Quark anti-quark expectation value in finite volume

TL;DR

This paper calculates the quark-antiquark expectation value in finite volume using two-loop chiral perturbation theory and compares it with a Luscher-like formula, highlighting the limitations of current finite size correction methods.

Contribution

It provides a two-loop calculation of the quark-antiquark expectation value in finite volume and assesses the applicability of Luscher-like formulas in this context.

Findings

Finite size corrections are small at two loops.

Luscher-like formula accuracy cannot be conclusively tested.

Highlights limitations of current finite volume correction approaches.

Abstract

We have computed the quark anti-quark expectation value in finite volume at two loop in chiral perturbation theory and compare it with a formula obtained in analogy to the Luscher formula for pion mass in finite volume. We observe that due to the small finite size correction at two loop it is not possible to obtain conclusions on the accuracy of the extended Luscher formula.