Sunset integrals at finite volume

TL;DR

This paper develops two-loop finite-volume integrals in Chiral Perturbation Theory to improve lattice QCD extrapolations, especially for small quark masses, and compares computational methods for efficiency.

Contribution

It introduces new two-loop integrals at finite volume for all mass cases in ChPT, enhancing lattice QCD analysis capabilities.

Findings

Expansion in Bessel functions and theta functions compared for efficiency.

Results facilitate more accurate finite-volume corrections in lattice QCD.

Work ongoing to integrate these integrals with two-loop ChPT calculations.

Abstract

Chiral Perturbation Theory is a useful tool to aid in performing the various extrapolations needed in lattice QCD calculations of physical quantities. These include extrapolations in quark mass, finite lattice spacing and finite size of the lattice. Especially the latter will become more important when the quark masses on the lattice become smaller. Here we develop the needed two-loop integrals at finite volume to do the calculations for masses and decay constants for all general mass cases. I will present results based on an expansion in Bessel functions as well as on a version using theta functions and compare their efficiency. Work is in progress to combine these results with two-loop ChPT calculations.