Pseudoscalar mesons in a finite cubic volume with twisted boundary conditions

TL;DR

This paper investigates how finite cubic volumes with twisted boundary conditions affect pseudoscalar mesons, providing theoretical calculations and asymptotic formulas to understand finite-volume effects on their properties.

Contribution

It extends chiral perturbation theory to include twisted boundary conditions and derives asymptotic Luscher-like formulas for finite-volume corrections on pseudoscalar mesons.

Findings

Chiral Ward identities are satisfied in finite volume.

Asymptotic formulas accurately estimate finite-volume corrections.

Next-to-leading order corrections are quantified for twisted boundary conditions.

Abstract

We study the effects of a finite cubic volume with twisted boundary conditions on pseudoscalar mesons. We first apply chiral perturbation theory in the p-regime and calculate the corrections for masses, decay constants, pseudoscalar coupling constants and form factors at next-to-leading order. We show that the Feynman-Hellmann theorem and the relevant Ward-Takahashi identity are satisfied. We then derive asymptotic formulae a la Luscher for twisted boundary conditions. We show that chiral Ward identities for masses and decay constants are satisfied by the asymptotic formulae in finite volume as a consequence of infinite-volume Ward identities. Applying asymptotic formulae in combination with chiral perturbation theory we estimate corrections beyond next-to-leading order for twisted boundary conditions.