Model independent evaluation of the Wilson coefficient of the Weinberg operator in QCD

TL;DR

This paper calculates a model-independent Wilson coefficient for the Weinberg operator, a CP-violating gluonic interaction, at two-loop level, enabling broader application to beyond Standard Model physics and highlighting the significance of EDM measurements.

Contribution

It provides a two-loop level, model-independent calculation of the Wilson coefficient for the Weinberg operator applicable to various BSM models.

Findings

Future EDM measurements can probe higher energy scales than colliders.

The derived Wilson coefficient aids in estimating nucleon EDMs induced by the Weinberg operator.

The results are applicable regardless of the SU(3)$_c$ representation of involved particles.

Abstract

We derive a Wilson coefficient of a CP-violating purely gluonic dimension-6 operator called the Weinberg operator ($GG\tilde{G}$) generated by a scalar and two fermions at the two-loop level. We do not specify the representation of SU(3)$_c$ for the scalar and the fermions, and thus our result can be applied to a variety of models beyond the standard model. We estimate the nucleon EDMs induced by the Weinberg operator in some examples and discuss the importance of measuring EDMs. It is found that future measurements of the EDMs can probe physics at higher energy scale beyond the reach of collider experiments.