One-loop matching of the $CP$-odd three-gluon operator to the gradient flow

TL;DR

This paper computes one-loop matching coefficients for the $CP$-odd three-gluon operator between lattice and continuum schemes, enabling precise lattice QCD calculations of the neutron electric dipole moment within effective field theories.

Contribution

It provides the first one-loop matching coefficients for the $CP$-odd three-gluon operator between the 't Hooft-Veltman scheme and the gradient flow, completing the set for dimension-six operators.

Findings

Calculated one-loop matching coefficients for the three-gluon operator.

Enabled scheme translation for lattice QCD to effective field theory.

Supports precise neutron EDM computations in beyond Standard Model physics.

Abstract

The calculation of the neutron electric dipole moment within effective field theories for physics beyond the Standard Model requires non-perturbative hadronic matrix elements of effective operators composed of quark and gluon fields. In order to use input from lattice computations, these matrix elements must be translated from a scheme suitable for lattice QCD to the minimal-subtraction scheme used in the effective-field-theory framework. The accuracy goal in the context of the neutron electric dipole moment necessitates at least a one-loop matching calculation. Here, we provide the one-loop matching coefficients for the $CP$-odd three-gluon operator between two different minimally subtracted 't Hooft-Veltman schemes and the gradient flow. This completes our program to obtain the one-loop gradient-flow matching coefficients for all $CP$-violating and flavor-conserving operators in the low-energy effective field theory up to dimension six.