External Momentum, Volume Effects, and the Nucleon Magnetic Moment

TL;DR

This paper investigates finite volume effects on nucleon magnetic moment calculations, highlighting the importance of momentum transfer dependence and the limitations of zero-mode photon assumptions in lattice QCD.

Contribution

It provides a detailed analysis of volume corrections for momentum-dependent correlation functions and clarifies conditions under which magnetic moment extraction is affected.

Findings

Finite volume corrections depend on momentum transfer.

Zero-mode photon coupling vanishes at next-to-leading order.

Volume effects are crucial for accurate lattice QCD magnetic moment measurements.

Abstract

We analyze the determination of volume effects for correlation functions that depend on an external momentum. As a specific example, we consider finite volume nucleon current correlators, and focus on the nucleon magnetic moment. Because the multipole decomposition relies on SO(3) rotational invariance, the structure of such finite volume corrections is unrelated to infinite volume multipole form factors. One can deduce volume corrections to the magnetic moment only when a zero-mode photon coupling vanishes, as occurs at next-to-leading order in heavy baryon chiral perturbation theory. To deduce such finite volume corrections, however, one must assume continuous momentum transfer. In practice, volume corrections with momentum transfer dependence are required to address the extraction of the magnetic moment, or other observables that arise in momentum dependent correlation functions. Additionally we shed some light on a puzzle concerning differences in lattice form factor data at equal values of momentum transfer squared.