A nucleon in a tiny box

TL;DR

This paper employs Chiral Perturbation Theory to analyze how finite volume and temperature affect the nucleon mass, providing a framework to interpret lattice QCD results in small volumes.

Contribution

It extends the analysis of nucleon mass shifts to both the ps- and p-regimes, offering a method to extrapolate lattice data from small volumes.

Findings

Valid up to next-to-leading order in both regimes

Discussion on convergence of the expansion

Potential to extract low-energy constants from lattice data

Abstract

We use Chiral Perturbation Theory to compute the nucleon mass-shift due to finite volume and temperature effects. Our results are valid up to next-to-leading order in the "\eps-regime" (mL ~ m\beta << 1) as well as in the "p-regime" (mL ~ m\beta >> 1). Based on the two leading orders, we discuss the convergence of the expansion as a function of the lattice size and quark masses. This result can be used to extrapolate lattice results obtained from lattice sizes smaller than the pion cloud, avoiding the numerical simulation of physics under theoretical control. An extraction of the low-energy coefficient c_3 of the chiral Lagrangean from lattice simulations at small volumes and a ``magic'' ratio \beta=1.22262 L might be possible.