we observe that they approach the glueball spectrum of U(1) gauge theory.
Searching for the dark matter is one of the major goals of contemporary astronomy and particle physics. Many experiments have performed the searches for the J/ψ radiative decays into invisible particles, and no signal was observed. In the future, several experiments have the great potential to significantly improve the upper limit on the branching fraction of J/ψ + invisible. In this talk, we present the first lattice QCD study on J/ψ→γνν, which serving as a standard model background for this invisible decay. After a continuous extrapolation for three different lattice spacings, an exact value of the branching fraction is obtained.
Suzuki-Trotter decompositions of exponential operators like exp(Ht) are required in almost every branch of numerical physics. Often the exponent under consideration has to be split into more than two operators, for instance as local gates on quantum computers.
In this talk, I will demonstrate how highly optimised schemes originally derived for exactly two operators can be applied to such generic Suzuki-Trotter decompositions.
After this first trick, I will explain what makes an efficient decomposition and how to choose from the large variety available.
Furthermore I will demonstrate that many problems for which a Suzuki-Trotter decomposition might appear to be the canonical ansatz, are better approached with different methods like Taylor expansions.
We will investigate the effectiveness of tuning HMC parameters using
information from the gradients of the HMC acceptance probability with
respect to the parameters. In particular, the optimization of the
trajectory length and parameters for higher order integrators will be
studied in the context of pure gauge and dynamical fermion actions.
We introduce nested sampling as a generic simulation technique to integrate over the space of lattice field configurations and to obtain the density of states. In particular, we apply it as a tool for performing integrations in systems with ergodicity problems due to non-efficient tunneling, e.g., in case of topological freezing or when computing first order phase transitions. As a proof of principle, we show how this technique avoids topological freezing in 2D U(1), allowing us to compute topological charge and susceptibility for a range of usually inaccessible values of $\beta$.
In the hybrid Monte Carlo simulation of $\mathrm{SU}(3)$ pure gauge theory, we explore a Fourier acceleration algorithm to reduce critical slowing down. By introducing a soft-gauge-fixing term in the action, we can identify the eigenmodes in the weak-coupling expansion of the action and eliminate the differences in their evolution frequencies. A special unit-link boundary, in which the links lying in the boundary faces are fixed to be unit matrices, is also proposed to eliminate the $\mathbb{Z}_3$ symmetry and the tunneling between $\mathbb{Z}_3$ phases in which is not of interest here. We present the theoretical details and the numerical implementation of this algorithm, compare the autocorrelation times of certain observables with the usual hybrid Monte Carlo algorithm to show its acceleration effect for weak coupling and examine its potential application to physically relevant lattice spacings.
We apply Harris' ergodic theorem on Markov chains to prove
the geometric convergence of Hamiltonian Monte Carlo: first on compact
Riemannian manifolds, and secondly on a large class of non-compact Riemannian
manifolds by introducing an extra Metropolis step in the radial direction. We
shall use $\phi^4$ theory as an explicit example of the latter case.
We report on the study of a version of the Riemannian Manifold HMC (RMHMC) algorithm, where the mass term is replaced by rational functions of the SU(3) gauge covariant Laplace operater.
RMHMC on a 2+1+1-flavor ensemble with near physical masses is compared against HMC, where increased rate of change in Wilson flow scales per fermion Molculardynamics step is observed.
We present updated results of the excited and exotic spectra of $B, B_s$ and $B_c$ mesons. The calculations are performed on dynamical, anisotropic lattices with relativistic heavy quarks. A first look at finite volume effects and next steps are also discussed.
We use the method of optimal distillation profiles to compute the low-lying charmonium spectrum in an $N_f = 3+1$ ensemble at the $SU(3)$ light flavor symmetric point ($m_{\pi} \approx 420$ MeV), physical charm quark mass and lattice spacing $a\approx 0.0429$ fm. The spectrum and mass splittings display good agreement with their values in nature and the statistical errors are comparable, if not smaller, than those of state-of-the-art lattice calculations. We also present first results on the mixing of charmonium with glueballs and light hadrons obtained in a similar $N_f = 3+1$ ensemble but at larger pion mass ($m_{\pi} \approx 1$ GeV).
It has been demonstrated that distillation profiles can be employed
to build optimized quarkonium interpolators for spectroscopy calculations
in lattice QCD. We test their usefulness for heavy-light systems on
(3+1)-flavor ensembles with mass-degenerate light and a charm quark in
the sea in preparation for a future DDbar-scattering analysis.
The additional cost of light inversions naturally leads to the question
if knowledge of optimal profiles can be used to avoid superfluous
computations. We show such optimal profiles for different lattice sizes and pion masses and discuss general trends.
Furthermore, we discuss the handling of momenta in this framework.
Experimentally many exotic charmonium-like mesons have already been discovered, for example, the $Z_c$ mesons. We study the spectrum of such states with isospin 1 focusing on the $\bar cc \bar qq$ channels with $J^{P}=1^{+}$, $C=\pm$. This is the first study of four-quark states with these quantum numbers, where the total momentum is non-zero. The simulations are performed on two $N_{\textrm{f}}=2+1$ CLS ensembles with different volumes and $m_{\pi}\simeq~280\,$MeV. We extract the finite-volume energy levels and determine the scattering amplitude assuming decoupled $D\bar D^*$ scattering close to the threshold using Lüscher's formalism. Additionally, one-channel $J/\psi \pi$ scattering for $C=-$ is considered, and upper bounds are put on the scattering length and $1/(p \cot{\delta})$ in certain energy regions, which constrains the interaction between $J/\psi$ and $\pi$.
We present preliminary results of lattice QCD calculations for $D\pi$ scattering with isospin-$\frac{1}{2}$ and $\frac{3}{2}$. Using newly generated $N_f=2+1$ Wilson-Clover configurations by the CLQCD collaboration, we examine two volume extents ($L^3 \times T=32^3 \times 96$ and $48^3 \times 96$) at the same lattice spacing ($a=0.080$ fm) with a pion mass of $m_\pi \approx 290$ MeV. Employing various operators in both the rest and the moving frame, we determine $S$-wave scattering phase shifts from finite-volume spectra, assuming negligible contributions from higher partial waves. We identify a virtual state associated with the $D_0^*$ in these ensembles. Ongoing investigations aim to determine higher partial waves and explore the $m_{\pi}$ dependence and the continuum limit.
We present preliminary results for the $\rho(770)$ and $K^*(892)$ resonances using the Lüscher method. This work employs distillation on an RBC-UKQCD $N_f=2+1$ domain-wall fermion lattice with a physical pion mass. We consider irreducible representations with only leading $P-$wave contributions and extract the associated low-lying energy levels. These are used to parametrise the scattering phase shifts. We study systematic errors resulting from the choice of fit ranges through a model-averaging technique.
We solve the long-standing problem concerning the fate of the chiral $U(1)_A$
symmetry in QCD-like theories at high temperature in the chiral limit. We
introduce a simple instanton based random matrix model that precisely
reproduces the properties of the lowest part of the lattice overlap Dirac
spectrum. We show that in the chiral limit the instanton gas splits into a
free gas component with a density proportional to $m^{N_f}$ and a gas of
instanton-antiinstanton molecules. The latter do not influence the chiral
properties, but for any finite quark mass the free gas component produces a
singular spectral peak at zero that dominates Banks-Casher type spectral
sums. By calculating these we show that the difference of the pion and delta
susceptibility vanishes only for three or more massless flavors, however the
chiral condensate is zero already for two massless flavors.
We perform a finite-size scaling analysis of the critical point in the heavy-quark region of QCD at nonzero temperature. Our previous analysis at $N_t=4$ is extended to a finer lattice with $N_t=6$ and $8$. The aspect ratio is also extended up to 18 to suppress the non-singular contribution. High-precision analysis of the Binder cumulant is realized by an efficient Monte-Carlo simulation with the hopping parameter expansion (HPE). Effects of higher order terms in the HPE are incorporated by the reweighting method.
From the analysis of the Binder cumulant of the Polyakov loop, we show that the behavior of this quantity has a small but statistically-significant inconsistency with the scaling of the magnetic observable in the Z(2) universality class. We then try to construct the order parameter corresponding to the magnetic observable from the conditions between relevant observables at the critical point. It is shown that the scaling of the order parameter thus constructed reproduces the Z(2) scaling.
The deconfinement transition in QCD is understood as the spontaneous breaking of $\mathbb{Z}_N$ symmetry at high temperatures. Accordingly, quark-gluon plasma generally includes some partial cells called center domains, each with a homogeneous Polyakov-loop. In this work, constructing an effective action describing the deconfinement vacuum of QCD with $N$ colors, we discuss the properties of center domains.
First, we evaluate the mass of local Polyakov-loop fluctuation and demonstrate that some fluctuation becomes a Nambu-Goldstone mode in the large-$N$ limit. We also discuss surface tension between two $\mathbb{Z}_N$ center domains. Second, we estimate the global vacuum-to-vacuum transition in a single center domain. We find that some threshold volume exists, where a domain larger than this volume is stable, and vice versa. Identifying the threshold as the lower bound of a stable center domain volume, we quantitatively argue the typical volume scale of center domains.
We describe how the general mechanism of partial deconfinement applies to large-N QCD and the partially-deconfined phase inevitably appears between completely-confined and completely-deconfined phases. Furthermore, we propose how the partial deconfinement can be observed in the real-world QCD with SU(3) gauge group. We propose how the Polyakov loop and chiral condensate should behave and test the proposal against lattice simulation data.
The effect of a finite volume presents itself both in heavy ion experiments as well as in recent model calculations. The magnitude is sensitive to the proximity of a nearby critical point. We calculate the finite volume effects at finite temperature in continuum QCD using lattice simulations. We focus on the vicinity of the chiral crossover. We investigate the impact of finite volumes at zero and small chemical potentials on the QCD transition though the chiral observables.
The 't Hooft anomaly matching condition provides constraints on the phase structure at $\theta=\pi$ in 4D SU($N$) Yang-Mills theory. In particular, assuming that the CP symmetry is spontaneously broken at low temperature, it cannot be restored below the deconfining temperature at $\theta=\pi$. Here we investigate the CP restoration at $\theta=\pi$ in the 4D SU(2) case and provide numerical evidence that the CP restoration occurs at a temperature higher than the deconfining temperature unlike the known results in the large-$N$ limit, where the CP restoration occurs precisely at the deconfining temperature. The severe sign problem at $\theta=\pi$ is avoided by focusing on the tail of the topological charge distribution at $\theta=0$, which can be probed by performing simulations at imaginary $\theta$. In addition to this analysis, we carry out an alternative analysis based on the analytical continuation with respect to $\theta$ and discuss the consistency of the obtained results.
One possible approach to the quantum simulation of gauge theories involves replacing the gauge group, a compact Lie group, with one of its discrete finite subgroups. We show how the electric Hamiltonian may be interpreted as a Laplacian operator on the finite group and how this is related to the degeneracy of the electric ground state. Moreover, we discuss the dimension of the physical, gauge-invariant subspace, which is an important question for resource estimation. We give an exact formula for the dimension of the physical subspace of pure gauge theories with an arbitrary finite group on an arbitrary lattice and comment on the case of matter fields.
Hamiltonian simulations of quantum systems require a finite-dimensional representation of the operators acting on the Hilbert space. Here we present a discretization scheme for gauge links and canonical momenta of an SU(2) gauge theory which offers the possibility to freely refine the discretisation. This is achieved by discretising SU(2) and constructing the canonical momentum using the finite element method while the matrix representation of the gauge links is diagonal. We show that the fundamental commutation relations are fulfilled up to discretisation artefacts and the spectrum of the Hamiltonian is reproduced.
Numerical simulations of quantum Hamiltonians can be done representing the degrees of freedom as matrices acting on a truncated Hilbert space. Here we present a formulation for the lattice $SU(2)$ gauge theory in the so called "magnetic basis", where the gauge links are unitary and diagonal. The latter are obtained from a direct discretization of the group manifold, while the canonical momenta are built using an orthogonal transform on $S_3$. We discuss general considerations on the contraints of the spectrum of the free theory and the continuum manifold limit.
Simulations of bosonic field theories on quantum computers demand a truncation in field space to “fit” the theory onto limited quantum registers. We examine two different truncations preserving the same symmetries as the 1+1-dimensional $O(3)$ non-linear $\sigma$-model - one truncating the Hilbert space of functions on the unit sphere by setting an angular momentum cutoff and a fuzzy sphere truncation inspired by non-commutative geometry. We find evidence that the angular-momentum truncation fails to reproduce behavior of the $\sigma$-model, while the anti-ferromagnetic fuzzy model agrees with the full theory. These lessons will inform how we qubitize lattice gauge theories.
Formulating bosonic field theories for quantum simulation is a subtle task. Ideally, one wants the smallest truncation of the bosonic Hilbert space that simultaneously exhibits a high degree of universality. But many of the most straight-forward truncations probably do not exhibit much universality. Meanwhile, recent work on the so-called "fuzzy" sigma model has shown promise as a very efficient qubitization of the 1+1d sigma model, with only a 4-dimensional 1-site Hilbert space. In this talk we discuss the generalization of the fuzzy strategy to non-abelian gauge theories. We argue that a promising gauge theory can be constructed based on the Orland-Rohrlich gauge magnet, and we contrast this "fuzzy" gauge theory with the traditional Laplacian truncation strategy.
I will present ongoing efforts, by the Budapest-Marseille-Wuppertal collaboration, concerning the staggered-fermion computation of the HVP two-point function, on new 0.048 fm lattices. In particular, I will focus on aspects of our GPU determination of the Omega baryon mass, used for scale setting, and that of the connected, light-quark contribution to the muon g-2.
I review the status of the RBC/UKQCD g-2 program with focus on updates for the hadronic vacuum polarization.
We present an update, from the Fermilab Lattice, HPQCD, and MILC collaborations, of our results for the hadronic vacuum polarization contribution to the muon’s anomalous magnetic moment. Preliminary results for light-quark-connected contributions to the intermediate and long-distance window quantities employ new, low-mode-improved, data sets on our finest ensembles. We also present updated results for sub-leading contributions. The calculations are performed on 2+1+1 highly-improved staggered quark (HISQ) ensembles with physical pion mass at a range of lattice spacings (0.15fm-0.06fm).
In this study we employ staggered fermions to calculate the two-pion taste singlet states at rest. Leveraging the Clebsch-Gordan coefficients of the symmetry group associated with staggered fermions, we effectively compute the $\pi\pi$ contributions to the resting $\rho$-meson. To discern the distinct energy states involved, we adopt a generalized eigenvalue problem-solving approach. This work will provide insight into the important role played by the two-pion contribution to the anomalous magnetic moment of the muon.
In this talk, we present our group theoretic considerations and preliminary results on the contribution of two-pion states to the rho meson.
As several lattice collaborations agree on the result for the
window quantity of the hadronic vacuum polarization (HVP) contribution to
(g-2)_\mu, whilst being in tension with the calculation using the dispersive
approach, further effort is needed in order to pin down the cause for this
difference.
Here we investigate the isospin breaking corrections to the leading order HVP.
In many lattice applications, the photon propagator is treated
stochastically; however, by analogy with the hadronic light-by-light
contribution (HLbL) to (g-2),
we apply a coordinate-space approach to the HVP at NLO. We
present a calculation of the two diagrams of the (2+2) topology at
unphysical pion mass, where we apply a Pauli-Villars regularization for the
photon propagator in the diagram that is UV-divergent. We compare the
UV-finite diagram to the pseudoscalar exchange contributions.
We provide estimates for the light-quark-connected component of the RBC/UKQCD intermediate-window-hadronic contribution to the muon anomalous magnetic moment. We find significant tensions between our data-driven result,
$a_\mu^{W1,{\rmlqc}}=198.8(1.1)\times 10^{-10}$, and recent lattice computations.
We determine the scales $r_0$, $r_1$, and the ratio $r_0/r_1$ for 2 + 1 flavour QCD ensembles generated by CLS. These scales are determined from an improved definition of the static force which we measure using Wilson loops and furthermore use to study the shape of the static potential. Our analysis involves various continuum and chiral extrapolations of data that covers pion masses between 130 MeV and 420 MeV and five lattice spacings down to 0.038 fm.
Lattice QCD with Wilson quarks near the continuum limit can be described by Symanzik's effective continuum action which contains the dimension 5 operator, $m \,tr(F_{\mu\nu}F_{\mu\nu})$. Its effect can be eliminated by an O$(am)$ rescaling of the bare lattice coupling constant.The corresponding improvement coefficient, $b_g$, is currently only known to 1-loop order and the resulting uncertainty is now one of the dominant systematic errors in the recent determination of $\alpha_s(m_Z)$ with the decoupling method by the ALPHA collaboration. In this talk, I will discuss practical improvement conditions to determine $b_g$ non-perturbatively. A perturbative test reproduces the known 1-loop result and first non-perturbative results at parameters required for the alpha_s determination will be shown in a poster by Mattia Dalla Brida.
We present a first numerical implementation of a massive nonperturbative renormalisation scheme, RI/mSMOM, in the study of heavy quarks using the domain-wall fermion action. In particular, we calculate renormalisation constants for fermion bilinears at non-vanishing heavy quark masses and compare the approach to the continuum of the renormalised charm quark mass with that from a mass-independent scheme.
We report on the ongoing effort of improving the determination of the gradient flow scale on the 2+1+1 HISQ ensembles generated by the MILC collaboration. We measure the $t_0$ and $w_0$ scales with the Wilson and Symanzik flow using three discretizations for the action density: clover, Wilson and tree-level Symanzik-improved. For the absolute scale setting we intend to employ the Omega baryon mass but are also using the pion decay constant while the Omega-mass calculations are in progress.
We carry out a scale setting procedure of a mixed action setup
consisting of valence Wilson twisted mass fermions at maximal twist on
CLS ensembles with $N_f=2+1$ flavours of $O(a)$-improved Wilson sea
quarks. We determine the gradient flow scale $t_0$ using pion and kaon
isoQCD masses and decay constants as external input. We employ model
variation techniques to probe the systematic uncertainties in the
extraction of the ground state signals of lattice observables, as well
as for the continuum-chiral extrapolations used to compute $t_0$ at the
physical point.
We measure the static force directly by inserting chromo electric fields into the Wilson loop. We use the gradient flow to improve the signal-to-noise ratio, and to renormalize the field components. Furthermore, we can perform the continuum and zero flow time limit, obtaining a first direct determination of the QCD static force.
By comparing the lattice result with a perturbative calculation of the force, we can aim at a precise extraction of $\Lambda_0$. Additionally, we obtain a determination of the scales $r_1$, and $r_0$.
We present results for the electromagnetic form factors of the proton and neutron computed on the $(2 + 1)$-flavor Coordinated Lattice Simulations (CLS) ensembles including both quark-connected and -disconnected contributions. The $Q^2$-, pion-mass, lattice-spacing, and finite-volume dependence of our form factor data is fitted simultaneously to the expressions resulting from covariant chiral perturbation theory including vector mesons amended by models for lattice artefacts. From these fits, we determine the electric and magnetic charge radii and the magnetic moments of the proton and neutron. To assess the influence of systematic effects, we average over various cuts in the pion mass and the momentum transfer, as well as over different models for the lattice-spacing and finite-volume dependence, using weights derived from the Akaike Information Criterion (AIC). Our results for the magnetic moments of the proton and neutron are in good agreement with the experimental values and have a relative precision of about $2.5\,\%$ and $4\,\%$, respectively. For the electromagnetic charge radii of the proton, we achieve a $1.5\,\%$-level precision.
We present results of nucleon structure studies measured in 2+1 flavor QCD with the physical light quarks in a large spatial extent of about 10 fm. Our calculations are carried out with the PACS10 gauge configurations generated by the PACS Collaboration with the stout-smeared $O(a)$ improved Wilson fermions and Iwasaki gauge action at $\beta$=1.82 and 2.00 corresponding to the lattice spacings of 0.085 fm (coarser) and 0.063 fm (finer) respectively. At both lattice spacings, we evaluate nucleon form factors associated with lepton-nucleon elastic scattering measurements. In this talk, we will mainly report our preliminary results of the Root-Mean-Square radii and the discretization effects on them. In addition, the examination of the excited-states contaminations based on PCAC relation will be discussed using our data.
The Deep Underground Neutrino Experiment (DUNE) is an upcoming neutrino oscillation experiment that is poised to answer key questions about the nature of the neutrino. Lattice QCD has the ability to make significant impact upon DUNE by computing the interaction of a nucleon to a weak current. Nucleon amplitudes involving the axial form factor are part of the primary signal measurement process for DUNE, and precise calculations from LQCD can significantly reduce the uncertainty for inputs into Monte Carlo generators. Recent calculations of the nucleon axial charge have demonstrated that sub-percent precision is possible on this vital quantity. In this talk, I will discuss results for the Callat collaboration's calculation of the axial form factor of the nucleon. These computations are performed with M\"obius domain wall valence quarks on HISQ sea quark ensembles generated by the MILC and Callat collaborations. Preliminary results will be shown with a single ensemble at physical pion mass.
The current status of lattice-QCD numerical calculations by joint LHP and RBC collaborations of nucleon isovector vector- and axialvector-current form factors using a 2+1-flavor dynamical domain-wall fermions lattice QCD ensemble generated jointly by RBC and UKQCD collaborations will be presented. The lattice spacing is set at about 0.1141(3) fm, and the lattice spatial extent is 48 spacings or about 5.4750(14) fm. The dynamical strange and degenerate up and down quark mass values are set at their essentially physical values to provide the physical Ω mass and a degenerate pion mass of 0.1392(2) GeV. Our nucleon mass estimate is about 0.947(6) GeV. Possible excited-state contaminations in the calculated vector- and axialvector-current form factors are hidden below larger statistical noises. The numerical details of the form-factor shape parameters, such as the mean squared radii, the anomalous magnetic moment, or the pseudoscalar coupling extracted from the form factors, will be given, along with comparisons of different approaches used to extract them.
Proton and neutron electric and magnetic form factors are the primary characteristics of their spatial structure and have been studied extensively over the past half-century. At large values of the momentum transfer $Q^2$ they should reveal transition from nonperturbative to perturbative QCD dynamics and effects of quark orbital angular momenta and diquark correlations. Currently, these form factors are being measured at JLab at momentum transfer up to $Q^2=18$ GeV$^2$ for the proton and up to 14 GeV$^2$ for the neutron. We will report theoretical study of these form factors using nonperturbative QCD on the lattice, including $G_E$ and $G_M$ nucleon form factors with momenta up to $Q^2=12$ GeV$^2$, pion masses down to the almost-physical $m_\pi$=170 MeV, several lattice spacings down to $a=0.073$ fm, and high $O(10^5)$ statistics. Specifically, we study the $G_E/G_M$ ratios, asymptotic behavior of the $F_2/F_1$ ratios, and flavor dependence of contributions to the form factors. We observe qualitative agreement of our ab initio theory calculations with experiment. Comparison of our calculations and upcoming JLab experimental results will be an important test of nonperturbative QCD methods in the almost-perturbative regime.
The electromagnetic form factor, especially its asymptotic behavior for large momentum transfer ($Q^2$), of pion and kaon provides crucial insight into the partonic structure of a Nambu-Goldstone boson in the strong interaction. Studies of the electromagnetic form factor of pion and kaon up to $Q^2$ ~ 6 GeV$^2$ are underway at the ongoing JLab12 experiment and its measurements in an extended range of $Q^2$ ~ 10 – 40 GeV$^2$ are planned at the future Electron-Ion Collider (EIC). For the first time, we will present results for the pion and kaon electromagnetic form factor in the range of $Q^2$ ~ 0 – 10 and 28 GeV$^2$, respectively, from state-of-the-art lattice QCD calculations carried out using physical values of up, down, and strange quark masses. These results will provide benchmark QCD predictions for model-based studies and the experimental measurements, in particular at the boundaries between the JLab12 and the EIC.
I derive a formulation of the 2-dimensional critical Ising model on non-uniform simplicial lattices. Surprisingly, the derivation leads to a set of geometric constraints that a lattice must satisfy in order for the model to have a well-defined continuum limit. I perform Monte Carlo simulations of the critical Ising model on discretizations of a 2-sphere and I show that the simulations are in agreement with the 2d Ising CFT in the continuum limit. I discuss the inherent benefits of using non-uniform simplicial lattices to study quantum field theory and how the methods developed here can potentially be generalized for use with other theories.
A general geometrical framework is explored for quantum field theory on curved manifolds motivated by the recent map of the 2d Ising model on a triangulated grid to reproduce the integrable conformal field theory (CFT) on the modular torus ($\mathbb T^2$) and the Riemann sphere ($\mathbb S^2$). This talk will emphasize the special role of affine transformations as a bridge between Regge's simplicial Einstein gravity and simplicial lattice field theory at or near to an infrared critical point. To test and refine this geometrical framework a gradual sequence of lattice fields theories is being considered, including fermionic and gauge fields on cylindrical ($\mathbb R \times \mathbb S^{d-1}$) manifolds.
At its critical point, the three-dimensional Ising model is described by a conformal field theory (CFT), the 3d Ising CFT. While the critical exponents of the Ising model, which are related to the scaling dimensions of certain primary operators of the CFT, have been well-investigated in lattice calculations over the past few decades, the theory’s operator product expansion (OPE) coefficients have not been accessible with traditional Monte Carlo methods. If, however, instead of carrying out simulations on Euclidean lattices we use the Quantum Finite Elements method to radially quantize critical $\phi^4$-theory on simplicial lattices approaching $\mathbb{R} \times \mathbb{S}^2$, we show in this work that not only the scaling dimensions but also the OPE coefficients of the 3d Ising CFT can be extracted from the four-point function. We obtain these quantities by measuring the four-point function of identical scalars in a special antipodal frame on $\mathbb{R} \times \mathbb{S}^2$ at different lattice refinements, fitting the data with expectations from the OPE in radial quantization, and extrapolating to the continuum. Having already shown preliminary findings at LATTICE 2022, we present our final results for the scaling dimensions $\Delta_{\epsilon}$, $\Delta_{T}$ and the OPE coefficients $f_{\sigma \sigma \epsilon}$, $f_{\sigma \sigma T}$ of the first spin-0 and spin-2 primary operators $\epsilon$ and $T$, from which also the central charge of the theory can be calculated, and compare to values obtained with the conformal bootstrap and Hamiltonian methods on the fuzzy sphere.
Dynamical Triangulations might provide a tool to discover asymptotic safety in quantum gravity. This scenario is based on scale invariance which is realized at an interacting fixed point of the renormalization group flow. In this spirit, asymptotically safe quantum gravity is a quantum field theoretic approach to quantum gravity. On the lattice, asymptotic safety would be realized as a continuous phase transition in Dynamical Triangulations. The original formulation of Euclidean Dynamical Triangulations (EDT) is known to lack a continuous phase transition in d=4 dimensions. However, recent studies suggest that a modified version of EDT, which includes a local measure term, could exhibit a phase transition, leading to a well-behaved semi-classical limit. In this talk, I will review the current status of EDT with a non-trivial measure term and highlight emerging evidence that supports the possibility of a continuous phase transition. Finally, I will provide an outlook on ongoing research and on future studies.
I will discuss a discretization of Euclidean, weak-field General Relativity allowing the generation of a Markov chain of dynamic, pure gravity spacetimes at non-zero temperature via Metropolis algorithm with importance sampling. A positive action conjecture is implemented on the lattice, ensuring a probabilistic interpretation of exp(-S) and that dS=0 yields the Einstein field equations. Preliminary results demonstrating discretization and finite volume systematic effects will be presented and the coupling of dynamic spacetime to the QCD vacuum will be discussed.
The conventional discretisation of space-time entails a breaking of continuum symmetries and spoils the conservation of the associated Noether charges with ramifications for particle spectra and the renormalisation of central quantities, such as the Energy Momentum Tensor on the lattice.
In this work [1] we take first steps towards discretizing classical actions, while retaining its continuum space-time symmetries. Our proof-of-principle for a point particle in (1+1)d adopts the action formalism from general relativity, where both space $x(\gamma)$ and time $t(\gamma)$ are dependent variables of a worldline parameter $\gamma$. Discretizing in $\gamma$, leaves the values of both x and t continuous and thus the invariance under infinitesimal translations in (1+1)d remains intact. Building upon our previous work on solving initial values on the level of the system action [2], we show that the new relativistic approach allows to compute numerically the classical trajectory of a particle under an arbitrary bounded potential, while conserving the relativistic Noether charge for time translation symmetry exactly and at its continuum value in the interior of the simulated domain.
[1] A. Rothkopf, J. Nordström, (in preparation)
[2] A. Rothkopf, J. Nordström, J.Comput.Phys. 477 (2023) 111942 (2205.14028)
I will present a new method, developed in collaboration with M. Buzzicotti and N. Tantalo and based on deep learning techniques, to extract hadronic spectral densities from lattice correlators. Hadronic spectral densities play a crucial role in the study of the phenomenology of strong-interacting particles and the problem of their extraction from Euclidean lattice correlators has already been approached in the literature by using machine learning techniques. In devising a new method the big challenge to be faced can be summarized in two pivotal questions: 1) is it possible to devise a model independent training strategy? 2) if such a strategy is found, is it then possible to quantify reliably, together with the statistical errors, also the unavoidable systematic uncertainties? We faced the challenge and our answers to these questions will be the subject of the talk.
We present our sparse modeling study to extract spectral functions from Euclidean-time correlation functions. In this study covariance between different Euclidean times of the correlation function is taken into account, which was not done in previous studies. In order to check applicability of the method, we firstly test it with mock data which imitate possible charmonium spectral functions. Then, we extract spectral functions from correlation functions obtained from lattice QCD at finite temperature.
Distillation has been a useful tool in lattice spectroscopy calculations for more than a decade, enabling the efficient computation of hadron correlation functions. Nevertheless higher-dimensional compact operators such as baryons and tetraquarks pose a computational challenge as the time complexity of the Wick contractions grows exponentially in the number of quarks. This talk introduces a new method of performing Wick contractions efficiently in distillation space by exploiting the locality of smeared hadron sources combined with stochastic sampling procedures. The viability of the algorithm is demonstrated in a computation of $\Delta$-baryon and nucleon correlation functions.
The computation of the glueball spectrum is particularly challenging due to the rapid decay of the signal-to-noise ratio of the correlation functions. To address this issue, advanced techniques such as gauge link smearing and the variational method are commonly employed to identify the spectrum before the signal diminishes significantly. However, a significant improvement in the signal-to-noise ratio can be achieved by utilising multilevel techniques. In this talk, we present a study of the glueball spectrum in pure gauge theory with a two-level algorithm. Specifically, we explore the relation between noise reduction and the various multilevel parameters, such as the width of the dynamical regions and the number of two-level configurations.
The problem of extracting spectral densities from Euclidean correlators
evaluated on the lattice has been receiving increasing attention.
Spectral densities provide a way to access quantities of crucial
importance in hadronic physics, such as inclusive decay rates,
scattering amplitudes, finite-volume energies, as well as transport
coefficients at finite temperature. Many approaches have been developed
to tackle this challenging problem. In this talk, we review how
Backus-Gilbert methods can be interpreted in the Bayesian framework,
focusing on the systematics of the two approaches.
Euclidean Dynamical Triangulation as a lattice approach to quantum gravity has produced results that are compatible with semiclassical gravity in four dimensions. We explore the cosmological application of EDT by studying the behavior of the vacuum energy on the lattice. Although the lattice gravity calculations are broadly consistent with an emergent four-dimensional de Sitter space geometry, the calculations give corrections to a purely constant cosmological constant term. These corrections are well described by a simple model for running vacuum energy. The parameters of this model are fully determined by the lattice and can be compared with observational cosmology, which will strongly constrain this picture over the coming decade.
Euclidean Dynamical Triangulation (EDT) is a lattice approach to quantum gravity that has produced results compatible with semiclassical gravity in four dimensions. Although the lattice gravity calculations are broadly consistent with an emergent four-dimensional de Sitter space geometry, the calculations give corrections to a purely constant cosmological constant term. These corrections are well described by a simple model for running vacuum energy. A determination of the parameters of the model from the lattice is presented, along with a discussion of the implications for cosmology.
We present results from simulations of a spin(4) lattice gauge theory in four
dimensions containing a single flavor of massless reduced staggered fermion. This model does not
allow for single site gauge invariant bilinear fermion terms and instead
we show that it develops a four fermion condensate in the confining regime. The absence of symmetry breaking is consistent with the cancellation of a 't Hooft anomaly corresponding to a discrete $Z_4$ symmetry.
If the spin(4) symmetry is extended to SU(4) we argue that in the naive continuum limit the model contains the matter representations and global symmetries
of the Pati-Salam GUT model in which we can embed a single family of the Standard
Model
In this work we perform calculations in order to determine the renormalization factors and the mixing coefficients of the Yukawa and the quartic couplings in $\mathcal{N} = 1$ Supersymmetric QCD. The Yukawa couplings describe the interactions between gluino, quark and squark fields whereas the quartic couplings describe four-squark interactions. We discretize the action on a Euclidean lattice using the Wilson formulation for the gluino, quark and gluon fields; for squark fields (scalar fields) we employ naïve discretization. At the quantum level Yukawa and quartic interactions suffer from mixing with other operators which have the same transformation properties. Exploiting parity and charge conjugation symmetries of the Supersymmetric QCD action, we reduce the allowed mixing patterns. We compute, perturbatively to one-loop and to the lowest order in the lattice spacing, the relevant three-point Green’s functions so as to fine tune the Yukawa couplings and the relevant four-point Green’s functions to fine tune the quartic couplings. We use both dimensional and lattice regularizations as required for implementing the Modified Minimal Subtraction scheme. This work is a sequel to our earlier investigations on SCQD and completes the one-loop fine-tuning of the SQCD action on the lattice, thus paving the way for numerical simulations of SQCD.
We present our lattice simulations of gauge theories coupled to fermions and scalar fields in adjoint and fundamental representation. Supersymmetric gauge theories emerge as specific limiting cases within this theory space. We discuss our efforts to tune the parameters towards the supersymmetric limit.
Contour deformation methods have succesfully tamed sign problems in low-dimensional fermionic lattice fields theories at finite density. However, one obstacle with these methods is that they do not guarantee the existence of an integration contour which solves the sign problem completely, thus making it difficult for the methods to be applied to larger and more complex systems, such as lattice QCD. In this talk, I will introduce a strict generalization of the contour deformation methods: complex control variates. In the path integral, we subtract a function from the distribution function such that the phase fluctuations in the distribution are reduced while the physics does not change. Subtraction functions which entirely remove the sign problem exist for any lattice theories, although it is difficult to find them. In practice, subtraction functions, which remove the sign problem sufficiently, can be constructed analytically or numerically with the help of machine learning. I will demonstrate this method with the classical Ising model and the 1+1-dimensional Thirring model at finite density.
The sign problem has been an obstacle to first-principles calculations based on the Monte Carlo method. The Worldvolume Hybrid Monte Carlo (WV-HMC) method [Fukuma-Matsumoto 2020] is an efficient method to reduce the sign problem with low cost. In this talk, I apply the WV-HMC to the complex $\phi^4$ theory at finite density, and show that the computational cost is proportional to the degrees of freedom, $N$, in contrast to the $N^3$ scaling for other Lefschetz thimble methods.
The sign problem has been a major obstacle to first-principles calculations in various important physical systems. The Worldvolume Hybrid Monte Carlo (WV-HMC) method [Fukuma-Matsumoto 2020] may be a promising method towards solving the sign problem due to its versatility, reliability and low numerical cost. In this talk, I would like to report recent results on the application of the WV-HMC method to dynamical fermion systems. The emphasis will be on the Hubbard model, which is one of the simplest dynamical fermion systems that have the sign problem.
In the conventional lattice formulation, conducting a Monte Carlo study of the Schwinger model (quantum electrodynamics in 1 + 1 dimensions) with a topological $\theta$ term or at finite density is almost impossible due to the sign problem. In this talk, I present the lattice formulation of the bosonized Schwinger model, which allows us to study the model using the Monte Carlo method without encountering the sign problem. I demonstrate the validity of the formulation by presenting numerical results at a finite $\theta$ angle and finite density. I also discuss possible applications of this formulation to other models.
Relativistic fermionic theories with four-Fermi interactions have a broad range of applications, e.g., as toy models for QCD as well as in condensed-matter physics. We study the simplest such theory, the so-called Gross-Neveu model, exposed to a background magnetic field in 2+1 dimensions. In the mean-field limit the model exhibits a rich phase structure when the magnetic field and the chemical potential are both non-zero. We investigate the phase diagram of the full (i.e., beyond-mean-field) Gross-Neveu model on the lattice, using overlap fermions, and find that it is much simpler than in the mean-field limit.
We compute the screening masses of fields with nucleon quantum numbers for a wide range of temperatures between $T \sim 1$ GeV and $T\sim 160$ GeV. The computation has been performed by means of Monte Carlo simulations of lattice QCD with $N_f=2+1$ flavors of $O(a)$-improved Wilson fermions: we exploit a novel strategy which has recently allowed to determine for the first time non-singlet mesonic screening masses up to extremely high temperatures. The baryonic screening masses are measured with a few per-mille precision in the continuum limit, and percent deviations from the free theory result $3\pi T$ are clearly visible even at the highest temperatures. The observed degeneracy of the positive and negative parity state's screening mass, expected from Ward identities associated to non-singlet axial transformations, provides further evidence for the restoration of chiral symmetry in the high temperature regime of QCD.
We establish that the charmed hadrons start dissociating at the chiral crossover temperature, $\mathrm{T_{pc}}$, leading to the appearance of charm degrees freedom carrying fractional baryon number. Our method is based on analyzing the second and fourth-order cumulants of charm ($\mathrm{C}$) fluctuations, and their correlations with baryon number ($\mathrm{B}$), electric charge ($\mathrm{Q}$) and strangeness ($\mathrm{S}$) fluctuations. First-time calculation of the $\mathrm{QC}$ correlations on the high statistics ($\mathrm{N_\tau=8}$) datasets of the HotQCD Collaboration enables us to disentangle the contributions from different electrically-charged charm subsectors at and close to $\mathrm{T_{pc}}$. In particular, we see an enhancement over the PDG expectation in the fractional contribution of the $\mathrm{|Q|}=2$ charm subsector to the total charm partial pressure for $\mathrm{T
For $\mathrm{T_{pc}
We investigate a possible relation between the chiral susceptibility and axial U(1) anomaly in lattice QCD at high temperatures. Employing the exactly chiral symmetric Dirac operator, we can separate the purely axial U(1) breaking effect in the connected and disconnected chiral susceptibilitesin a theoretically clean manner. Preliminary results for 2 and 2+1 flavor lattice QCD near the critical temperature will be presented.
'Fit' independent methods are used to investigate temperature effects for the singly and doubly charmed spin $1/2$ baryons on the anisotropic FASTSUM 'Generation 2L' ensembles. Thereafter we determine where it is appropriate to apply standard fitting procedures in order to report the change in mass as the temperature increases. The negative parity sector is observed to be more strongly effected by temperature than the positive parity. Finally we examine the parity doubling due to the (partial) restoration of chiral symmetry and find estimates for the pseudo-critical temperature which are in good agreement with the measurement from the renormalised chiral condensate.
Significant tensions are observed between the dispersive and the lattice QCD results for hadronic vacuum polarization (HVP). We will present a general framework that allows to compare the two approaches and to combine them, if they can be reconciled. We have applied this framework to determine the distance or energy scales that could be responsible for the observed tensions and we will present the ensuing results. We will also discuss the limits in the information that can be extracted from a finite set of moment integrals of the R-ratio.
We present the first ab-initio calculation of the $\pi^0$, $\eta$ and $\eta^{\prime}$ transition form factors at the physical point using lattice QCD with staggered fermions on $N_f = 2 + 1 + 1$ gauge ensembles, generated by the Budapest-Marseille-Wuppertal collaboration. We compare our results with existing measurements and with other theoretical estimates. Using these transition form factors, we compute the pseudoscalar-pole contribution to the hadronic light-by-light scattering in the muon $g-2$ with a precision well below 10%, as needed for future experimental precision.
We present our computation of the pion and eta-meson transition form factors from twisted mass lattice QCD at physical quark masses. In particular, we report on the improvements we recently made in the calculation of the pion transition form factor, which finalizes the calculation with data presently available to us. We use the form factors to determine the pseudoscalar-pole contributions to the hadronic light-by-light scattering in the muon g-2, as well as the two-photon decay widths and pseudoscalar transition form factor slopes.
Our continuum estimate of the pion-pole g-2 contribution is comparable with other lattice and data-driven determinations while achieving a sub-10% precision. For the eta-pole contribution estimate at a single lattice spacing of 0.08 fm we achieve a sub-40% precision and are also compatible with other lattice and data-driven results. We further indicate the planned steps needed to achieve a continuum result for the eta-pole calculation.
We present the status of the Mainz group's lattice QCD calculation of the transition form factor $\mathcal{F}_{\pi^0\gamma^\ast\gamma^\ast}$, which describes the interaction of an on-shell pion with two off-shell photons. This form factor is the main ingredient in the calculation of the pion-pole contribution to hadronic light-by-light scattering in the muon $g-2$, $a^{\mathrm{HLbL};\pi^0}$.
We use the $N_f = 2 + 1$ CLS gauge ensembles, and we update our previous work by including a physical pion mass ensemble (E250). We compute the transition form factor in a moving frame as well as in the pion rest frame in order to have access to a wider range of photon virtualities. In addition to the quark-line connected correlator we also compute the quark-line disconnected diagrams that contribute to the form factor.
At the final stage of the analysis, the result on E250 will be combined with the previous work published in 2019 to extrapolate the form factor to the continuum and to physical quark masses.
Hadronic contributions dominate the uncertainty of the standard model prediction for the anomalous magnetic moment of the muon. In this talk, we will describe an ongoing lattice calculation of the hadronic, light-by-light, four-point function, performed with staggered fermions. The presence of quarks with different tastes complicates the analysis of this position-space correlation function. We present a suitable adaption of the “Mainz method". As a first numerical test, we reproduce the well-known lepton-loop contribution. Results at a single lattice spacing for the light quark contribution, using several volumes from 3 to 6 fm, will then be discussed. Our study of the long distance behavior and finite-volume effects is supplemented by considering the contribution of the light pseudoscalar-pole. The corresponding transition form factors have been evaluated in previous simulations on the same ensembles.
Deep Learning Models in the Machine Learning Community relies heavily on GPU-based tensor calculations. In recent years, Tensor Networks Methods have been explored to estimate the Partition Function of a system deterministically. One of the reasons Tensor Networks have not been yet utilised to the maximum potential in the Lattice Gauge Theories is their time complexity issue of the algorithms. Drawing motivation from these Machine Learning Models, we present a GPU-based acceleration of existing Tensor Networks Methods that reduces the simulation time.
For thermodynamics studies it is desirable to simulate two degenerate flavors and retain chiral symmetry. Staggered fermions can achieve this by rooting the determinant. Rooting can be avoided using minimally doubled fermions. This discretization describes two degenerate quark flavors while explicitly breaking hypercubic symmetry, thus requiring additional counterterms. We use one particular formulation of minimally doubled fermions called the Karsten-Wilczek action and mitigate lattice artifacts by improving the spatial derivatives in the Dirac operator. In this pilot study we determine the counter terms non-perturbatively to facilitate proper dynamical simulations.
The Karsten-Wilczek action is a formulation of minimally doubled fermions on the lattice which explicitly breaks hypercubic symmetry and introduces three counterterms with respective bare parameters. We present a tuning of the bare parameters of the Karsten-Wilczek action on 4-stout configurations at the physical point.
We present our implementation of the all-to-all meson field and low mode averaging (LMA) calculations, built on the Grid and Hadrons libraries. We discuss code optimizations made for staggered fermions and GPU offloading, as well as benchmark comparisons on leadership-class resources. We conclude with the statistical gains achieved using LMA for vector-current two-point functions relevant for computing the HVP contribution to muon $g-2$. The calculation is performed on 2+1+1 HISQ ensembles at physical pion mass and lattice spacings as small as 0.06 fm. We discuss the effect of this low-mode--improved data set on long-distance noise and the results of combining our new data with our previous high-statistics data.
The application of normalizing flows for sampling in lattice field theory has garnered considerable attention in recent years. Despite the growing community at the intersection of machine learning and lattice field theory, there is currently a lack of a software package that facilitates efficient software development for new ideas in this field. We present the idea of NeuLat, a fully customizable software package that unifies recent advances in the fast-growing field of deep generative models for lattice field theory in a single software library. NeuLat is designed to be modular, supports a variety of lattice field theories as well as normalizing flow architectures, and is easily extensible.
We believe that NeuLat has the potential to considerably simplify the application and benchmarking of machine learning methods for lattice quantum field theories and beyond.
In lattice-QCD calculations of parton distribution functions (PDFs) via large-momentum effective theory, the leading power (twist-three) correction appears as ${\cal O}(\Lambda_{\rm QCD}/P^z)$ due to the linear-divergent self-energy of Wilson line in quasi-PDF operators. For lattice data with hadron momentum $P^z$ of a few GeV, this correction is dominant in matching, as large as 30\% or more. We show how to eliminate this uncertainty through choosing the mass renormalization parameter consistently with the resummation scheme of the infrared-renormalon series in perturbative matching coefficients. An example on the lattice pion PDF data at $P^z = 1.9$ GeV shows an improvement of matching accuracy by a factor of more than $3\sim 5$ in the expansion region $x= 0.2\sim 0.5$.
We present recent updates on the lattice calculations of the valence-quark GPDs of the pion, the pion and kaon gluon PDF, and their first gluon moment in the physical-continuum limit. All these calculations are done on ensembles with $N_f = 2 + 1 + 1$ highly improved staggered quarks (HISQ), generated by the MILC Collaboration. The valence-quark GPD of the pion is done at lattice spacing 0.09~fm with physical pion masses and boosted pion momentum around 1.7~GeV with four additional nonzero transfer momenta in the Breit frame, using LaMET method with next-to-next-to-leading order perturbative matching. We update MSULat's previous meson gluon PDF calculations using pseudo-PDFs with a third lattice spacing at 0.09~fm with 310-Mev pion mass. We also present the first pion and kaon gluon moments at the continuum-physical limit with 3 pion masses and 3 lattice spacings.
The Light-Cone Distribution Amplitude (DA) encodes the non-perturbative information of the leading Fock-component of the hadron wave function, therefore required for processes including exclusive hadron production. As the Pseudo-Nambu-Goldstone boson of QCD, nonperturbative structure of the pion is of particular interest. We present a lattice QCD calculation of the pion DA on ensembles with O(a)-improved Wilson fermions on lattice spacings in the range of 0.0483fm-0.0749fm, and pion masses ranging from physical to 440MeV. The Pseudo-Distribution formalism is employed to match the Renormalization Group Invariant (RGI) matrix element to the DA.
The light-cone distribution amplitude (LCDA) of the pion carries information about the parton momentum distribution and is an important theoretical input into various predictions of exclusive measurements at high energy, including the pion electromagnetic form factor. We provide constraints on the fourth Mellin moment of the LCDA using the heavy quark operator product expansion (HOPE) method.
In this talk, we will discuss a new method to calculate parton distribution functions (PDFs) from correlations of boosted quarks and gluons in the Coulomb gauge.
Compared to the widely used quasi-PDFs defined from gauge-invariant Wilson-line operators, such correlations offer advantages including absence of linear power divergence, enhanced long-range precision, and accessibility to larger off-axis momenta. We verify the validity of this method at next-to-leading order in perturbation theory and use it to calculate the pion valence quark PDF on a lattice with spacing $a=0.06$ fm and valence pion mass $m_\pi=300$ MeV.
Our result agrees with that from the gauge-invariant quasi-PDF at similar precision, achieved with only half the computational cost through a large off-axis momentum $|\vec{p}|\sim2.2$ GeV.
When QCD is described by a non-relativistic EFT, operators consisting of gluonic correlators of two chromoelectric or -magnetic fields will often appear in descriptions of quarkonium physics. At zero T, these correlators give the masses of gluelumps and the moments of these correlators can be used to understand the inclusive P-wave decay of quarkonium. At finite T these correlators definite the diffusion of the heavy quarkonium. However, these correlators come with a divergent term in lattice spacing which needs to be taken care of. We inspect these correlators in pure gauge theory with gradient flow smearing, which should allow us to reduce and remove the divergence more carefully. At this talk we focus on the effect of gradient flow to these correlators and the reduction of this divergence.
The lattice gauge-scalar model with the scalar field in the fundamental representation of the gauge group has a single confinement-Higgs phase which is well-known as the Fradkin-Shenker-Osterwalder-Seiler analytic continuity theorem: Confinement and Higgs regions are subregions of an analytically continued single phase and there are no thermodynamics phase transitions between them.
In this talk, however, we show that we can define new type of operators which enable to separate completely the confinement phase and the Higgs phase. In fact, they are constructed in the gauge-invariant procedure by combining the original scalar field and the so-called color-direction field which is obtained by change of field variables based on the gauge-covariant decomposition of the gauge field due to Cho-Duan-Ge-Shabanov and Faddeev-Niemi.
We perform the numerical simulations for the model with SU(2) gauge group without any gauge fixing and found a new transition line which agrees with the conventional thermodynamical transition line in the weak gauge coupling and divides the confinement-Higgs phase into two separate phases, confinement and the Higgs, in the strong gauge coupling. All results are obtained in the gauge-independent way, since no gauge fixing has been imposed in the numerical simulations.
Moreover, we give a physical interpretation for the new transition from the viewpoint of the spontaneous breaking of a global (custodial) symmetry.
The lattice gauge-scalar model with the scalar field in the adjoint representation of the gauge group has two completely separated confinement and Higgs phases according to the preceding studies based on numerical simulations which have been performed in the specific gauge fixing based on the conventional understanding of the Brout-Englert-Higgs mechanism.
In this talk, we re-examine this phase structure in the gauge-independent way based on the numerical simulations for the model with SU(2) gauge group performed without any gauge fixing which is motivated to confirm the recently proposed gauge-independent Brout-Englert-Higgs mechanics for the mass of the gauge field without relying on any spontaneous symmetry breaking.
For this purpose we investigate correlation functions between gauge-invariant operators obtained by combining the original adjoint scalar field and the new field called the color-direction field constructed from the gauge field based on the gauge-covariant gauge-field decomposition due to Cho-Duan-Ge-Shabanov and Faddeev-Niemi.
We reproduce gauge-independently the transition line separating confinement and Higgs phase, and discover surprisingly a new transition line that divides the confinement phase into two parts.
Finally, we discuss the physical meaning of the new transition and implications to confinement mechanism.
In this talk, I summarize phenomenological results on topology, in particular the extraction of distinct topological sectors that resemble instantons, and support the picture of the QCD vacuum being filled with highly localized topological excitations.
Combining the identification of topological sectors (connected regions of either left- or right-handed winding in $n_f=2+1+1$ configurations) with a simple charge gradient approach increases the number of instanton sectors found. Such sectors deviate from the background by a distinct charge-volume behavior and, in addition, by a high degree of self-duality.
Defining the topological charge density with an improved $O(a^6)$ field strength removes leading UV lattice artifacts that would otherwise contribute to the multiplicative renormalization constant. As a result, we find that the total charge of the configurations Q is very close to integers and the charge content of the instanton sectors is close to $\pm1$.
In addition, I show that the topological charge density contains a wave standing in the simulation box and present evidence for a physical phenomenon as well as hints in favor of a link to the (auto)correlation oscillations introduced by the HMC [1].
[1] https://pos.sissa.it/430/045/pdf
Non-Abelian gauge fields having a line-singularity of the Dirac type lead us to violation of the non-Abelian Bianchi identity. The violation as an operator is equivalent to violation of Abelian-like Bianchi identities
corresponding to eight Abelian-like conserved magnetic monopole currents of the Dirac type in $SU(3)$ QCD. It is very interesting to study if these new Abelian-like monopoles are responsible for color confinement in the continuum $SU(3)$ QCD, since any reliable candidate of color magnetic monopoles is not known yet. If these new Abelian-like monopoles exist in the continuum limit, the Abelian dual Meissner effect occurs, so that the linear part of the static potential between a quark-antiquark pair is reproduced fully by those of Abelian and monopole static potentials. These phenomena are called here as perfect Abelian and monopole dominances. It is shown that the perfect Abelian dominance is reproduced fairly well, whereas the perfect monopole dominance seems to be realized for large $\beta$ when use is made of the smooth lattice configurations in the maximally Abelian (MA) gauge. Making use of a block spin transformation with respect to monopoles, the scaling behaviors of the monopole density and the effective monopole action are studied. Both monopole density and the effective monopole action which are usually a two-point function of $\beta$ and the number of times $n$ of the block spin transformation are a function of $b=na(\beta)$ alone for $n=1,2,3,4,6,8,12$. If the scaling behavior is seen for up to larger $n$, it shows the existence of the continuum limit, since $a(\beta)\to 0$ when $n\to\infty$ for fixed $b=na(\beta)$. Along with the previous results without any gauge fixing, these new results obtained in MA gauge suggest that the new Abelian-like monopoles play the role of color confinement in $SU(3)$ QCD.
We review the level of welcomeness that members of the lattice field theory community feel based on the results of a survey performed in May and June 2023. While respondents reported generally high levels of feeling welcome at the lattice conference, women and people with diverse gender identities, sexual orientations, ethnic backgrounds and religious affiliations feel less included and have more negative experiences at the lattice conference than their peers. Respondents report that they are actively informing themselves about inequities in the community, however a large fraction of survey participants underestimate the severity of the problem, as was found in previous surveys. The survey data indicate that this situation can be most effectively improved by organizing talks and events about issues of diversity and inclusion within the lattice community. Respondents also reported that individual readings of scientific papers on equity and inclusion are effective in giving people agency in making a change and hence it may be helpful to collate a collection of important articles on these topics.
In this study we present lattice results on the QCD $\beta$-function in the presence of a quark mass. The $\beta$-function is calculated to three loops in perturbation theory and for improved lattice actions; it is extracted from the renormalization of the coupling constant $Z_g$. The background field method is used to compute $Z_g$, where it is simply related to the background gluon field renormalization constant $Z_A$. We address quark mass effects on the background gluon propagator; its dependence on the number of colors $N_c$, the number of fermionic flavors $N_f$ and the quark mass, $m$, is shown explicitly. The perturbative results for the QCD $\beta$-function will be applied to the precise determination of the strong coupling constant, calculated by Monte Carlo simulations, removing the mass effects from the nonperturbative Green's functions.
We report basic properties of our new configuration set.We calculated the topological charge, the mass spectra for hadrons, and so on.The lattice spacing, $a^{-1}=2.339$[GeV], is fixed using the Omega baryon mass.
The ``Sphaleron Rate'' (imaginary linear-in-frequency part of the topological density retarded Green's function) determines the real-time relaxation rate of axial quark number for light quarks in a hot medium, and is relevant in heavy-ion collisions and electroweak baryogenesis. We recently showed how it can be determined in pure-glue QCD via standard Euclidean simulations, via a novel saddlepoint method.
We extend this work to find the sphaleron rate for (2+1)-flavor QCD with $N_\tau=8 - 16$ and HISQ action at almost physical pion masses in the temperature range $0.2 - 3$ GeV or $1.2 - 18$ times the crossover temperature $T_{pc}$. Similar to the pure gauge case, the QCD result is well described across the range of $1.6 - 8$ times $T_{pc}$ as $\Gamma_s \simeq 20 (\alpha_s T)^4$, where $\alpha_s$ is the MSbar coupling at $\overline{\mu}=2\pi T$, determined using the gradient-flow technique.
We report recent progress in data analysis on the two point correlation functions
which will be used to obtain form factors for the semileptonic decays $B_{(s)} \to D_{(s)}\ell\nu$.
We use a MILC HISQ ensemble ($a=0.12fm$ and $m_\pi = 310 MeV$) to produce the measurement data
using the HISQ light quarks and Oktay-Kronfeld (OK) action for the heavy quarks($N_f=2+1+1$ flavor).
We used a sequential Bayesian method for the analysis and adopt the Newton
method to improve the fitting quality and logistics.
We present recent progress in evaluatinging $\varepsilon_K$, the indirect
CP violation parameter in the neutral kaon system, calculated using
lattice QCD inputs directly from the standard model.
We report recent progress on data analysis for 2-point correlation functions with HYP-smeared staggered quarks. We use the sequential Bayesian fitting method. We present how to obtain a good initial guess using the Newton method. We report results of fitting 2-point correlation functions, including the excited states, for $P \times P$ and $P \times A$ operators.
Workflow management has become an important topic in many research communities. Here, we focus on the particular aspect of provenance tracking. We follow the W3C PROV standard and formulate a provenance model for Lattice QCD that includes the ensemble-generation and the measurement parts of the Lattice QCD workflow. Since many important provenance questions in our community require extensions of this model, we propose a multi-layered provenance approach that combines prospective and retrospective elements.
How and when do people become physicists? Are they always certain about their career choice? What are physicists like outside work? A team of physics students and faculty aim to answer these questions through the “My Journey as a Physicist” podcast. In each episode, a student host(s) interviews professional physicists to learn about their professional journey of how they ended up where they are today.
Guest physicists discuss their research, what got them interested in physics, obstacles they overcame, and what their typical day looks like. They also provide tips and suggestions for students who may be interested in studying physics and becoming physicists. Guests also share about their interests and hobbies outside of research; there are scoops about physicists that you only learn about in this podcast. We find that no two career paths are the same. This podcast provides insights on life as a physicist that listeners may not have otherwise learned.
Each season features physicists involved in different subfields of physics: Season 1 features physicists involved with lattice QCD (LQCD), associated with the 2021 INT Lattice Summer School [1], Season 2 features physicists involved with Snowmass [2], the US particle-physics planning community, and the latest Season 3 interviews those involved in the ongoing Nuclear Science Advisory Committee Long Range Plan (LRP) [3].
References:
[1] INT Summer School on Problem Solving in Lattice QCD https://sites.google.com/uw.edu/lqcdschool2021/home
[2] Snowmass, the US particle physics planning community https://snowmass21.org/
[3] Nuclear-Science Advisory Committee Long Range Plan (LRP) https://science.osti.gov/np/nsac
We examine the renormalized lattice spacing anisotropy in SU(2) Yang-Mills theory. We determine the physical anisotropy by performing anisotropic Wilson flow. Our preliminary findings indicate that, at high bare anisotropies, the physical anisotropy reaches a plateau. Further increase of the bare anisotropy results in a slight increase of the lattice spacings. Our findings can be then applied to the highly anisotropic lattices that have recently been utilised in real-time Yang-Mills simulations using the Complex Langevin method on complex time contours.
Here we present a lattice QCD determination of the first few Mellin moments of the pion distribution amplitude by analyzing the quasi-DA matrix elements using a lattice spacing of $a=0.836 \; \text{fm}$. Our work differs from previous work in that we use domain-wall fermions in order to respect chiral symmetry and that calculations are performed at the physical pion mass. First, we analyze ratios of the pion-pion correlator and the pion-quasiDA correlator to determine the bare matrix elements. We then renormalize these using the double-ratio scheme. Finally, we fit these data using the leading-twist Mellin operator product expansion (OPE) to determine the Mellin moments.
The extraction of the QCD coupling via non-perturbative decoupling methods has been recently shown to be a compelling strategy for high-precision determinations [Eur. Phys. J. C 82 (2022) 12, 1092]. One of the key ingredients of this strategy is the determination of a (finite-volume) non-perturbative massive coupling at large values of the quark-mass, $M$. Robust continuum limit extrapolations for this coupling require control over potentially large $O((aM)^n)$ discretization errors. In the case of Wilson-fermions, particular care must be taken, as $O(aM)$ effects are in principle also present. Once the quark-mass has been properly renormalized and $O(a)$-improved, the remaining $O(aM)$ effects can be eliminated by the proper tuning of a single $O(aM)$-improvement coefficient, $b_g(g_0^2)$. Following a novel strategy [see S. Sint parallel talk], in this poster we present first preliminary results for $b_g(g_0^2)$ for $N_f=3$ non-perturbatively $O(a)$-improved Wilson-fermions and Lüscher-Weisz gauge action in the range of bare couplings $g_0^2< 1.5$.
Ab-initio calculations of real-time evolution for lattice gauge theory have very interesting potential applications but present challenging computational aspects.
We show that tensor renormalization group methods developed in the context of Euclidean-time lattice field theory can be applied to calculation of Trotterized evolution operators at real time. We discuss the optimization of truncation procedures for various observables. We apply the numerical methods to the 1D Quantum Ising Model with an external transverse field in both the ordered and disordered phase and compare with universal quantum computing for $N_{s}=4,8,$ and $16$ sites.
General positivity constraints linking various powers of observables in energy eigenstates can be used to sharply locate acceptable regions for the energy eigenvalues, provided that efficient recursive methods are available to calculate the matrix elements. These recursive methods are derived by looking at the commutation relations of the observables with the Hamiltonian. We discuss how this self-consistent (bootstrap) approach can be applied to the study of digitized scalar field theory in the harmonic basis. Using known results, we develop the method by testing on quantum systems, including the harmonic and anharmonic oscillators. We report recent numerical results for up to four coupled anharmonic oscillators. From here, we consider the possibility of using the groundwork of this method as a means of studying phase transitions in 1+1 dimensions.
The Pauli strings appearing in the decomposition of an operator can be can be grouped into commuting families, reducing the number of quantum circuits needed to measure the expectation value of the operator. We detail an algorithm to completely partition the full set of Pauli strings acting on any number of qubits into the minimal number of sets of commuting families, and we provide python code to perform the partitioning. The partitioning method scales linearly with the size of the set of Pauli strings and it naturally provides a fast method of diagonalizing the commuting families with quantum gates. We provide a package that integrates the partitioning into Qiskit, and use this to benchmark the algorithm with dense Hamiltonians, such as those that arise in matrix quantum mechanics models, on IBM hardware. We demonstrate computational speedups close to the theoretical limit of $(3/2)^m$ relative to qubit-wise commuting groupings, for $m=2,\dotsc,6$ qubits.
Multilevel integration schemes are easy to couple with distillation, our current approach for computing highly optimized interpolating fields for hadrons. The locality of the distillation basis in the time direction can be exploited in accelerating the propagator computations with domain decomposition. Currently, we are exploring the use of asymmetric domain decomposition schemas in which the domains have only direct connections to a non-local domain. However, computing the contributions from the non-local domain may dominate the global performance of the calculation. We will show the impact on the accuracy and performance of preconditioning techniques for the resolution of linear systems with the non-local domain.
Numerous studies have demonstrated that the rapid decline in the efficiency of traditional sampling algorithms caused by Critical Slowing Down can be alleviated or even sidestepped completely using flow-based sampling. Such approaches trade off a reduction in autocorrelation times with an increase in the cost of generating new field configurations and an up-front training cost. The two-dimensional $\mathrm{CP}^{N−1}$ models exhibit severe Critical Slowing Down in their topological observables, making them good candidates for testing flow-based sampling in a more challenging setting without invoking the full complexity of QCD.
Part of the difficulty with the flow-based approach is in identifying suitable ways of parametrising families of invertible transformations, which need to balance expressivity with efficiency in computing the Jacobian determinant. Equivariance with respect to known symmetries of the action is widely understood to be desirable, or even crucial, depending on which theory is being studied. Here we consider parametrisations of flows based on coupling layers (pointwise transformations with triangular Jacobian), and look at the effect of enforcing equivariance under $\mathrm{U}(1)$ transformations.
We present our ongoing work on the distribution amplitudes of the charmonia states $\eta_c(1s)$ and $J/\psi(1s)$. We use the so-called pseudo approach developed by A. Radyushkin in a set of three CLS $N_f=2$ ensembles at three different lattice spacings between $0.08~\text{fm}$ and $0.05~\text{fm}$ and a pion mass around $270~\text{MeV}$. The resulting momentum distributions can be studied in the region of Ioffe times $|\nu|<4$, where we observe a non-trivial functional dependence which can be compared to the NRQCD expectation of a flat behaviour.
This work presents a study of Wuppertal smearing, comparing different mesons and kinematic configurations.
We propose a parametrization of the optimal smearing radius in terms of the reduced masses of the mesons, giving, at the same time, an estimate of the efficiency of the smearing in suppressing the excited states.
The relation between Momentum Smearing and ordinary Wuppertal smearing with Twisted Boundary conditions is discussed and the two are found to be substantially equivalent.
These results will lay the ground for future calculations of the form factors for heavy-light to heavy-light semileptonic decays, where the smearing will be fundamental to extracting physical quantities from regions with better signal-to-noise ratios.
Hadronic scattering amplitudes determined in Lattice QCD using Lüscher’s formalism depend crucially on the finite-volume energy spectrum. This work presents some of the technical details of the determination of such spectra within the study of the two-poles nature of the $\Lambda(1405)$ from Lattice QCD. Starting with the extraction of energy states from correlation functions, the GEVP technique has shown to be a useful tool to investigate the desired states, and two independent analyses were done in parallel, the so-called: Single Pivot and Rolling Pivot. This procedure was followed by a detailed analysis of the fits to ratios of correlators, which results in the energy difference of a certain level to the close-by energies of non-interacting mesons. The final results were in good agreement between both implementations and were ultimately used as input for the computation of the scattering amplitude.
In this poster, I present preliminary results from the Fermilab Lattice and MILC collaborations on the nucleon axial charge and nucleon axial and vector form factors with the HISQ action for both valence and 2+1+1 sea quarks. For the nucleon axial charge, we compute correlators across four physical mass ensembles with approximate lattice spacings of 0.15, 0.12, 0.09, and 0.06 fm, and perform continuum extrapolation; for the nucleon form factors, we compute correlators on a 300 MeV pion-mass ensemble with the approximate lattice spacing of 0.12 fm and demonstrate the method to extract nucleon form factors with staggered action.
Normalizing flow based methods for sampling lattice gauge theories has shown some recent progress. Here, we present rudimentary results for observables with finite temperature on small lattices in 2+1 dimensions.
The phase diagram of QCD at finite density remains largely unknown due to the sign problem. We propose a 1+1 dimensional model which mimics some of the features of QCD in order to study how quantum computers can avoid the sign problem and allow computations at the finite density. The model is a Z(3) gauge theory coupled to 3 flavors of staggered fermions, and it features baryon-like excitations in addition to meson-like bound states. We present the study of the phase diagram of this model using tensor networks.
We present results on three-particle scattering in the (1+1)-dimensional O(3) non-linear sigma model using lattice-determined finite-volume energies and the relativistic-field-theory (RFT) finite-volume formalism. We focus on the isospin-3 and isospin-2 three-particle channels, and perform lattice computations for four different volumes with three values of the lattice spacing each. The continuum-extrapolated finite-volume energies are compared to the RFT formalism predictions assuming a zero three-particle divergence-free $K$-matrix, $K_\mathrm{df,3}=0$. We study the effect of changing the cutoff function appearing in the quantization condition. Finally, the numerical results are used to constrain the value of $K_\mathrm{df,3}$. The eventual aim is to match the results for $K_\mathrm{df,3}$ to the analytically known three-to-three $S$-matrix, to build experience and confidence in the formalism, as it is also applied to three-hadron QCD calculations.
While Wick rotation to Euclidean spacetime is necessary for lattice QCD calculations, the subsequent rotation back to Minkowski spacetime from discrete correlator data is an ill-posed problem. In this proof-of-concept calculation, we compute correlation functions necessary for computing the hadronic tensor of the pion using existing ensembles generated by the MILC collaboration and $N_f=2+1+1$ dynamical HISQ-like fermions at the physical point. Using a modification of the Backus-Gilbert method developed by Hansen, Lupo, and Tantalo (HLT), we apply the HLT method to the Euclidean lattice correlators to extract smeared finite-volume spectral functions. Our future goal is to apply these techniques to more complicated systems such as the nucleon.
The Landau gauge four-gluon vertex is studied using high
statistical lattice simulations for several momentum configurations.
Furthermore, the outcome of the lattice QCD simulations are compared
with calculations performed with continuum Schwinger-Dyson equations.
Normalizing flow based methods for efficient sampling in lattice gauge theories have shown impressive progress. We have extended these methods to generate ensembles for SU(3) in 2+1 dimensions at a range of temporal extents. Preliminary results for observables are presented and future prospectives for finite temperature simulations are discussed
We present a new take on low-mode averaging, where the dimension of the low-mode subspace is multiplied by exploiting local coherence of low modes. The fraction of the quark propagator captured by this subspace can easily be volume averaged or sampled excessively and reaches gauge variance with lower computational cost than the traditional methods. The remainder piece can be sampled stochastically by solving the Dirac equation to low precision without compromising the correctness of the solution.
We present an evaluation of the glueball spectrum for configurations produced with $N_f=1$ dynamical fermions as a function of the $m_{\rm PCAC}$ mass. We obtained masses of states that fall into the irreducible representations of the octagonal group of rotations in combination with the quantum numbers of charge conjugation $C$ and parity $P$. Due to the low signal to noise ratio, practically, we can only extract masses for the irreducible representations $A_1^{++}$, $E^{++}$, $T_2^{++}$ as well as $A_1^{-+}$. We make use of the Generalized Eigenvalue Problem (GEVP) with a basis operators consisting only of gluonic operators. Throughout this work we are aiming towards the identification of the effects of light dynamical quarks on the glueball spectrum and how this compares to the statistically more precise spectrum of $SU(3)$ pure gauge theory. We used large gauge ensembles which consist of ${\sim {~\cal O}}(10 {\rm K})$ configurations. Our findings demonstrate that the low lying spectrum of the scalar, tensor as well as pseudo-scalar glueballs receive negligible contributions from the inclusion of $N_f=1$ dynamical fermions.
In lattice QCD calculations, the trace of operator products involving the inverse Dirac operator is often necessary for evaluating various observables, such as cumulants of the chiral order parameter and conserved charge fluctuations. Since the Dirac operator is represented by a large sparse matrix on the lattice, the exact calculation of the trace is typically impractical. Instead, it is commonly estimated by solving systems of linear equations for stochastic sources, which remains computationally demanding, particularly when dealing with numerous sources.
As an alternative approach to trace estimation, we explore a method of adapting a regression algorithm that enables us to predict the relationship between variables. By successfully capturing the correlation between the traces and other observables, it is anticipated that the desired quantity can be inferred without solving linear equations.
In this poster, we present our preliminary results of utilizing the boosting tree algorithm to predict the trace of a power of the inverse Dirac operator. Additionally, we discuss the effectiveness of this method in computing observables, comparing it to the conventional approach.
Two analysis techniques, the generalized eigenvalue method (GEM) or Prony's method (PM), are commonly used to analyze statistical estimates of correlation functions produced in lattice quantum field theory calculations. GEM takes full advantage of the matrix structure of correlation functions but only considers individual pairs of time separations when much more data exists. PM can be applied to many time separations and many individual matrix elements simultaneously but does not fully exploit the matrix structure of the correlation function. We combine both these methods into a single framework based on matrix polynomials which we call block Prony method (BPM).
Python is a particularly appealing language to carry out data analysis, owing in part to its user-friendly character as well as its access to well maintained and powerful libraries like NumPy and SciPy. Still, for the purpose of analyzing data in a lattice QCD context, some desirable functionality is missing from these libraries. Moreover, scripting languages tend to be slower than compiled ones. To help address these points we present the LatticeToolbox, a collection of Python modules to facilitate lattice QCD data analysis. Some highlighted features include general-purpose jackknife and bootstrap routines; modules for reading in and storing gauge configurations; a module to carry out hadron resonance gas model calculations; and convenience wrappers for SciPy integration, curve fitting, and splines. These features are sped up behind the scenes using Numba and concurrent.futures.
Common to many analysis pipelines in lattice field theory is the need to fit data to a model that is determined partially by a finite number of model parameters. Familiar examples include analyses of finite-size scaling and ground state spectroscopy. We propose a Bayesian fit method that utilizes a neural network to approximate the component of such models that is a priori unknown. The viability of our method is tested on a number of finite-size scaling problems with increasing complexity.
We use a regular tessellation of AdS$_2$ based on the (2,3,7) triangle group, with an extension to Euclidean AdS$_3$, to study the AdS/CFT correspondence. Perturbative calculations are verified and initial tests of monte carlo calculations for non-perturbative $𝜙^4$ theory exhibit critical phenomena on the boundary.
The density of any observable is equal to how large a volume there exist for each possible value of the observable. By considering the relative change to the volume along the direction of change of the observable, the relative change to the density of the observable can be obtained. I will show how one can calculate the change to the log of the density function rho and use this to calculate several observables, which in some cases like wilson line correlators can give errorbars 4 times smaller than standard methods.
Monte Carlo simulations with continuous auxiliary fields encounter challenges when dealing with fermionic systems due to the infinite variance problem observed in fermionic observables. This issue renders the estimation of observables unreliable, even with an infinite number of samples. In this talk, I will propose an approach to address this problem by employing a reweighting method that utilizes the distribution from an extra time-slice. I will explore two strategies to compute the reweighting factor using Hubbard model: one involves truncating and analytically calculating the reweighting factor, while the other employs a secondary Monte Carlo estimation. Through our findings, I will demonstrate that utilizing the sub-Monte Carlo reweighting technique, coupled with an unbiased estimator, offers a solution that effectively mitigates the infinite variance problem at a minimal additional cost.
Many applications in Lattice field theory require to determine the Taylor
series of observables with respect to action parameters. A primary example is
the determination of electromagnetic corrections to hadronic processes. We show
two possible solutions to this general problem, one based on reweigting, that
can be considered a generalization of the RM123 method. The other based on the
ideas of Numerical Stochastic Perturbation Theory (NSPT) in the Hamiltonian
formulation. We show that 1) the NSPT-based approach shows a much reduced
variance in the determination of the Taylor coefficients, and 2) That both
approaches are related by a change of variables. Numerical results are shown for
the case of Lambda-phi^4 in 4 dimensions, but we expect these observations to be
general. We conclude by commenting on the possible use of Machine Learning
techniques to find similar change of variables that can potentially reduce the
variance in Taylor coefficients.
We study the various tensor renormalization group (TRG), such as the Higher-order TRG (HOTRG), Anisotropic TRG (ATRG), Triad TRG, and Tensor network renormalization (TNR) with the idea of projective truncation and truncated singularvalue decomposition (SVD) such as the randomized SVD (RSVD). The details of the cost function for the isometry determine the precision, stability, and calculation time. In our study, we show calculation order improvement using RSVD. We also propose that the internal line respect for any TRG method improves the calculation without changing the order of the computational cost.
Machine learning, deep learning, has been accelerating computational physics, which has been used to simulate systems on a lattice. Equivariance is essential to simulate a physical system because it imposes a strong induction bias for the probability distribution described by a machine learning model. However, imposing symmetry on the model sometimes occur a poor acceptance rate in self-learning Monte-Carlo (SLMC). On the other hand, Attention used in Transformers like GPT realizes a large model capacity. We introduce symmetry equivariant attention to SLMC. To evaluate our architecture, we apply it to our proposed new architecture on a spin-fermion model on a two-dimensional lattice. We find that it overcomes poor acceptance rates for linear models and observe the scaling law of the acceptance rate in machine learning. This talk is based on arXiv:2306.11527.
The excited states contamination in the nucleon three-point function is one of the major systematic errors in calculating nucleon form factors. We use Bayesian Reconstruction to study the nucleon excited states in the two-point nucleon and S11 correlators which are constructed from the valence overlap fermions on DWF configurations at the physical pion mass with a lattice size of 5.5 fm. We will show the observed Roper state and discuss the non-observation of the pion-nucleon states in the nucleon positive and negative parity channels. We will discuss its consequence in the nucleon three-point functions in the context of the pion-nucleon contamination due the current-enhanced boomerang diagram for the pseudoscalar current.
We present an analysis of the $N \pi$ contribution to the determination of the nucleon mass spectrum using constrained fits. Our study involves simultaneous fitting of $N \to N$ and $N \to N \pi$ correlation functions. The analysis is performed on a $24^3 \times 48 \times 24$ lattice with $2 + 1$ dynamical Domain-Wall fermions. We employ a lattice spacing of $a^{-1} = 1.74 \text{ GeV}$ and a pion mass of $m_{\pi} = 279 \text{ MeV}$. Further, we will discuss our preliminary results for the computation of the nucleon axial charge.
We investigate contributions of excited states to nucleon matrix elements by studying the two- and three-point functions using nucleon and pion-nucleon interpolating fields. This study is made using twisted mass fermion ensembles with pion masses 346 MeV and 131 MeV. We compare results obtained using these two ensembles and show preliminary results for nucleon charges.
Neutrino oscillation experiments require accurate reconstructions of neutrino energies, which depend in part on a theoretical understanding of the axial $N \rightarrow \Delta$ transition form factors. A lattice QCD study of this transition will require construction of all hadronic states with energies up to $m_\Delta$, which at the physical point includes $N\pi$ and $N\pi\pi$. Building interpolating operators from sparse grids at the source and sink is a versatile method that allows construction of a wide range of diagram topologies and has successfully been used in other multi-hadron calculations. We will discuss application of this method to nucleon-pion systems and present preliminary results.
Studies of the $\Delta$ baryon resonance and the $K_0^\ast(700)$ and $a_0(980)$ meson resonances using $N_f=2+1$ lattice QCD for pion masses near 200 MeV are presented. The role of tetraquark operators in the mesonic systems is detailed. The $s$-wave scattering lengths for both the $I=1/2$ $N \pi$ and $I=3/2$ $N \pi$ channels and properties of the $\Delta$ resonance are identified from the finite-volume energy levels of the lattice simulation.
Macroscopic properties of the strong interaction near its chiral phase transition exhibit scaling behaviors, which are the same as those observed close to the magnetic transition in a 3-dimensional classical spin system with $O(4)$ symmetry. We show the universal scaling properties of the chiral phase transition in Quantum Chromodynamics (QCD) at the macroscale are, in fact, encoded within the microscopic energy levels of its fundamental constituents, the quarks. We establish a connection between the cumulants of the chiral order parameter, i.e. the chiral condensate, and the correlations among the energy levels of quarks in the background of gluons, i.e. the eigenspectra of the massless QCD Dirac operator. This relation elucidates how the fluctuations of the chiral condensate arise from the correlations within the infrared part of the energy spectra of quarks, and naturally leads to generalizations of the Banks–Casher relation for the cumulants of the chiral condensate. Then, through (2+1)-flavor lattice QCD calculations with varying light quark masses near the QCD chiral transition, we demonstrate the correlations among the infrared part of the Dirac eigenvalue spectra exhibit same universal scaling behaviors as expected of the cumulants of the chiral condensate. We find that these universal scaling behaviors extend up to the physical values of the up and down quark masses. Our study reveals how the hidden scaling features at the microscale give rise to the macroscopic universal properties of QCD.
We investigate the chiral transition of $U(N)$ lattice gauge theory based on the strong coupling expansion. A generalized vertex model with vertices and weights derived from the tensor network approach of the dual representation of lattice QCD with staggered fermions is used and the configurations are sampled by the Metropolis algorithm. We study the chiral transition in the chiral limit and focus on the beta dependence of the second order chiral transition temperature $T_c$ for different values of the gauge coupling. We compare different orders of truncations of the strong coupling expansion: $\mathcal{O}(\beta^0)$, $\mathcal{O}(\beta^1)$, and $\mathcal{O}(\beta^2)$. We comment on the prospects of extending to $SU(3)$ at finite density.
We present first non-perturbative results for the renormalization constants of the QCD energy momentum tensor, based on the framework of thermal QCD with shifted and twisted (for quarks only) boundary conditions in the compact direction. We also show preliminary results for the entropy density obtained with the very same numerical strategy. This opens the way to the determination of the QCD Equation of State up to very high temperatures.
Non-orthogonal background electromagnetic fields generate a non-zero expectation value for the topological charge in QCD. For sufficiently weak fields, a linear response is expected. This linear response has been studied and related to the QCD contribution to the axion-photon coupling, for which we give preliminary results at finite lattice spacing. We also investigated the dependence of the topological susceptibility with the magnetic field around $T_c$. A reweighting of the fermion determinant to mimic the zero modes of the Dirac operator is shown to significantly reduce the lattice artifacts for the susceptibility. In this work we use lattice simulations with 2+1 flavors of improved staggered quarks at the physical point, including background magnetic and (imaginary) electric fields.
We present the first lattice QCD results of the second order fluctuations of and correlations among net baryon number, electric charge and strangeness in (2+1)-flavor lattice QCD in the presence of a background magnetic field with physical pion mass $m_\pi$ = 135 MeV. To mimic the magnetic field strength produced in the early stage of heavy-ion collision experiments we use 6 different values of the magnetic field strength up to ∼10 $m_{\pi}^2$. The simulations were performed using the Highly Improved Staggered Quarks with physical pion mass on $N_\tau=8$ and 12 lattices. By comparing lattice QCD results to results from the hadron resonance gas model, possible proxies are proposed to study the imprints of magnetic fields in high-energy heavy ion collision experiments.
Quadratic Unconstrained Binary Optimization (QUBO) problems can be addressed on quantum annealing systems. We reformulate the strong coupling lattice QCD dual representation as a QUBO matrix. We confirm that importance sampling is feasible on the D-Wave Advantage quantum annealer. We describe the setup of the system and present the first results obtained on a D-wave quantum annealer for U(N) gauge group. Furthermore, we outline a strategy for going to larger volumes and tackling the SU(N) gauge theory which has the sign problem.
We propose three independent methods to compute the hadron mass spectra of gauge theories in the Hamiltonian formalism. The determination of hadron masses is one of the key issues in QCD, which has been precisely calculated by the Monte Carlo method in the Lagrangian formalism. We confirm that the mass of hadrons can be calculated by examining correlation functions, the one-point function, or the dispersion relation in Hamiltonian formalism. These methods are suitable for quantum computation and tensor network approaches. The methods are demonstrated with the tensor network (DMRG) in the 2-flavor Schwinger model, which shares important properties with QCD. We show that the numerical results are consistent with each other and with the analytic prediction of the bosonization technique. We also discuss their efficiency and potential applications to other models.
We compute the low-lying spectrum of 4D SU(2) Yang-Mills in a finite volume using quantum simulations. In contrast to small-volume lattice truncations of the Hilbert space, we employ toroidal dimensional reduction to the ``femtouniverse" matrix quantum mechanics model. In this limit the theory is equivalent to the quantum mechanics of three interacting particles moving inside a 3-ball with certain boundary conditions. We use the variational quantum eigensolver and quantum subspace expansion techniques to compute the string tension to glueball mass ratio near the small/large-volume transition point, finding qualitatively good agreement with large volume Euclidean lattice simulations.
We express non-linear sigma O(3) model in a form suited to continuous variable (CV) approach to quantum computing by rewriting the model in terms of boson operators in an infinite-dimensional Hilbert space. We show that it is possible to reach the scaling regime with truncation of the Fock space by considering $\mathcal{O}(10)$ photons at each site. This is an indication that it might be possible to reach the scaling regime with resources within the reach of photonics quantum hardware by the end of this decade.
We review recent suggestions to quantum simulate scalar electrodynamics (the lattice Abelian Higgs model) in 1+1 dimensions with rectangular arrays of Rydberg atoms. We show that platforms made publicly available recently allow empirical explorations of the critical behavior of quantum simulators. We discuss recent progress regarding the phase diagram of two-leg ladders, effective Hamiltonian approaches and the construction of hybrid quantum algorithms targeting hadronization in collider physics event generators.
Position-space schemes are very natural gauge-invariant non-perturbative renormalization schemes to implement on the lattice. The tradeoff is that the perturbative calculations required to convert to more typically used schemes such as MS are more theoretically involved. We present dimensionally regulated perturbative calculations of a set of HQET operators in position-space, allowing for conversion of bare matrix elements measured on the lattice to MS. The operators of interest include those appearing in the OPE for lifetime measurements of B-hadrons.
We present an update of the study of bag parameters of neutral $B_{(s)}$-meson mixing, which constrains the Standard Model as well as BSM scenarios. Our calculations use an all-domain-wall-fermion approach. We combine three lattice spacings ($1.7 \mathrm{GeV} \leq a^{-1} \leq 2.7 \mathrm{GeV}$) including 2 physical pion mass ensembles generated by RBC/UKQCD with ensembles with three finer lattice spacings ($2.5\,\mathrm{GeV} \leq a^{-1} \leq 4.5\,\mathrm{GeV}$) generated by the JLQCD collaboration. We will show preliminary non-perturbatively renormalised results for bag parameters and demonstrate that all required limits are controlled.
Neutral meson mixing and meson lifetimes are theory-side parametrised in terms four-quark operators which can be determined by calculating weak decay matrix elements using lattice QCD.
While calculations of meson mixing matrix elements are standard, determinations of lifetimes typically suffer from complications in renormalisation procedures because dimension-6 four-quark operators can mix with operators of lower mass dimension and, moreover, quark-line disconnected diagrams contribute.
We present work detailing the idea to use fermionic gradient flow to non-perturbatively renormalise matrix elements describing meson mixing or lifetimes, which later is to be combined with a perturbative calculation to match to the $\overline{\rm MS}$ scheme.
In a not well known paper [JHEP01(2008)076] it was shown how to perform interpolations between relativistic and static computations in order to obtain results for heavy-light observables for masses from (say) $m_{\rm charm}$ to $m_{\rm bottom}$. All quantities are first continuum extrapolated and then interpolated in $1/m=1/m_{\rm heavy}$. Large volume computations are combined with finite volume ones where a relativistic bottom quark is accessible with small $am$. We discuss how this strategy is extended to semileptonic form factors and other quantities of phenomenological interest. The essential point is to form quantities which cancel all $alpha_s(m)^(n+\gamma)$ perturbative corrections to large mass scaling. We also point out how such an approach can help to control systematics in semileptonic decays with just large volume data. First numerical results with $N_f = 2 + 1$ and lattice spacings down to 0.039 fm are presented in a companion talk.
We present preliminary results for B-physics from a combination of non-perturbative results in the static limit with relativistic computations satisfying $am_{\rm heavy}<<1$. Relativistic computations are carried out at the physical b-quark mass using the Schrödinger Functional in a $(0.5~{\rm fm})^4$ box. They are connected to large volume observables through step scaling functions that trace the mass dependence between the physical charm region and the static limit, such that B-physics results can be obtained by interpolation; the procedure is designed to exactly cancel the troublesome $\alpha_s(m_{\rm heavy})^{n+\gamma}$ corrections to large mass scaling. Large volume computations for both static and relativistic quantities use CLS $N_f=2+1$ ensembles at $m_u=m_d=m_s$, and with five values of the lattice spacing down to 0.039 fm.
Our preliminary results for the b-quark mass and leptonic decay constants have competitive uncertainties, which are furthermore dominated by statistics, allowing for substantial future improvement. This talk focusses on numerical results, while the underlying strategy is discussed in detail in a companion talk.
We present an update on our lattice calculations of the Mellin moments of PDFs and GPDs for the pion and kaon, using momentum-boosted meson states. In particular, we focus on the calculation of the scalar and tensor local operators, as well as the vector operator with up to three-covariant derivatives. The corresponding matrix elements allow us to extract the scalar and tensor charges, as well as $\langle x^n \rangle$ with $n=1,2,3$. In addition, we introduce momentum transfer between the initial and final meson state that leads to the scalar, vector, and tensor form factors, and the generalized form factors up to three covariant derivatives. The above results are obtained using two ensembles of maximally twisted mass fermions with clover improvement with two degenerate light, a strange, and a charm quark $(N_f=2+1+1)$ at lattice spacings of 0.093 fm and 0.081 fm. The pion mass of the ensembles is about 260 MeV. We study excited-states effects by analyzing four values of the source-sink time separation (1.12 - 1.67 fm). We also examine discretization and volume effects. The lattice data are renormalized non-perturbatively, and the results are presented in the MS scheme at a scale of 2 GeV.
The gravitational form factors (GFFs) of hadrons are related to the second Mellin moments of their generalized parton distributions. They can be extracted from matrix elements of the energy-momentum tensor of QCD. We present the gluon and quark flavor contributions to the GFFs of the pion and the nucleon in the kinematic region $0 \leq -t \leq 2~\text{GeV}^2$ on a clover improved ensemble with $a = 0.091~\text{fm}$, $N_f=2+1$, and $m_{\pi} = 170~\text{MeV}$. The results are renormalized non-perturbatively via the RI-MOM scheme. We obtain estimates for the energy and mechanical distributions, and for the forward limit momentum fraction, spin, and $D$-term flavor decompositions.
The trace of the energy momentum tensor (ETM) in the hadron gives the hadron mass. The trace anomaly due to the conformal symmetry breaking is believed to be an important ingredient for confinement. In this talk, I will show the trace anomaly form factors of the pion, nucleon and $\rho$ meson as functions of the squared momentum transfer $Q^2$ up to $\sim 4.3~\mathrm{GeV}^2$ which are calculated on a domain wall fermion (DWF) ensemble with overlap valence quarks at $m_{\pi}=340$ MeV. We found a sign change behavior of the trace anomaly form factor of the pion. This is consistent with the sign change of the radial distribution of the trace anomaly matrix element in a recent lattice calculation.
Quark orbital angular momentum in the proton is evaluated via a Lattice QCD calculation of the second Mellin moment of the twist-3 generalized parton distribution $\widetilde{E}_{2T} $ in the forward limit. The connection between this approach to quark orbital angular momentum and approaches previously utilized in Lattice QCD calculations, via generalized transverse momentum-dependent parton distributions and via Ji's sum rule, is reviewed. This connection can be given in terms of Lorentz invariance and equation of motion relations. The calculation of the second Mellin moment of $\widetilde{E}_{2T} $ proceeds via a finite-momentum proton matrix element of a quark bilocal operator with a straight-line gauge connection and separation in both the longitudinal and transverse directions. The dependence on the former component serves to extract the second Mellin moment, whereas the dependence on the latter component provides a transverse momentum cutoff for the matrix element. Furthermore, a derivative of the matrix element with respect to momentum transfer in the forward limit is required, which is obtained using a direct derivative method. The calculation utilizes a clover fermion ensemble at pion mass 317 MeV. The resulting quark orbital angular momentum is consistent with previous evaluations through alternative approaches, albeit with greater statistical uncertainty using a comparable number of samples.
We report on a lattice fermion formulation with
a curved domain-wall mass term to nonperturbatively
describe fermions in a gravitational background.
In our previous work in 2022, we showed in the free
fermion theory on one and two-dimensional spherical domain-walls
that the spin connection is induced on the lattice
in a consistent way with continuum theory.
In this talk we add nontrivial $U(1)$ link variables
to the spherical domain-wall fermion systems and
study the anomaly inflow between the bulk and curved edge.
We also extend our study to a Shamir type curved domain-wall fermions.
Although one domain-wall apparently admits a single Weyl fermion
on the spherical surface, we find nontrivial obstacles
in formulating chiral gauge theory.
Minimally doubled fermions realize one degenerate pair of Dirac fermions on the lattice. Similarities to staggered fermions exist, namely, spin and taste degrees of freedom become intertwined, and a remnant, non-singlet chiral symmetry and ultralocality are maintained. However, charge conjugation, isotropy and some space-time reflection symmetries are broken by the cutoff.
For two variants, i.e., Karsten-Wilcek (KW) or Borici-Creutz (BC) fermions, a tasted charge conjugation symmetry can be identified, and the respective representations of the spin-taste algebra can be constructed explicitly. In the case of BC fermions, the tasted symmetry indicates that amendments to the published counterterms are necessary.
The spin-taste representation on the quark level permits construction of local or extended hadron interpolating operators for any spin-taste combination, albeit with contamination by parity partners and taste-symmetry violation. The few available numerical results for KW fermions are in line with expectations.
We present a novel approach to construct effective descriptions of a confining string. We consider a string pinned with heavy quark-antiquark endpoints on the lattice Yang-Mills theory (Kogut-Susskind Hamiltonian) as background with $SU(N_c)$ gauge symmetry with large $N_c$. Our approach describes the dynamics of the confining string as two different spin chains, which are both integrable. In the talk, I will demonstrate it in 2+1-D as the simplest example, but it is also applicable for gauge theories in higher dimensions.
Laboratory setups and astrophysical circumstances may confine fermions to two spatial dimensions. Leading-order nonrelativistic pionless EFT in 2D has an anomalously broken conformal symmetry, and exhibits BKT phase transition. We use classic tools from lattice field theory to make predictions about this strongly correlated system.
Gapped fermion theories with gapless boundary fermions can exist in any number of dimensions.
When the boundary has even space-time dimensions and hosts chiral fermions, a quantum Hall current
flows from the bulk to the boundary in a background electric field. This current compensate for the
boundary chiral anomaly. Such a current inflow picture is absent when the boundary theory is odd
dimensional. However, in recent work, the idea of quantum Hall current has been generalized to
describe odd dimensional boundary theories in continuous Euclidean space-time dimension of infinite
volume. In this talk we extend this idea to a lattice regulated finite volume theory of 1+1 dimensional
Wilson-Dirac fermions. This fermion theory with a domain wall in fermion mass can host gapless
modes on the wall. The number of gapless fermions is equal to the integral of the divergence of the
lattice generalized Hall current.
In this review, I will cover the status of the calculations of quantities that are needed in the analysis of neutrinos off nuclear targets. These include the axial charge and the form factors of the nucleon. A discussion of systematics—removing excited state contributions and obtaining results at the physical point will be included. Looking ahead, I will conclude with prospects of calculating transition matrix elements.
Kenneth Wilson Award for Excellence in Lattice Field Theory
The so-called trivializing flows were proposed to speed up Hybrid Monte Carlo
simulations, where the Wilson flow was used as an approximation of a
trivializing map, a transformation of the gauge fields which trivializes the
theory. It was shown that the scaling of the computational costs towards the
continuum did not change with respect to HMC. The introduction of machine
learning tecniques, especially normalizing flows, for the sampling of lattice
gauge theories has shed some hope on solving topology freezing in lattice QCD
simulations. In this talk I will present our work using normalizing flows as
trivializing flows, given its similarity with the idea of a trivializing map,
and study its benefits with respect to standard HMC.
The 2D O(3) model has been widely used as a toy model for quantum chromodynamics and ferromagnetism. It shares fundamental features with quantum chromodynamics, such as being asymptotically free. It is possible to define a trivializing map, a field transformation from a given theory to trivial variables, through a gradient flow. An analytic solution to this trivializing flow may be obtained by a perturbative expansion in the flow parameter. Utilizing this solution allows for new approaches to be considered when proposing updates for a Markov Chain algorithm.
While approximations of trivializing field transformations for lattice path integrals were considered already by early practitioners, more recent efforts aimed at ergodicity restoration and thermodynamic integration formulate trivialization as a variational generative modeling problem. This enables the application of modern machine learning algorithms for optimization over expressive parametric function classes, such as deep neural networks. After a brief review of the historical origins of this research program, I will focus on spectral coupling flows as a particular parameterization of gauge-covariant field diffeomorphisms. The concept will be introduced by explicitly constructing a systematically improvable semi-analytic solution for SU(3) gauge theory in (1+1)d, followed by a discussion and outlook on recent results in (3+1)d from a proof-of-principle application of machine-learned flow maps.
We construct neural networks that work for any Lie group and maintain gauge covariance, allowing smooth and invertible transformations of gauge fields. We implement the transformations for 4D SU(3) lattice gauge fields, and explore their use in HMC. Our current research develops various loss functions and optimizes field transformation accordingly. We show the effect of these transformations on HMC's molecular dynamics evolution and discuss the scalability of this approach.
I will highlight existing limitations of the current architecture of Normalizing flows as applied to the generation of lqcd samples. From the Geometric Deep Learning perspective, existing architecture utilized the most basic features - invariant quantities that correspond to isotropic filters. In order to establish an expressive flow model transforming base distribution to target, I will formulate an equation and demonstrate the necessity of incorporating equivariant features. Furthermore, I will delve into the algorithm that enables us to identify approximate solutions and approach analytic trivialization. The limitations associated with coupling transformations will be discussed, emphasizing the need for a hierarchical model to attain an exact solution. Lastly, I will elucidate how the analysis of flow equation leads us to consider geometry. From a geometric standpoint, it is argued that trivializing 2D SU(3) gauge theory is relatively straightforward, while the presence of geometrical "defects" in 3D and 4D scenarios significantly complicates the process of trivialization.
Normalizing flows are machine-learned maps between different lattice theories which can be used as components in exact sampling and inference schemes. Ongoing work yields increasingly expressive flows on gauge fields, but it remains an open question how flows can improve lattice QCD at state-of-the-art scales. This talk discusses and demonstrates several useful applications which are viable with presently available flows, highlighting replica exchange sampling and a new approach to Feynman-Hellmann calculations.
The Lüscher formalism is a well-known and widely used method for extracting scattering amplitudes from the finite-volume spectrum. Recent lattice QCD calculations involving systems where a lighter particle couples to heavier scattering particles (e.g. baryon-baryon scattering) have highlighted the limitations of the standard formalism below threshold. This is due to the presence of left-hand cuts in the partial-wave-projected scattering amplitudes. In this talk, we describe an extension of the existing framework to the left-hand cut, summarising the complete procedure including the solving of integral equations to extract physical observables. We further describe first numerical tests on mock data, and explicitly show the equivalence between our method and the familiar formalism in the regime where both are valid.
Understanding three-body dynamics is crucial in comprehending the behavior of hadronic states that decay into three or more particles under strong interactions. Recent advances in Lattice QCD techniques allow us to calculate three-particle interactions from QCD and access finite volume energies. Connecting these energies to physical observables involves multiple steps. Firstly, we use the Lüscher formalism and its extensions to map these energies to intermediate quantities in infinite volume. These quantities serve as input in a set of integral equations, yielding the three-body scattering amplitude. Before applying this method to actual Lattice QCD calculations, we must verify its consistency with various toy models. In this study, we numerically solve relativistic three-body integral equations for a toy model of three identical scalar bosons. The model's two-body sub-channel, defined by scattering length, permits bound states. Our results for a bound-state+particle system are compared to established results using Lüscher formalism for the same toy model. We discuss methods of solving the integral equations above the bound-state+particle threshold and provide a prescription for analytically continuing solutions below threshold. Although our solutions agree well with previous results, we find evidence of Lüscher formalism breaking down near the left-hand cut resulting from exchange particle interactions. This talk primarily focuses on our solution techniques and the breakdown of the finite volume formalism.
The recently discovered I = 0, JP = 1+ doubly-charmed tetraquark Tcc(3875) is an exotic meson that is a candidate for a DD molecule. In nature, it decays to DDπ, since the D is unstable. It has been studied on the lattice for heavier-than-physical quark masses for which the D is stable, so that two-particle methods can be used. However, a major drawback of this methodology is that the tentative position of the (virtual) bound state lies very close to, or even below, the left-hand cut, which is the subthreshold energy below which the two-body formalism breaks down. We present a method to overcome this limitation, in which we apply the three-particle formalism to the DDπ system and incorporate the D as a bound state in the p-wave Dπ subsystem. Using this formalism below the three-particle threshold allows us to study the Tcc while incorporating the physics responsible for the left-hand cut. The new approach has the additional advantage of remaining valid when the quark masses are reduced into the regime where the D decays to Dπ, so that the Tcc becomes a resonance with a three-body decay.
The K-matrix parametrizes short-range interactions in the relativistic-field-theory finite-volume formalism. It is related to the infinite-volume scattering amplitude, thus providing a bridge between the lattice and perturbation theory, as well as a handle on finite-volume effects and the pion mass dependence. However, leading-order perturbative calculations agree very poorly with the results for systems of three interacting light mesons. I describe the calculation of the three-pion K-matrix from chiral perturbation theory at next-to-leading order, and demonstrate how this resolves most of the disagreement between perturbation theory and the lattice. Thereby, the two main tools for studying these interesting and experimentally inaccessible systems are reconciled.
Many hadronic resonances, including the most intriguing ones (Roper, $\pi_1$(1600), or $T^+_{cc}$(3872)), decay into three or more particles. In principle, one can determine their properties from the multi-body version of the Luscher finite-volume scattering formalism. However, one of the obstacles in specifying their masses from Lattice QCD is the lack of developed three-body amplitude analysis techniques that would allow one to translate a finite-volume output into physically meaningful quantities. In particular, an amplitude obtained from the Lattice QCD calculation must be analytically continued to the complex energy plane, where resonances exist as pole singularities.
In the talk, I will explore the relativistic scattering of three identical scalar bosons interacting via pair-wise interactions. I will describe a general prescription for solving and analytically continuing integral equations describing the three-body process. As an illustration, I will use these techniques to analyze a system governed by a single scattering length leading to a bound state in a two-body sub-channel. I will present the resulting three-body scattering amplitudes for complex energies in the physical and unphysical Riemann sheets. In particular, I will discuss the emergence of three-particle bound states in the system under study that agrees with previous work utilizing relativistic finite-volume formalism. Finally, I will also comment on the obtained numerical evidence of the breakdown of the two-body finite-volume formalism in the vicinity of left-hand cuts.
We generalize the relativistic field-theoretic (RFT) three-particle finite-volume formalism to systems of three identical, massive, spin-$1/2$ fermions, such as three neutrons. This allows, in principle, for the determination of the three-neutron interaction from the finite-volume spectrum of three-neutron states, which can be obtained from lattice QCD calculations.
In this talk, I will focus on naturalness considerations in SM/2HDM augmented by a Triplet field, here dubbed as Higgs Triplet Models. I will show that the Veltman conditions in HTM are modified by virtue of the additional scalar charged states and that one loop quadratic divergencies can be driven to zero within the allowed respective parameter spaces, usually constrained by unitarity and boundedness from below, as well as the LHC data regarding several Higgs decay channels. In addition, the analysis will also illustrates how the naturalness condition affect drastically the heavy Higgs masses H^0, H^0, H± and H±± (when they exist).
We present an analysis of newly expanded and refined data from lattice studies of the SU(3) gauge theory with $N_f=8$ light Dirac fermions, a theory which lies close to the boundary of the conformal window. We first assume that this theory is just outside the conformal window and identify a light unflavored scalar meson in this case as an approximate dilaton. We show fits of the lattice data to a dilaton effective field theory and demonstrate that it yields a good fit even at lowest order. Our fit incorporates new data for a scalar decay constant $F_S$. For comparison, we then assume that the theory is inside the conformal window. In this case, the fermion mass provides a deformation, triggering confinement. We employ simple scaling laws to fit the lattice data, but find that it is of lesser quality.
The mesonic $f_{PS} / m_V$ and $f_V / m_V$ ratios, with f the decay constant and m the meson mass, are calculated in mass perturbed conformal gauge theories to NNLO and N$^3$LO orders, respectively. Here NNLO and N$^3$LO refer to the non-relativistic effective theory expansion which is the applicable framework. The results are expanded a la Banks-Zaks in order to end up with scheme-independent predictions. These perturbative results are unambiguously reliable close to the upper end of the conformal window, $N_f = 16.5$ and it is shown that they might be reliable down to $N_f = 12$. An attempt is made to match these to previous non-perturbative lattice results in the range $2 \leq N_f \leq 10$ range. An abrupt change in the ratios is observed at around $N_f = 12 - 13$, which may signal the lower end of the conformal window.
The LSD collaboration is studying Stealth Dark Matter, an SU(4) gauge theory, whose ground state spin-0 baryon is the dark matter candidate. We are investigating Stealth Dark Matter with two fermions in the fundamental representation using the quenched approximation. I will discuss our baryon operator construction using LapH and lattice octahedral group irreps. Then I will present the latest results of the meson and baryon spectrum.
Several SU(N) gauge theories have been explored as candidates for producing stable dark matter particles that can explain their relative abundance, while also evading current constraints from direct, indirect and collider searches. In this talk, I will present the confinement and spectral properties of a new model we name Hyper Stealth Dark Matter
, which involves an SU(4) gauge theory with 1 quark flavor. The lightest baryon in this theory can be a potential dark matter candidate as it is protected from decay and hence can evade detection with a mass of just a few GeV. Existence of a first order confinement transition would open the possibility of potential detection of gravitational waves from such a transition at future observatories.
We are examining one-flavour $SU(N_c)$ gauge theories with one fermion in the antisymmetric representation as a candidate to approximate $\mathcal{N}=1 $ SYM due to their equivalence in the large-$N_c$ limit. Summarising results on spectral evaluations of $N_c=3$, we will report on the progress of dynamical calculations for $N_c > 3$. Here we will discuss cutoff effects and challenges in configuration generation.
We present the first continuum extrapolated results for the chiral magnetic effect (CME) and the chiral separation effect (CSE) conductivities in equilibrium with staggered fermions at physical masses. We simulate QCD in a constant magnetic background and measure respective chemical potential derivatives of the currents appearing in each effect. The conductivities are calculated as a function of relevant parameters as the temperature and the mass of the quarks. We emphasize the importance of choosing the correct discretization of the currents, which we verify by turning off gluonic interactions and comparing to analytical results; as well as by comparing to results using the Wilson fermion formulation. We also present results for the quenched theory for both staggered and Wilson fermions, where the role of the Polyakov loop for the CSE will be discussed.
The complex Langevin method shows great promise in enabling the calculation of observables for theories with complex actions. Nevertheless, real-time quantum field theories have remained largely unsolved due to the particular severity of the sign problem. In this contribution, we will discuss our recent progress in applying the complex Langevin method to SU(2) Yang-Mills theory in 3+1 dimensions. We introduce an anisotropic kernel that stabilises systems for real times longer than the inverse temperature - a first in this field. We provide explicit evidence of reproducing thermal relations among different types of propagators when the complex time path approaches the Schwinger-Keldysh contour. This method could pave the way for calculating transport coefficients and other real-time observables from first principles.
We compute the sphaleron rate on the lattice. We adopt a novel strategy based on the extraction of the spectral density via a modified version of the Backus-Gilbert method from finite-lattice-spacing and finite-smoothing-radius Euclidean topological charge density correlators. The physical sphaleron rate is computed by performing controlled continuum limit and zero-smoothing extrapolations.
The thermal photon emissivity at the QCD chiral crossover is
investigated using imaginary momentum correlators. These have been
measured on a newly generated $20 \times 96^3$ lattice-QCD ensemble
with $\mathrm{O}(a)$-improved Wilson quarks and physical up, down and
strange quark masses at a temperature $T=154$ MeV near the
pseudo-critical temperature. In order to realize the photon on-shell
condition, the spatially transverse Euclidean correlators have to be
evaluated at imaginary spatial momenta.
Employing a bounding method, we present a preliminary result on the
quantity $H_E(\omega_1)$, which corresponds to an energy-moment of the
photon spectral function $\sigma(\omega)$.
Using numerical lattice simulations, we analyze the influence of uniform rotation on the equation of state of gluodynamics. For a sufficiently slow rotation, the free energy of the system can be expanded into a series of powers of angular velocity. We calculate the moment of inertia given by the quadratic coefficient of this expansion and determine its dependence on the temperature We find that the moment of inertia unexpectedly takes a negative value below the ``supervortical temperature'' $𝑇_𝑠 \sim 1.5 𝑇_𝑐$, vanishes at $𝑇=𝑇_𝑠$, and becomes a positive quantity at higher temperatures. The negative moment of inertia indicates a thermodynamic instability of plasma with respect to rigid rotation, which resembles the rotational instability of spinning Kerr black holes. We discuss how this instability is related to the scale anomaly and the magnetic gluon condensate. We argue that our results are in qualitative agreement with previous lattice calculations indicating that the rigid rotation increases the critical temperature in gluodynamics.
This talk will discuss a method for computing the energy spectra of quantum field theory utilizing digital quantum simulation. A quantum algorithm called coherent imaging spectroscopy quenches the vacuum with a time-oscillating perturbation and reads off the excited energy levels from the loss in the vacuum-to-vacuum probability following the quench. As a demonstration, we apply this algorithm to the (1+1)-dimensional quantum electrodynamics with a topological term known as the Schwinger model, where the conventional Monte Carlo approach is practically inaccessible. In particular, on a classical simulator, we prepare the vacuum of the Schwinger model on a lattice by adiabatic state preparation and then apply various types of quenches to the approximate vacuum through Suzuki-Trotter time evolution. We compare the simulation result with exact diagonalization and the continuum limit expectation. We discuss its dependence on the types of quenches as well. Furthermore, we estimate the computational complexity required to obtain physically reasonable results and conclude that the method is likely efficient in the coming era of early fault-tolerant quantum computers.
Quantum simulations of lattice gauge theories are currently limited by the noisiness of the physical
hardware. Various error mitigation strategies exist to extend the use of quantum computers. We perform quantum simulations to compute two-point correlation functions of the 1 + 1d Z2 gauge theory with matter to determine the mass gap for this theory. These simulations are used as a laboratory for investigating the efficacy and interplay of different error mitigation methods: readout
error mitigation, randomized compiling, rescaling, and dynamical decoupling. We find interesting synergies between these methods and that their combined application increase the simulation times at a given level of accuracy by a factor of six or more compared to unmitigated results
We have studied the chiral and confinement-screening phase transitions in the Schwinger model at finite temperature and density using the quantum algorithm.
The theoretical exploration of the phase diagram for strongly interacting systems at finite temperature and density remains incomplete mainly due to the sign problem in the conventional Lattice Monte Carlo method.
However, quantum computation offers a promising solution to circumvent the sign problem as it deals with quantum field theories in the Hamiltonian formalism.
The preparation of thermal states on quantum circuits is a non-trivial challenge.
We have successfully implemented the thermal state preparation on quantum circuits using a theoretical framework known as Thermal Pure Quantum states (TPQs) and the Quantum Imaginary Time Evolution (QITE) algorithm.
The details of the algorithm, our improvements, and the results will be presented in the talk.
An effective way to design quantum algorithms is by heuristics. One of the representatives is Farhi et al.’s quantum approximate optimization algorithm (QAOA), which provides a powerful variational ansatz for ground state preparation. QAOA is inspired by the adiabatic evolution of a quantum system, and the ansatz can encode the real time evolution of the system Hamiltonian. In this work, we provide a guidance to design the variational ansatz, which can encode general quantum evolution, including the quantum real time evolution (QRTE) and quantum imaginary time evolution (QITE). These heuristic variational ans\"atze preserve symmetries of the target quantum system. We construct the symmetry-preserving QITE-inspired and QRTE-inspired ans\"atze for the Schwinger model and Fermi-Hubbard model. We show the advantage of the QITE-inspired ans\"atze for the ground state preparation of these two models, compared to the one inspired by QRTE in the accuracy and efficiency. We demonstrate that the ground state and excited state properties of the Schwinger model can be studied using the QITE-inspired ansatz.
Lattice studies of spontaneous supersymmetry breaking suffer from a sign problem that in principle can be evaded through novel methods enabled by quantum computing. I will present ongoing work exploring ways quantum computing could be used to study spontaneous supersymmetry breaking in lower-dimensional lattice systems including the (1+1)d N=1 Wess--Zumino model. A particularly promising recent development is to apply the variational quantum deflation algorithm, which generalizes the variational quantum eigensolver so as to resolve multiple low-energy states.
In this talk we introduce a novel quantum algorithm for the estimation of thermal averages
in the NISQ-era through an iterative combination of Variational Quantum Eigensolver techniques and reweighting.
We discuss the details of the algorithm and the scaling of resources and systematical errors,
showing some results of the application to compelling test cases.
We discuss the applicability of lattice QCD to the long-distance (LD) two-photon contribution to the decay of a long-lived neutral kaon into a charged-muon pair (KL2mu). In the absence of QED, the flavor-changing neutral-current KL2mu process requires exchanging at least two W-bosons or a W- and a Z-boson, the short-distance (SD) contribution. Such a process is suppressed by two factors of the Fermi constant $G_F$ and the appearance of loop diagrams makes it sensitive to physics at higher energy scales. Despite its rareness, the experimental KL2mu decay rate is known to 1.6 percent, which makes it an appealing precision probe of the Standard Model. With QED, the two-photon exchange contribution to KL2mu enters at O($G_F\alpha_{QED}^2$). This LD two-photon contribution is of the same order as the SD contribution predicted by electroweak perturbation theory. We demonstrate that it is possible to make a first-principles calculation of the full complex LD two-photon decay amplitude using lattice QCD; in particular, the dispersive part of the amplitude, which is inaccessible from phenomenology, can be obtained. Preliminary numerical results of the quark-connected contribution will be presented.
Dilepton decays of the pseudoscalar mesons have been drawing particular interest, thanks to their sensitivity to both the QCD dynamics at low energy and also signals beyond the Standard model. In the first part of the talk, we present our work on an improved Standard-Model prediction for the rare decay $\pi^0 \to e^+e^-$, and compare it with the first determination on the lattice that predicted a lower $\pi^0 \to \gamma \gamma$ decay width as byproduct. In the second part, we discuss the ongoing work on $K_L \to \ell^+\ell^−$ decays and its connection to lattice QCD.
Rare decays of charged and neutral Kaons will be discussed. Phenomenological works being done in collaboration with Enrico Lunghi and another one with Stefan Schacht will be discussed. Mode(s) that should be target for precision lattice study will be highlighted.
We report our recent results for $K\to\pi\pi$ matrix elements and $\varepsilon'$, the measure of direct CP violation, released on arXiv:2306.06781. This is RBC/UKQCD's first result for $\varepsilon'$ with periodic boundary conditions (PBC), while our earlier calculations were performed with G-parity boundary conditions, where the isospin-0 two-pion ground state corresponds to the on-shell kinematics. Using the GEVP method with multiple two-pion operators, we overcome the difficulty that PBC require us to calculate the matrix elements with excited two-pion final states to obtain the on-shell kinematics. We therefore continue measurements with more configurations and on finer lattices to improve the precision. This talk includes the report on the latest status of new calculations.
We present progress towards extracting multi-hadron $D$ decay amplitudes, such as $D \to \pi \pi$, in a pilot study using three ensembles of stabilised Wilson fermions at the SU(3) flavour symmetric point, with $M_\pi = 410$ MeV. As the three ensembles differ only in the lattice spacing, with well matched physical volumes, it is possible to perform a continuum limit for finite-volume energies (and eventually weak-decay matrix elements) at fixed physical volume. The talk will summarise the work-flow and challenges of the ongoing calculation with a focus on results for the $a^2$-dependence and continuum limit of the two-to-two pseudoscalar S-wave scattering amplitude, determined via the GEVP+Lüscher approach in an exact distillation setup implemented in the Grid and Hadrons software libraries.
The rare hyperon decay $\Sigma \to p \ell^+ \ell^-$ is a flavour changing neutral current process that is sensitive to new physics beyond the Standard Model.
We present the current status of the first exploratory calculation of this decay on the lattice with 340 MeV pions using domain wall fermions.
Recently, significant progress has been made in improving the efficiency and computational speed of lattice QCD calculations associated with Generalized Parton Distributions (GPDs). These advancements are a result of employing asymmetric frames, which differ from the commonly used symmetric frames, and introducing flexibility in the distribution of transferred momentum. A key element of our approach involves utilizing a Lorentz covariant parameterization for the matrix elements in terms of Lorentz-invariant amplitudes. This enables us to establish connections between matrix elements in different frames. Furthermore, we utilize the amplitude-based approach to propose an alternative definition of quasi-GPDs. This alternative definition not only maintains frame independence but also holds the potential for reduced power corrections when matching with light-cone GPDs. We thoroughly explore the interpretations of these new definitions, carefully examining the intricacies involved, and addressing the important issue of uniqueness/non-uniqueness in their formulation. In this presentation, we discuss these theoretical advancements, focusing specifically on the axial-vector GPDs $\widetilde{H}$ and $\widetilde{E}$.
First lattice QCD calculations of x-dependent GPD have been performed in the Breit frame, where the momentum transfer is evenly divided between the initial and final hadron states. Employing the asymmetric frame proposed in PRD 106 (2022) 11, 114512, we are able to obtain proton GPDs for multiple momentum transfers in a computationally efficient setup. In this presentation, we focus on the helicity twist-2 GPD at zero skewness that gives access to the $\tilde{H}$ GPD. We will cover the implementation of the asymmetric frame, its comparison to the Breit Frame, and the dependence of the GPD on the four-vector momentum transfer squared. The calculation is performed on an $N_f = 2+1+1$ ensemble of twisted mass fermions with a clover improvement. The mass of the pion for this ensemble is roughly 260 MeV.
Generalized parton distribution functions (GPDs) describe the longitudinal momentum distribution within a hadron among its constituent partons as well as information about the momentum in the transverse direction. We calculate unpolarized and helicity GPDs using 2+1+1 flavors of highly improved staggered quarks in ensembles generated by the MILC collaboration at a=0.09 fm with a physical pion mass using the method of large-momentum effective theory (LaMET). We use boosting momentum $\sim 1.7$ GeV for multiple $\xi=0$ and $\xi = 0.25$ with multiple transfer momenta renormalized in the hybrid scheme. In addition, we study the effects of systematic errors by applying leading renormalon resummation and renormalization group resummation in the matching process.
Generalized Parton Distributions (GPDs) are related to one aspect of nucleon tomography, the 3D imagining the proton. In one limit, the GPD can describe both the longitudinal momentum and the transverse position of a parton. In other limits, the GPD can describe how each parton contributes to the total spin or mass of the nucleon. Nucleon tomography has sparked great interest as a goal of many experiments, including at JLab and the future EIC. In recent years, many groups have begun lattice QCD calculations of matrix elements related to GPDs. In this talk, I will present the recent calculations performed by the HadStruc collaboration to determine the pseudo-Generalized Ioffe Time Distribution and how GPDs can be extracted from them. The GPD, being a function of three momentum dependent variables, requires studying matrix elements with many combinations of initial and final momenta. This is naturally done within the distillation framework which we employed to obtain quality signal at the requisite large momenta.
Understanding the intricate three-dimensional internal structure of the nucleon has been a long-standing challenge. The main quantitative tool to map this structure are the generalized parton distributions (GPDs). In this talk, we present the first extraction of unpolarized GPDs using the pseudo-distribution approach on the lattice. We use one ensemble of $N_f=2+1+1$ twisted mass fermions at a non-physical pion mass of $260 \textrm{ MeV}$ and a lattice spacing of $0.093 \textrm{ fm}$.
We present the first lattice calculation of the four twist-3 axial quark GPDs for the proton in the $N_f=2+1+1$ twisted-mass formulation with a clover improvement. The ensemble has a