Effective Field Theory in The Study of Long Range Nuclear Parity Violation on Lattice

TL;DR

This paper discusses the use of effective field theory and lattice QCD to study the long-range nuclear parity violation, focusing on the parity-odd pion-nucleon coupling constant and its experimental determination.

Contribution

It relates the parity-odd pion-nucleon coupling to nucleon mass-splitting and proposes lattice calculation strategies for related quark contraction diagrams.

Findings

Experimental value of gamma-ray asymmetry measured.

Effective field theory links coupling to nucleon mass-splitting.

Lattice calculations of connected diagrams inform chiral extrapolation.

Abstract

A non-zero signal $A_\gamma^\mathrm{np}=(-3.0\pm1.4\pm0.2)\times 10^{-8}$ of the gamma-ray asymmetry in the neutron-proton capture was recently reported by the NPDGamma Collaboration which provides the first determination of the $\Delta I=1$ parity-odd pion-nucleon coupling constant $h_\pi^1=(2.6\pm 1.2\pm 0.2)\times 10^{-7}$. 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 $h_\pi^1$, 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.