Exploring a new approach to Hadronic Parity Violation from Lattice QCD

Abstract

The long-range, parity-odd nucleon interaction generated by single pion exchange is captured in the parity-odd pion-nucleon coupling $h_{\pi }^1$. Its calculation in lattice QCD requires the evaluation of 4-quark operator nucleon 3-point functions. We investigate a new numerical approach to compute $h_{\pi }^1$ based on nucleon matrix elements of parity-even 4-quark operators and related to the parity-violating electro-weak theory by PCAC and chiral perturbation theory. This study is performed with 2+1+1 dynamical flavors of twisted mass fermions at pion mass $m_{\pi }\approx 260\text{MeV}$ in a lattice box of $L\approx 3\text{fm}$ and with a lattice spacing of $a\approx 0.091\text{fm}$. From a calculation excluding fermion loop diagrams we find a bare coupling of $h_{\pi }^1=8.08(98)\cdot 10^{-7}$.

Comments: 14 pages, 9 figures, 4 tables. Parity-violating Lagrangian Eq. (1), PCAC relation Eq. (2), details on 4-quark operators Eq. (4), summary of statistics Tab. I., summary of our results for the bare matrix elements weighted by the Wilson coefficients Tab. IV. and references to our preliminary results of this work added. Results of the paper are unaffected