Finite Volume for Three-Flavour Partially Quenched Chiral Perturbation Theory through NNLO in the Meson Sector

TL;DR

This paper calculates finite volume corrections to meson masses and decay constants in three-flavour Partially Quenched Chiral Perturbation Theory up to two-loop order, providing analytical results and numerical tools relevant for lattice QCD.

Contribution

It provides the first two-loop order finite volume correction calculations in three-flavour PQChPT, including analytical formulas and numerical implementations.

Findings

Reproduces known infinite volume results.

Derives finite volume corrections for various sea quark masses.

Provides numerical tools for lattice QCD applications.

Abstract

We present a calculation of the finite volume corrections to meson masses and decay constants in three flavour Partially Quenched Chiral Perturbation Theory (PQChPT) through two-loop order in the chiral expansion for the flavour-charged (or off-diagonal) pseudoscalar mesons. The analytical results are obtained for three sea quark flavours with one, two or three different masses. We reproduce the known infinite volume results and the finite volume results in the unquenched case. The calculation has been performed using the supersymmetric formulation of PQChPT as well as with a quark-flow technique. Partial analytical results can be found in the appendices. Some examples of cases relevant to lattice QCD are studied numerically. Numerical programs for all results are available as part of the CHIRON package.