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

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 $\overline{\mathrm{MS}}$ 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 $\overline{\mathrm{MS}}$ scheme to one-loop in perturbation theory, using both the naive dimensional regularization and 't Hooft-Veltman prescriptions for ${\gamma }_5$.

Comments: 52 pages, 5 figures, 6 tables. Added section with comparison to DeltaS=1 chromo-magnetic operator