Nonperturbative computations with the CP-violating Weinberg three-gluon operator

The CP-violating Weinberg three-gluon operator describes the chromo-electric moment of the gluon and is an important source of CP-violation in many theories of physics beyond the standard model. The electric dipole moment due to this operator has been difficult to calculate nonperturbatively because of its power-divergent mixing with lower-dimensional operators. Such power-divergence is, however, absent when at least one of the quarks is massless. Here we study this mixing as a function of the quark mass using a lattice discretization of QCD and using the gradient-flow scheme in to preserve chiral symmetry. This analysis sets the stage for obtaining the electric dipole moment of the nucleon nonperturbatively. It also allows us to obtain the induced topological term due to the Weinberg term in a Peccei-Quinn solution to the stron CP problem.