Zγ production at NNLO

Tobias Neumann, University at Buffalo
in collaboration with John Campbell and Ciaran Williams

June 1, 2017

Motivation / Overview

  • Second implementation of \(Z\gamma\) at NNLO using jettiness-subtractions (Gaunt, Stahlhofen, Tackmann, Walsh '15; Boughezal, Focke, Liu, Petriello '15)
  • Validation of previous calculation (Grazzini, Kallweit, Rathlev, Torre ’13+’15)
    using \(q_T\)-subtractions (Catani, Grazzini '07)

  • How can we improve/extend two year old computation?
    • Performance: Power corrections? Slicing parameter?
    • Updated SM phenomenology
    • BSM: Anomalous couplings & Dark Matter

Setup and assembly

  • MCFM NNLO 0-jettiness subtractions implementation (Boughezal, Petriello, et al. '16)
  • Amplitude ingredients:
    • 2-loop \(Z\gamma\) amplitudes (Gehrmann, Tancredi '12)
    • Electron radiation: 2-loop form-factor (Matsuura, van der Marck, van Neerven '89)
    • Tree and one-loop amplitudes reimplemented
      (Campbell, Hartanto, Williams '12), (Bern, Dixon, Kosower '98)
  • Anomalous \(Z\gamma\gamma\) and \(ZZ\gamma\) couplings:
    • Vertices (Hagiwara, Peccei, Zeppenfeld, Hikasa '87)
    • Four parton + V off-shell current (Berends, Giele, Kuijf '89)
    • V decay to three partons one-loop current (Garland, Gehrmann, Glover '02)
      and analytical continuation (Gehrmann, Remiddi '02)
  • Our data points/performance:
    • NLO: 150-250 cpu hours on 2009/2010 Intel Xeons
    • NNLO: 600-1200 cpu hours (24 cores, 24-48 hours)

How to extrapolate the slicing parameter to zero?

(Grazzini, Kallweit, Rathlev ’15)

Power corrections

Subleading terms for \(q\bar q \to \text{color-singlet}\)
(Moult, Rothen, Stewart, Tackmann, Zhu '16), (Boughezal, Liu, Petriello '17)

Jettiness definition:
Boosted vs. hadronic center of mass system

Boosted: 0-jettiness \(\tau_0\) defined in color singlet c.o.m. frame

MCFM-8.0: \(\tau_0\) defined in hadronic c.o.m. frame

Comparison to Grazzini, Kallweit, Rathlev ’15

Charged lepton decay

Neutrino decay

Comparison for neutrino decay

Our NLO results agree to better than 0.2%

\(\sigma_\text{NNLO} = 80.7(1)~\text{fb}\),  \(\sigma_\text{NNLO}^\text{GKR} = 80.8(4)~\text{fb}\)

(0.1% num. uncertainty)

Comparison for charged lepton decay

\(\sigma_\text{NNLO} = 178.6(4)~\text{fb}\),  \(\sigma_\text{NNLO}^\text{GKR} = 180(1)~\text{fb}\)

(0.2% num. uncertainty)

How about \(13~\text{TeV}\) results?

(ATLAS neutrino-channel cuts for \(13~\text{TeV}\))

Total cross section for \(Z\to \nu\bar\nu\): NLO coefficient

Total cross section for \(Z\to \nu\bar\nu\): NNLO coefficient

\(\sigma_\text{NNLO} = 86.0(2)\text{fb}\) (0.2% num. uncertainty)

Total cross section for \(Z\to l\bar l\): NNLO coefficient

\(\sigma_\text{NNLO} = 306(2)\text{fb}\) (0.7% num. uncertainty)

\(13~\text{TeV}\,\, p_T^\gamma\) for \(Z\to \nu\bar\nu\)

\(13~\text{TeV}\,\, m_T^{\nu\bar\nu\gamma}\) for \(Z\to \nu\bar\nu\)

Anomalous \(ZZ\gamma\) and \(Z\gamma\gamma\) couplings

ATLAS, 1604.05232 using NNLO SM prediction (Grazzini, Kallweit, Rathlev '15) + NLO anomalous couplings (MCFM-8.0)

Anomalous Couplings: \(h_3^Z\), \(13~\text{TeV}\, Z\to\nu\bar\nu\)

"Now": NNLO SM + NNLO anomalous couplings in MCFM


\( p_T^\gamma>400~\text{GeV}\), no jets
No form factor applied. Very similar results for \(h_4^\gamma\).

How much do current limits change?

Another topic: \(Z(\to\nu\bar\nu)\gamma\) mono-photon signal:
Background for Dark Matter

Summary

  • Second implementation of \(Z\gamma\) at NNLO
  • Successful verification of previous results ✔
  • Numerically stable and fast even without power corrections ✔
    (~1000 cpu hours for sub-percent precision NNLO results)
  • Ready for \(13~\text{TeV}\) phenomenology
    • NNLO Standard Model ✔
    • NNLO BSM: Anomalous \(ZZ\gamma\) \(Z\gamma\gamma\) couplings ✔
  • Public in MCFM (soon) and usable by non-experts (already)
    (no excessive parameter tinkering)