Hadronic parity violation at next-to-leading order

The flavor-conserving nonleptonic weak interaction can be studied experimentally through the observation of parity violation in nuclear and few-body systems. At hadronic scales, matrix elements of parity-violating four-quark operators ultimately give rise to the parity-violating couplings between hadrons, and such matrix elements can be calculated nonperturbatively using lattice QCD. In this work, we investigate the running of isovector parity-violating operators from the weak scale down to hadronic scales using the renormalization group. We work at next-to-leading order in the QCD coupling, and include both neutral-current and charged-current interactions. At this order, results are renormalization-scheme dependent, and we utilize 't Hooft-Veltman dimensional regularization. The evolution of Wilson coefficients at leading and next-to-leading order is compared. Next-to-leading-order effects are shown to be non-negligible at hadronic scales.