Decay Constants of Pseudoscalar Mesons to Two Loops in Three-Flavor Partially Quenched $\chi$PT

TL;DR

This paper calculates the decay constants of charged pseudoscalar mesons to two loops in three-flavor partially quenched chiral perturbation theory, providing explicit formulas and numerical estimates of corrections.

Contribution

It provides the first analytical two-loop expressions for decay constants in three-flavor PQχPT using the supersymmetric formulation.

Findings

Explicit ${ m O}(p^6)$ analytical expressions are derived.

Numerical estimates show the size of two-loop corrections.

The supersymmetric formulation facilitates the calculations.

Abstract

This paper presents a first study of the decay constants of the charged, or flavor-off-diagonal, pseudoscalar mesons to two loops for three flavors of sea quarks, in Partially Quenched Chiral Perturbation Theory (PQ$\chi$PT). Explicit analytical expressions up to ${\cal O}(p^6)$ in the momentum expansion are given. The calculations have been performed within the supersymmetric formulation of PQ$\chi$PT. We also present some numerical results to indicate the size of the corrections.