Hadronic Parity Violation from Twisted Mass Lattice QCD

We present results for an exploratory lattice calculation of the leading parity-violating pion-nucleon coupling $h_{\pi }^1$. Based on the PCAC relation we use a parity-conserving Lagrangian and focus on the techniques to determine the nucleon matrix elements of the effective 4-quark operators. For our study we employ an ensemble of twisted mass fermions with $260$ MeV pion mass. Barring mixing with lower-dimensional operators and renormalization at this stage, we discuss our estimate for $h_{\pi }^1$.