Renormalization Group Running of Dimension-Six Sources of Parity and Time-Reversal Violation

TL;DR

This paper systematically studies how dimension-six operators violating parity and time-reversal symmetry evolve from high-energy scales to low energies, providing bounds on new physics from neutron EDM measurements.

Contribution

It offers a comprehensive calculation of the renormalization group evolution of dimension-six operators, including QCD and electroweak corrections, from high to low energies.

Findings

QCD corrections are generally modest for most operators.

Derived low-energy operator set relevant for hadronic and nuclear EDMs.

Established bounds on high-energy operators using neutron EDM limits.

Abstract

We perform a systematic study of flavor-diagonal parity- and time-reversal-violating operators of dimension six which could arise from physics beyond the SM. We begin at the unknown high-energy scale where these operators originate. At this scale the operators are constrained by gauge invariance which has important consequences for the form of effective operators at lower energies. In particular for the four-quark operators. We calculate one-loop QCD and, when necessary, electroweak corrections to the operators and evolve them down to the electroweak scale and subsequently to hadronic scales. We find that for most operators QCD corrections are not particularly significant. We derive a set of operators at low energy which is expected to dominate hadronic and nuclear EDMs due to physics beyond the SM and obtain quantitative relations between these operators and the original dimension-six operators at the high-energy scale. We use the limit on the neutron EDM to set bounds on the dimension-six operators.