Dimension-5 CP-odd operators: QCD mixing and renormalization

TL;DR

This paper analyzes the mixing and renormalization of dimension-5 CP-odd operators involving quarks, gluons, and photons, providing one-loop renormalization matrices and matching schemes for lattice calculations.

Contribution

It offers the first detailed one-loop renormalization and mixing matrix for dimension-5 CP-odd operators, including definitions suitable for non-perturbative lattice computations.

Findings

Renormalization matrix computed to one-loop in MS scheme.

Defined a regularization-independent scheme for lattice calculations.

Provided matching coefficients between schemes using different gamma_5 prescriptions.

Abstract

We study the off-shell mixing and renormalization of flavor-diagonal dimension-5 T- and P-odd operators involving quarks, gluons, and photons, including quark electric dipole and chromo-electric dipole operators. We present the renormalization matrix to one-loop in the $\bar{\rm MS}$ scheme. We also provide a definition of the quark chromo-electric dipole operator in a regularization-independent momentum-subtraction scheme suitable for non-perturbative lattice calculations and present the matching coefficients with the $\bar{\rm MS}$ scheme to one-loop in perturbation theory, using both the naive dimensional regularization and 't Hooft-Veltman prescriptions for $\gamma_5$.