Lattice QCD calculation of nuclear parity violation

Abstract

We present a lattice QCD calculation of the leading-order momentum-independent parity-violating coupling between pions and nucleons, ${h}_{\ensuremath{\pi}NN}^{1}$. The calculation performs measurements on dynamical anisotropic clover gauge configurations, with a spatial extent of $L\ensuremath{\sim}2.5$ fm, a spatial lattice spacing of ${a}_{s}\ensuremath{\sim}0.123$ fm, and a pion mass of ${m}_{\ensuremath{\pi}}\ensuremath{\sim}389$ MeV. While this calculation does not include nonperturbative 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 ${h}_{\ensuremath{\pi}NN}^{1,\mathrm{con}}=(1.099\ifmmode\pm\else\textpm\fi{}{0.505}_{\ensuremath{-}0.064}^{+0.058})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$, consistent with current experimental bounds and previous model-dependent theoretical predictions.