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

Understand

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.