Lattice QCD Calculation of Nuclear Parity Violation

TL;DR

This paper reports the first lattice QCD calculation of the leading-order parity-violating pion-nucleon coupling, providing results consistent with experimental bounds and previous models, despite some systematic uncertainties.

Contribution

It introduces the first lattice QCD computation of the parity-violating pion-nucleon coupling $h_{ ext{piNN}}^1$, advancing theoretical understanding in this area.

Findings

Connected diagram contribution: $(1.099\, ext{±}\,0.505^{+0.058}_{-0.064})\times10^{-7}$

Results are consistent with experimental bounds and prior models

Systematic errors due to omitted renormalization, chiral extrapolation, and disconnected diagrams are acknowledged.

Abstract

We present the first lattice QCD calculation of the leading-order momentum-independent parity violating coupling between pions and nucleons, $h_{\pi{NN}}^1$. The calculation performs measurements on dynamical anisotropic clover gauge configurations, with a spatial extent of $L\sim2.5$ fm, a spatial lattice spacing of $a_s\sim0.123$ fm, and a pion mass of $m_{\pi}\sim389$ MeV. While this first calculation does not include non-perturbative renormalization of the bare parity-violating operators, a chiral extrapolation to the physical pion mass, or contributions from disconnected (quark-loop) diagrams, these are expected to result in systematic errors within the quoted statistical error. We find a contribution from the `connected' diagrams of $h_{\pi{NN}}^{1,con}=(1.099\pm0.505^{+0.058}_{-0.064})\times10^{-7}$, consistent with current experimental bounds and previous model-dependent theoretical predictions.