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

Understand

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.