Nucleon matrix element of Weinberg's CP-odd gluon operator from the instanton vacuum

TL;DR

This paper computes the nucleon matrix element of Weinberg's CP-odd gluon operator using the instanton vacuum model, finding a larger value than previous estimates, with implications for neutron EDM constraints.

Contribution

It provides a novel calculation of the nucleon matrix element of a dimension-6 CP-odd gluon operator within the instanton vacuum framework.

Findings

The matrix element is significantly larger than previous estimates.

The strong localization of gluon fields in the instanton vacuum influences the result.

The induced neutron electric dipole moment remains within conventional bounds.

Abstract

We calculate the nucleon matrix element of Weinberg's dimension-6 CP-odd gluon operator $f^{abc} (\tilde F_{\mu\nu})^a (F^{\mu\rho})^b (F^{\nu}_{\;\;\rho})^c$ in the instanton vacuum. In leading order of the instanton packing fraction, the dimension-6 operator is effectively proportional to the topological charge density $(\tilde F_{\mu\nu})^a (F^{\mu\nu})^a$, whose nucleon matrix element is given by the flavor-singlet axial charge and constrained by the $U(1)_A$ anomaly. The nucleon matrix element of the dimension-6 operator is obtained substantially larger than in other estimates, because of the strong localization of the nonperturbative gluon fields in the instanton vacuum. We argue that the neutron electric dipole moment induced by the dimension-6 operator is nevertheless of conventional size.