Effective field theory in the study of long range nuclear parity violation on lattice

Abstract

A non-zero signal A np γ = (−3.0 ± 1.4 ± 0.2) × 10 −8 of the gamma-ray asymmetry in the neutronproton capture was recently reported by the NPDGamma Collaboration which provides the first determination of the ∆I = 1 parity-odd pion-nucleon coupling constant h 1 π = (2.6±1.2±0.2)×10 −7 .The ability to reproduce this value from first principles serves as a direct test of our current understanding of the interplay between the strong and weak interaction at low energy. To motivate new lattice studies of h 1 π , we review the current status of the theoretical understanding of this coupling, which includes our recent work that relates it to a nucleon mass-splitting by a soft-pion theorem. We further investigate the possibility of calculating the mass-splitting on the lattice by providing effective field theory parameterizations of all the involved quark contraction diagrams.We show that the lattice calculations of the easier connected diagrams will provide information of the chiral logarithms in the much harder quark loop diagrams and thus help in the chiral extrapolation of the latter.

Parity- and Time-Reversal-Violating Nuclear Forces

“…Furthermore, large N c analysis may help in reducing the number of contact LECs. Also Lattice QCD calculations start to give valuable information [132,232].…”

Parity- and time-reversal-violating nuclear forces

“…Furthermore, large N c analysis may help in reducing the number of contact LECs. Also Lattice QCD calculations start to give valuable information [132,226]. 8 Notice that the values of the LECs c i obtained from the pion-nucleon amplitude at NLO, which would be appropriate for V…”

Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes

“…These processes are more straightforward to connect to the underlying SM mechanism. In this context, EFTs have provided a systematic framework to identify leading parity-violating interactions at low energies [583][584][585][586][587][588][589][590][591][592][593][594][595][596], improve upon conventional phenomenological approaches [597], and pave the way for a systematic extension to larger nuclei. These EFTs, however, introduce new two-nucleon LECs that need to be constrained by experimental data where it exists, or by LQCD.…”