We present a 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 $L\sim 2.5$ fm, a spatial lattice spacing of $a_s\sim 0.123$ fm, and a pion mass of $m_{\pi }\sim 389$ 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 $h_{\pi NN}^{1,\mathrm{con}}=(1.099\pm {0.505}_{-0.064}^{+0.058})\times {10}^{-7}$, consistent with current experimental bounds and previous model-dependent theoretical predictions.

• Received 15 August 2011

DOI:https://doi.org/10.1103/PhysRevC.85.022501