Finite size effects on $M_\pi$ in QCD from Chiral Perturbation Theory

TL;DR

This paper investigates how finite spatial volume affects the pion mass in QCD using Chiral Perturbation Theory and L"uscher's formula, discussing the limits of the theoretical predictions.

Contribution

It provides a detailed analysis of finite size effects on $M_$ in QCD within the framework of Chiral Perturbation Theory and evaluates the applicability of these predictions.

Findings

Finite size effects on $M_$ are quantified using Chiral Perturbation Theory.

The applicability range of the chiral predictions is discussed.

L"uscher's formula is employed to relate finite volume effects to pion mass shifts.

Abstract

We present a determination of the shift $M_\pi(L)-M_\pi$ due to the finite spatial box size $L$ by means of $N_f=2$ Chiral Perturbation Theory and L\"uscher's formula. The range of applicability of the chiral prediction is discussed.