Neutron Electric Dipole Moment at Fixed Topology

TL;DR

This paper investigates how fixed topological sectors in finite volume affect CP-odd observables like the neutron electric dipole moment, highlighting the role of zero modes and divergences in lattice QCD calculations.

Contribution

It provides a detailed analysis of finite volume effects on CP-odd quantities in fixed topology, including the evaluation of three-point functions and the impact of zero modes.

Findings

Finite volume effects significantly influence CP-odd observables.

Zero modes play a crucial role in the behavior of CP-odd Green's functions.

Power divergences in quark mass appear in quenched approximation at finite volume.

Abstract

We describe the finite volume effects of CP-odd quantities, such as the neutron electric dipole moment and the anapole moment in the $\theta$-vacuum, under different topological sectors. We evaluate the three-point Green's functions for the electromagnetic current in a fixed non-trivial topological sector in order to extract these CP-odd observables. We discuss the role of zero modes in the CP-odd Green's function and show that, in the quenched approximation, there is a power divergence in the quark mass for CP-odd quantities at finite volume.