Gradient flow of the Weinberg operator

TL;DR

This paper investigates the CP-violating Weinberg three-gluon operator using gradient flow techniques to estimate its contribution to electric dipole moments and CP violation, aiding constraints on new physics.

Contribution

It provides preliminary lattice QCD results on susceptibilities involving the Weinberg operator and the $ heta$ term, with continuum and chiral extrapolations, advancing understanding of CP violation in BSM theories.

Findings

Preliminary susceptibility estimates for the Weinberg operator.

Continuum and chiral extrapolations performed.

Framework for combining matrix elements to constrain BSM physics.

Abstract

We present preliminary results on the susceptibilities involving the CP-violating (CPV) Weinberg three-gluon operator and the topological $\Theta$ term using the gradient flow scheme, and study their continuum and chiral extrapolations. These are used to provide an estimate of the $\Theta$ induced by the Weinberg operator in theories with the Peccei-Quinn (PQ) mechanism. Combined with the calculations of the matrix elements (MEs) of quark-bilinears between nucleon states, such calculations will enable estimates of the electric dipole moments (EDMs) and CPV pion-nucleon couplings due to the Weinberg operator, thereby providing robust constraints on beyond the standard model (BSM) physics.