Hadronic Parity Violation from 4-quark Interactions

TL;DR

This paper explores the calculation of hadronic parity violation, specifically the $ ext{h}_ ext{π}^1$ coupling, using lattice QCD techniques to analyze nucleon mass shifts caused by 4-quark interactions.

Contribution

It introduces a lattice QCD method to estimate the parity-odd pion-nucleon coupling from nucleon mass splitting, providing preliminary results at near-physical pion mass.

Findings

Preliminary mass shift results for a $32^3 imes 64$ lattice ensemble.

Estimation of the parity-odd coupling $h_ ext{π}^1$ from nucleon mass splitting.

Use of the Feynman-Hellmann theorem in lattice QCD calculations.

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.