Exploring a new approach to hadronic parity violation from lattice QCD

The long-range, parity-odd nucleon interaction generated by single-pion exchange is captured in the parity-odd pion–nucleon coupling h^1_π . Its calculation in lattice QCD requires the evaluation of four-quark operator nucleon three-point functions. We investigate a new numerical approach to compute h^1_π based on nucleon matrix elements of parity-even four-quark operators and related to the parity-violating electroweak theory by partial conservation of axial current (PCAC) and chiral perturbation theory. This study is performed with 2+1+1 dynamical flavors of twisted mass fermions at pion mass m_π≈ 260 MeV in a lattice box of L ≈ 3 fm and with lattice spacing of a ≈ 0.091 fm . From a calculation excluding fermion loop diagrams we find a bare coupling of h^1_π= 8.08 (98) · 10^-7 .