Nucleon Properties at Finite Volume: the Epsilon Prime Regime

TL;DR

This paper develops a new power-counting scheme called epsilon prime for analyzing nucleon properties in small, asymmetric volumes, and applies it to compute nucleon mass, magnetic moment, and axial matrix element.

Contribution

Introduces epsilon prime power-counting for finite volume chiral perturbation theory, enabling perturbative treatment of pion zero-modes in asymmetric volumes.

Findings

Derived nucleon mass, magnetic moment, and axial matrix element at first epsilon prime order.

Showed pion zero-modes are perturbative but enhanced in epsilon prime regime.

Provided a framework for finite volume nucleon property calculations.

Abstract

We study the properties of the nucleon in highly asymmetric volumes where the spatial dimensions are small but the time dimension is large in comparison to the inverse pion mass. To facilitate power-counting at the level of Feynman diagrams, we introduce $\epsilon^\prime$-power-counting which is a special case of Leutwyler's $\delta$-power-counting. Pion zero-modes enter the $\epsilon^\prime$-counting perturbatively, in contrast to both the $\epsilon$- and $\delta$-power-countings, since $m_q < q\bar{q}> V$ remains large. However, these modes are enhanced over those with non-zero momenta and enter at lower orders in the $\epsilon^\prime$-expansion than they would in large volume chiral perturbation theory. We discuss an application of $\epsilon^\prime$-counting by determining the nucleon mass, magnetic moment and axial matrix element at the first nontrivial order in the $\epsilon^\prime$-expansion.