Finite volume effects for meson masses and decay constants

TL;DR

This paper investigates finite volume effects on pseudoscalar meson masses and decay constants using chiral perturbation theory and Luscher's asymptotic formulae, proposing an extension to improve accuracy and exploring how these effects can help determine low energy constants.

Contribution

It introduces an extended formula beyond the leading exponential term for finite volume effects, accurate at one-loop and dominant at higher loops, aiding in extracting low energy constants.

Findings

Extended formula improves finite volume effect estimates.

Finite volume dependence can help determine low energy constants.

Numerical analysis confirms the dominance of the extended term.

Abstract

We present a detailed numerical study of finite volume effects for masses and decay constants of the octet of pseudoscalar mesons. For this analysis we use chiral perturbation theory and asymptotic formulae a la Luscher and propose an extension of the latter beyond the leading exponential term. We argue that such a formula, which is exact at the one-loop level, gives the numerically dominant part at two loops and beyond. Finally, we discuss the possibility to determine low energy constants from the finite volume dependence of masses and decay constants.