The extraction of the axial coupling from finite volume systems: The long and short of it

TL;DR

This paper investigates the delocalization of nucleon axial current matrix elements near the chiral limit and demonstrates that standard finite volume calculations of axial coupling are not significantly affected by this delocalization.

Contribution

It introduces a nonstandard axial current that avoids delocalization yet yields identical zero-momentum matrix elements, clarifying finite volume effects.

Findings

Delocalization occurs as the chiral limit is approached due to pion-pole contributions.

Standard finite volume calculations of axial coupling are not significantly impacted by delocalization.

A nonstandard current with no pion pole has identical matrix elements to the standard current in finite and infinite volumes.

Abstract

Due to a pion-pole contribution, the nucleon axial current matrix elements can be visualized in position space as becoming delocalized as the chiral limit is approached, with one-third of the current at distance of order the inverse pion mass. However, this delocalization effect will not cause calculations of the axial coupling in a finite system with standard boundary conditions (periodic for boson fields, antiperiodic for fermions) to have large finite volume effects. This is seen by calculating axial coupling using a nonstandard current with axial quantum numbers. The matrix elements of this new current lacks a pion pole and is not delocalized; however, its zero-momentum matrix element is identical to that of the standard axial current both for infinite and finite volumes.