Hadronic Parity Violation at Next-to-Leading Order

TL;DR

This paper studies how parity-violating four-quark operators evolve from the weak scale to hadronic scales using next-to-leading order QCD calculations, highlighting the importance of higher-order effects.

Contribution

It provides a detailed next-to-leading order analysis of the running of parity-violating operators, including scheme dependence and comparison with leading order results.

Findings

Next-to-leading order effects are significant at hadronic scales.

The evolution of Wilson coefficients differs notably between leading and next-to-leading order.

Results depend on the renormalization scheme used.

Abstract

The flavor-conserving non-leptonic 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 non-perturbatively 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.