Three-Flavor Partially Quenched Chiral Perturbation Theory at NNLO for Meson Masses and Decay Constants

TL;DR

This paper advances the theoretical understanding of meson properties in lattice QCD by providing NNLO calculations in three-flavor partially quenched chiral perturbation theory, including new decay constant expressions.

Contribution

It presents a complete NNLO calculation of meson masses and decay constants in three-flavor PQχPT, including new analytical formulas for nondegenerate sea quarks.

Findings

NNLO corrections are sizable in meson mass and decay constant calculations.

Provides explicit analytical results for three nondegenerate sea quark flavors.

Demonstrates the importance of NNLO terms in fitting lattice QCD data.

Abstract

We discuss Partially Quenched Chiral Perturbation Theory (PQ$\chi$PT) and possible fitting strategies to Lattice QCD data at next-to-next-to-leading order (NNLO) in the mesonic sector. We also present a complete calculation of the masses of the charged pseudoscalar mesons, in the supersymmetric formulation of PQ$\chi$PT. Explicit analytical results are given for up to three nondegenerate sea quark flavors, along with the previously unpublished expression for the pseudoscalar meson decay constant for three nondegenerate sea quark flavors. The numerical analysis in this paper demonstrates that the corrections at NNLO are sizable, as expected from earlier work.