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Lattice QCD Calculation of Nuclear Parity Violation

We present the first lattice QCD calculation of the leading-order momentum-independent parity violating coupling between pions and nucleons, $h_{π{NN}}^1$. 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 $m_π\sim389$ 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 $h_{π{NN}}^{1,con}=(1.099\pm0.505^{+0.058}_{-0.064})\times10^{-7}$, consistent with current experimental bounds and previous model-dependent theoretical predictions.