The pion and proton mass in finite volume

TL;DR

This paper calculates finite volume effects on pion and nucleon masses using two-loop chiral perturbation theory and validates a resummed Luscher formula, providing insights into mass shifts in finite volumes.

Contribution

It introduces a two-loop calculation for pion mass finite volume effects and validates a resummed Luscher formula, extending analysis to nucleon mass with preliminary estimates.

Findings

Resummed Luscher formula accurately approximates two-loop pion mass results.

Finite volume effects are significant for pion masses, less certain for nucleons.

Preliminary estimates suggest finite volume effects vary with quark mass.

Abstract

We calculate the finite volume effects for the pion and nucleon mass. For the pion mass we present the results of a full two-loop calculation in chiral perturbation theory. The outcome shows that the resummed version of the Luscher formula we presented in an earlier work does indeed give an excellent approximation to the two-loop result. In view of this result we apply the same resummed formula to the nucleon mass. In the nucleon sector the extension of the chiral expansion to higher quark masses appears to be more problematic and it is therefore more difficult to make reliable predictions for the size of the finite volume effects. We present some preliminary numerical estimates.