Hadronic Parity Violation from 4-quark Interactions

Abstract

We present an exploratory investigation of the parity odd $\Delta I=1$ pion-nucleon coupling $h_{\pi }^1$ from lattice QCD. Based on the PCAC relation, we study the parity-conserving effective Hamiltonian and extract the coupling by determining the nucleon mass splitting arising from the effective 4-quark interactions using the Feynman-Hellmann theorem. We present preliminary results of the mass shift for a $32^3\times 64$ ensemble of $N_f=2+1+1$ twisted mass fermions at pion mass $260$ MeV and lattice spacing $a=0.097$ fm.

LATTICE2021 proceedings