Finite volume effects for nucleon and heavy meson masses

TL;DR

This paper uses an advanced formula to analyze how finite volume effects influence the masses of nucleons and heavy mesons, expressing corrections through physical observables and assessing uncertainties.

Contribution

It applies the resummed L"uscher formula with subthreshold expansion to relate finite volume effects to physical quantities, including a detailed analysis for nucleons and a new derivation for heavy mesons.

Findings

Finite volume corrections can be expressed with few physical observables.

Assessment of uncertainties in nucleon mass corrections.

Derivation of L"uscher formula for heavy mesons in relativistic and nonrelativistic forms.

Abstract

We apply the resummed version of the L\"uscher formula to analyze finite volume corrections to the mass of the nucleon and of heavy mesons. We show that by applying the subthreshold expansion of the scattering amplitudes one can express the finite volume corrections in terms of only a few physical observables and the size of the box. In the case of the nucleon, the available information about the quark mass dependence of these physical quantities is discussed and used to assess the finite volume corrections to the nucleon mass as a function of the quark mass including a detailed analysis of the remaining uncertainties. For heavy mesons, the L\"uscher formula is derived both fully relativistically and in a nonrelativistic approximation and a first attempt at a numerical analysis is made.