Finite-volume corrections to the CP-odd nucleon matrix elements of the electromagnetic current from the QCD vacuum angle

TL;DR

This paper calculates finite-volume corrections to CP-odd nucleon matrix elements related to electric dipole moments using chiral perturbation theory, aiding the interpretation of lattice QCD results on strong CP violation.

Contribution

It provides a next-to-leading order chiral perturbation theory analysis of finite-volume effects on CP-odd nucleon matrix elements, improving the accuracy of lattice QCD extrapolations.

Findings

Finite-volume corrections are quantified for lattice QCD calculations.

Updated estimates of neutron and proton electric dipole moments are provided.

Results support more precise determination of strong CP-violation effects.

Abstract

Nucleon electric dipole moments originating from strong CP-violation are being calculated by several groups using lattice QCD. We revisit the finite volume corrections to the CP-odd nucleon matrix elements of the electromagnetic current, which can be related to the electric dipole moments in the continuum, in the framework of chiral perturbation theory up to next-to-leading order taking into account the breaking of Lorentz symmetry. A chiral extrapolation of the recent lattice results of both the neutron and proton electric dipole moments is performed, which results in $d_n=(-2.7\pm1.2)\times10^{-16}e\theta_0$cm and $d_p=(2.1\pm1.2)\times10^{-16}e\theta_0$cm.