Overview of some recent theoretical developments in neutron oscillation

• Rabindra Mohapatra (University of Maryland, College Park, USA)

There are a number of puzzles of beyond the standard model physics that can be probed directly by the process of neutron-anti-neutron oscillation in contrast with the othetr popular baryon violating process i.e. the typical GUT motivated proton decay mode $p\rightarrow e^+ π^0$. The most important of them is a direct understanding of the baryon asymmetry of the universe on which the typical GUT motivated baryon violation cannot. Also if neutron oscillation is observable, leptogenesis mechanism also does not work. The mechanism for such baryogenesis is the post sphaleron model which implemented in the context of $SU(2)_L \times SU(2)_R \times SU(4)_C$ model for neutron oscillation leads to an upper limit on neutron-antineutron oscillation time within the reach of currently proposed experiments. Furthermore, if neutrino-less double beta decay fails to yield a positive signal, an alternative way to establish that lepton number is violated and neutrinos are their own antiparticles is to discover both proton decay and neutron oscillations. Also the belief that neutrinos are likely to be Majorana fermions strongly suggests that there may be a small Majorana component to the neutron mass which leads to neutron oscillation. All these arguments provide strong arguments for a new search for neutron-anti-neutron oscillation. In the second part of the talk, I point out some constraints arising from big bang nucleosynthesis that suppress the neutron mirror neutron oscillation which is under study in several experiments.

Some Recent Results on Models with $n-\bar n$ Oscillations

• Robert Shrock

We discuss models that can feature $n-\bar n$ oscillations at observable levels. These are extra-dimensional theories with Standard-Model fermions propagating in the extra dimensions. Interestingly, while proton decay can be suppressed well below experimental limits in these models, $n-\bar n$ oscillations can occur at levels comparable to current limits. Thus, in these theories, $n-\bar n$ oscillations and the associated $\Delta B=-2$ dinucleon decays can be the dominant manfestation of baryon-number violation. Analyses are given within the context of a Standard-Model effective field theory and a theory involving a left-right symmetry group.

The European Spallation Source and Future Free Neutron Oscillations Searches

• Valentina Santoro (ESS)

The European Spallation Source ESS, presently under construction, in Lund, Sweden, is a multi-disciplinary international laboratory. It will operate the world's most powerful pulsed neutron source. Taking advantage of the unique potential of the ESS, the NNBAR collaboration proposed a two-stage program of experiments to perform high precision searches for neutron conversion in a range of baryon number violation (BNV) channels culminating in an ultimate sensitivity increase for $n\rightarrow\bar{n}$ oscillations of three orders of magnitude over the previously attained limit obtained at the Institut Laue-Langevin ILL. The first stage of this program HIBEAM (High Intensity Baryon Extraction and Measurement) will employ the fundamental physics beamline during the first phase of the ESS operation. This stage focuses principally on searches for neutron conversion to sterile neutrons n'. The second stage, NNBAR will exploit the Large Beam Port (LBP), a unique component of the ESS facility to search directly for $n\rightarrow\bar{n}$. In the talk, I will briefly discuss the scientific motivations for these searches, the status of the the European Spallation Source and the recent developments in the HIBEAM/NNBAR Collaboration.

Neutron-antineutron oscillation search at Super-Kamiokande

• Linyan WAN (Boston University)

As a baryon number violating process with $\Delta B = \Delta (B−L) = 2$, neutron-antineutron oscillation ($n\to\bar n$)provides an important candidate and a unique probe to the baryon asymmetry. We performed a search for $n\to\bar n$ oscillation with the Super-Kamiokande (SK) experiment. Full exposure data set of SK was analyzed using a multi-variate analysis based on kinematic variables and basic distributions from simulated $n\to\bar n$ signal events and atmospheric neutrino backgrounds. We observed 11 events, compared with the expected number of background events 9.3. The upper limit of nuclear lifetime is calculated as $3.6×10^{32}$ years at 90% CL, significantly improved from the present best-limit $1.9×10^{32}$ years of SK-I.

Search for $n\rightarrow\bar{n}$ in the Deep Underground Neutrino Experiment

• Joshua Barrow (The University of Tennessee)

The Deep Underground Neutrino Experiment (DUNE) utilizes Liquid Argon Time Projection Chamber (LArTPC) technology to deeply probe $\nu$ and beyond Standard Model (BSM) interactions with great granularity. The DUNE Technical Design Report (TDR) prioritizes BSM searches for baryon number violation (BNV) modes such as proton decay and neutron-antineutron transformation ($n\rightarrow\bar{n}$), showing expected lower limit targets for DUNE. The previous DUNE analysis techniques used for DUNE's $n\rightarrow\bar{n}$ target will be highlighted, as well as ongoing studies utilizing similar procedures which move toward understanding intranuclear modeling systematics related to this unknown rare process.

Possible Use Of Neutron Optics for Optimization of a Free Neutron-Antineutron Oscillation Search

• William Snow (Indiana University)

Neutron-antineutron oscillations can survive sufficiently coherent interactions with matter and external fields without suppressing the oscillation rate. I describe some examples of this phenomenon which might find practical applications in the design of future experiments.

Baryon-number violation by two units in chiral effective field theory

• Bingwei Long

I discuss a framework based on chiral effective filed theory for treating baryon-number violation by two units in nuclei. The deuteron lifetime is used as an application to illustrate this framework. The emphasis is given to how a consistent power counting is built and what statements can be drawn out of it.

Calculation of the Suppression Factor for Bound Neutron-Antineutron Transformation

• Jean-Marc Richard (IP2I,, IN2P3, U. of Lyon)

I review and revisit the calculation of the lifetime of nuclei due to neutron-antineutron oscillations. It is stressed that the oscillation and the subsequent annihilation take place mainly outside the nucleus and thus hardly suffer from drastic renormalization due to the nuclear medium. The ingredients of the calculation can be safely extracted from nuclear shell-model wave-functions, and optical models fitting the low-energy data on antinucleon-nucleus interaction. The main result is that the lifetime of a nucleus behaves as $T=T_R\,\tau_{n\bar n}^2$, with a factor $T_R$, often referred to as *reduced lifetime* or *suppression factor* of about $10^{22-23}\,$s$^{-1}$. A remarkable feature is that $T_R$ is stable against variations of the antinucleon-nucleus potential.

Lattice QCD matrix elements of Delta B = 2 operators

• Michael Wagman

Theories of B-L violation beyond the Standard Model (BSM) generically lead to the appearance of six-quark operators in Standard Model effective field theory that give rise to neutron-antineutron oscillations and Delta B = 2 nuclear decays. Reliably connecting the results of experimental searches for these processes to constraints on the parameters of BSM physics theories requires Standard Model calculations of the matrix elements of these six-quark operators between hadronic states. I will report on lattice quantum chromodyanmics calculations of a complete basis of Delta B = 2 six-quark operators and a few of their implications for current and future searches for Delta B = 2 processes.

Update on the post-sphaleron baryogenesis model prediction for neutron-antineutron oscillation time

• Bhupal Dev (University of Maryland)
• Bhupal Dev (University of Manchester/TUM)

Post-sphaleron baryogenesis (PSB) is an attractive low-scale mechanism to explain the observed matter-antimatter asymmetry of the Universe. The same \Delta B=2 operator that gives rise to baryogenesis in this scenario also leads to neutron-antineutron oscillation. We show that the PSB mechanism, when embedded in a quark-lepton unified model based on the Pati-Salam gauge group, leads to an absolute upper limit on the neutron-antineutron oscillation time, which might be within reach of future experiments. The multi-TeV-scale scalar diquarks in this model could also be searched for at the LHC and future hadron colliders.

Probing High Scale Theories with $n-\bar{n}$ Oscillations

• Ks Babu (Oklahoma State)
• K.S. Babu (Oklahoma State University)

$n-\bar{n}$ oscillations can be used to probe theories at a high energy scale, such as grand unified theories. In this talk I will illustrate this with two examples. In the first example, $n-\bar{n}$ oscillation arises in a left-right symmetric model realized near the GUT scale that provides a solution to the strong CP problem. The $n-\bar{n}$ oscillation time is closely tied to neutrino masses, and is expected to be in the range of $10^8-10^{10}$ sec. In the second example, $SO(10)$ grand unified theory breaks to the standard model directly, but leaves behind a color sextet scalar field at the TeV scale. This scalar helps with unification of gauge couplings and leads to $n-\bar{n}$ oscillations, which is closely tied to baryon asymmetry generation. For typical values of the model parameters, $\tau_{n-\bar{n}} \sim 10^9 - 10^{10}$ sec. is obtained.

Neutron-antineutron oscillation improvements and baryogenesis

• James Wells

Wherein I discuss how improvements on neutron-antineutron oscillations and its impact on a minimal theory of baryogenesis.

Search for NNbar with UCN

• Alexey Fomin (NRC "Kurchatov Institute" - PNPI)

The scheme of the experiment on search for neutron-antineutron oscillations based on the storage of ultracold neutrons in a material trap is presented. The idea of such an experiment becomes important due to creation of new powerful UCN sources. The sensitivity of the experiment was obtained in Monte Carlo simulation of UCN transport and storage. It mostly depends on the trap size and the amount of UCN in it. Design of the setup, magnetic shielding study, neutron storage and annihilation detection simulations are presented. The possibilities of increasing the sensitivity of the experiment due to the accumulation of the antineutron phase in the collisions of neutrons with the walls are considered.

New scenario for the neutron--antineutron oscillation: shortcut through mirror world

• Zurab Berezhiani (University of L'Aquila)

Existing bounds on the neutron-antineutron mass mixing, $\epsilon_{n\bar n} < {\rm few} \times 10^{-24}$~eV, impose a severe upper limit on $n - \bar n$ transition probability, $P_{n\bar n}(t) < (t/0.1 ~{\rm s})^2 \times 10^{-18}$ or so, where $t$ is the neutron flight time. Here we propose a new mechanism of $n- \bar n$ transition which is not induced by direct mass mixing $\epsilon_{n\bar n}$ but is mediated instead by the neutron mass mixings $\epsilon_{nn'}$ and $\epsilon_{n\bar{n}'}$ with the hypothetical states of mirror neutron $n'$ and mirror antineutron $\bar{n}'$ which can be as large as $\sim 10^{-14}$~eV or so, without contradicting the present experimental limits and nuclear stability bounds. The probabilities of $n-n'$ and $n-\bar{n}'$ transitions, $P_{nn'}$ and $P_{n\bar{n}'}$, depend on environmental conditions in mirror sector, and by scanning over the magnetic field values in experiments they can be resonantly amplified. This opens up a possibility of $n-\bar n$ transition with the probability $P_{n\bar n} = P_{nn'} P_{n\bar{n}'}$ which can reach the values up to $\sim 10^{-8} $. For finding this effect in real experiments, the magnetic field should be suppressed but properly varied. This scenario points towards the scale of few TeV of new physics which can be responsible for these mixings, and can also suggest a new low scale co-baryogenesis mechanism between ordinary and mirror sectors.

Search for neutron oscillations to a sterile state ($ n \rightarrow n^{'} $) and to an antineutron ($ n \rightarrow \overline{n} $)

• Yuri Kamyshkov (University of Tennessee)

As follows from theoretical conjectures of Z. Berezhiani et al. [2006-2020] the neutron that is part of the Standard Model ($SM$) can oscillate into sterile state $ n \rightarrow n^{'} $ , thus leading to neutron disappearance or baryon number violation $ \Delta B=-1 $. However, this can be only an apparent disappearance: if the sterile neutron $ n^{'}~ $ is part of the Mirror Standard Model ($ SM^{'} $) with corresponding mirror baryon number $ B^{'} $ the transformation $ n \rightarrow n^{'} $ can occur without violation of the global baryon number $ \Delta \left( B+B^{'} \right) =0 $. This process will be not necessarily suppressed by high mass scale and can have observable probability corresponding to oscillation times as small as 1-100 s. The $ SM^{'} $ sector is assumed to be an exact copy of $SM$ with the same particle content and the same gauge interactions within $ SM^{'} $, but these interactions are absent between $SM$ and $ SM^{'} $ particles, e.g. mirror photon $ \gamma^{'} $ will not interact with $SM$ charges and vice versa. The gravity however is a common interaction for both sectors thus making $ SM^{'} $ a good candidate for the Dark Matter. Also, additional new BSM interactions are conjectured that mix the neutral particles of $SM$ and $ SM^{'} $ sectors (like $ \gamma , \nu , n $ and possibly other neutral particles) that makes such interactions responsible for the direct detection of DM and for transformations like $ \gamma \rightarrow \gamma^{'},~ \nu \rightarrow \nu ^{'}~ $, and particularly interesting $ n \rightarrow n^{'} $, as a most convenient for experimental observation process. Existing neutron sources provide cold neutron beams with high intensities that can be used for rather simple and inexpensive experimental searches like $ n \rightarrow n^{'} $ disappearance, $ n \rightarrow n^{'} \rightarrow n $ regeneration, searches for neutron transition magnetic moment, and neutron – antineutron transformations through mirror-state oscillations $ n \rightarrow n^{'} \rightarrow \overline{n} $. Plans for such measurements with existing neutron sources at the Oak Ridge National Laboratory and at the future European Spallation Source and the sensitivity reach will be discussed in the workshop presentation.

Neutrons at ORNL and ESS: A Synergistic Program

• Marcellinus Demarteau
• Marcel Demarteau (Oak Ridge National Laboratory)
• Marcel Demarteau (Argonne National Laboratory)

Oak Ridge National Laboratory has some of the world’s most advanced neutron sources, the High Flux Isotope Reactor (HFIR) which is a continuous source of neutrons from nuclear fission, and the Spallation Neutron Source, a pulsed source created by an accelerated proton beam hitting a mercury target. Not only are both good sources for neutrons, they are also excellent neutrino sources with exceptional characteristics. An ambitious and growing fundamental neutron and neutrino science program is in operation at both the SNS and HFIR. Both facilities will undergo major upgrades. A Second Target Station will be built at the SNS, driven by a 2.8MW proton beam, and HFIR will be upgraded with a new pressure vessel and reflector. This provides a unique and timely opportunity to explore the opportunities these upgraded facilities offer for a compelling future fundamental physics program. The Physics Division invites the community to develop a strong synergistic program.

Searches for scalars that carry B or L, taken broadly: whither and wherefore

• Susan Gardner (U Kentucky)

In many models of new physics, the expected rate of processes that break baryon number by two units rests on the features of a poorly known scalar sector, whose members can carry B or L quantum numbers. Thus the BNV discovery prospects in these channels are controlled by the extent to which the associated scalars are excluded by experiments. Working in the context of minimal scalar models, I will survey and discuss the existing constraints and note what windows of opportunity remain for the discovery of light new scalars. With these, new experiments become tenable, and I emphasize the complementary of these to other ongoing efforts and their broader implications.

Covering baryon number violation with inclusive searches

• Julian Heeck (UC Irvine)

Baryon number violation is an extremely sensitive probe of physics beyond the Standard Model. However, the continued absence of any signals raises the question if we are actually looking in the right places or if we should broaden our search strategies. In this talk I will propose *inclusive* nucleon decay searches as a convenient method to cover a lot of parameter space, including sensitivity to new light particles and dark matter induced baryon number violation.

Measurements of Neutron Coupling to a Mirror Sector Using Spin Precession

• Albert Young (North Carolina State University/Triangle Universities Nuclear Laboratory)

Couplings between neutrons and a mirror sector can be formulated in terms of observable effects for precession-measurements (as has been pointed out by Berezhiani), bringing to bear the tools and experimental resources already in play for the measurement of static electric dipole moments.limits for measurements with the coupling strength for neutrons to mirror neutrons. Some details of measurements in an EDM-like geometry can be used to place limits on mirror couplings and provide information on the orientation and strength of a mirror magnetic field, should it exist in the mirror sector.

Exciting New Possibilities for Baryon Number Violation

• Sudhakantha Girmohanta (Stony Brook University)

Proton decay can be sufficiently suppressed in an extra-dimensional model where Standard-Model (SM) fermions are localized at different points in the extra dimension(s), whereas $n$-$\bar n$ oscillations can occur at a rate comparable to the current observable limit. We show that in a left-right symmetric model with extra dimensions this effect is even more enhanced. Several nucleon and dinucleon decays to leptonic final states are considered in the extra-dimensional framework and found to be sufficiently suppressed. $n$-$\bar n$ oscillations are special in this extra-dimensional framework as separating quark and lepton wavefunctions in the extra dimensions to suppress nucleon and dinucleon decays to leptonic final states does not suppress $n$-$\bar n$ oscillations, which only involve quarks.

Perspectives on Baryon Number Violation

• David McKeen (TRIUMF)

In this talk I discuss baryon number violation and the relationship between processes that violate it by one or two units. While proton decay searches currently probe baryon number violation by one unit up to very high scales, those that violate it by two units can be directly motivated by the baryon asymmetry of the universe and can be the leading baryon number violating signal in some models. I will also describe some recent work involving new signatures of baryon number violation such as the decay of atomic hydrogen.