The Pseudoscalar Meson Mass to Two Loops in Three-Flavor Partially Quenched $\chi$PT

TL;DR

This paper calculates the pseudoscalar meson masses to two loops in three-flavor partially quenched chiral perturbation theory, providing detailed expressions and numerical analysis for the first time.

Contribution

It presents the first two-loop (NNLO) calculation of pseudoscalar meson masses within the supersymmetric PQχPT framework for three flavors.

Findings

Derived ${ m O}(p^6)$ expressions for meson masses with three valence and sea quarks.

Provided numerical analysis of the two-loop mass expressions.

Enhanced understanding of meson mass behavior in partially quenched QCD.

Abstract

This paper presents a first study of the pseudoscalar meson masses to two loops, or NNLO, within the supersymmetric formulation of partially quenched chiral perturbation theory (PQ$\chi$PT). The expression for the pseudoscalar meson mass in the case of three valence and three sea quarks with equal masses, but different from each other, is given to ${\cal O}(p^6)$, along with a numerical analysis.