One-loop matching for quark dipole operators in a gradient-flow scheme

TL;DR

This paper defines renormalized quark dipole operators using the gradient flow scheme and computes one-loop matching coefficients to connect with MS scheme, aiding lattice QCD studies of CP violation.

Contribution

It introduces a regularization-independent scheme for quark dipole operators and calculates one-loop matching coefficients to MS scheme, facilitating future lattice QCD calculations.

Findings

Defined renormalized dipole operators in a gradient-flow scheme.

Calculated one-loop matching coefficients to MS scheme.

Provided basis for lattice QCD computations of CP-violating matrix elements.

Abstract

The quark chromoelectric dipole (qCEDM) operator is a CP-violating operator describing, at hadronic energies, beyond-the-standard-model contributions to the electric dipole moment of particles with nonzero spin. In this paper we define renormalized dipole operators in a regularization-independent scheme using the gradient flow, and we perform the matching at one loop in perturbation theory to renormalized operators of the same and lower dimension in the more familiar MS scheme. We also determine the matching coefficients for the quark chromomagnetic dipole operator (qCMDM), which contributes, for example, to matrix elements relevant to CP-violating and CP-conserving kaon decays. The calculation provides a basis for future lattice QCD computations of hadronic matrix elements of the qCEDM and qCMDM operators.