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 $$h^{1}_{\pi }$$ h π 1 . Its calculation in lattice QCD requires the evaluation of four-quark operator nucleon three-point functions. We investigate a new numerical approach to compute $$h^{1}_{\pi }$$ h π 1 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 $$m_{\pi } \approx 260 \,\text {MeV}$$ m π ≈ 260 MeV in a lattice box of $$L \approx 3 \,\text {fm}$$ L ≈ 3 fm and with lattice spacing of $$a \approx 0.091 \,\text {fm}$$ a ≈ 0.091 fm . From a calculation excluding fermion loop diagrams we find a bare coupling of $$h^{1}_{\pi }= 8.08 \,(98) \cdot 10^{-7}$$ h π 1 = 8.08 ( 98 ) · 10 - 7 .