The Pion Mass and Decay Constant at Three Loops in Two-Flavour Chiral Perturbation Theory

TL;DR

This paper presents a three-loop calculation of the pion mass and decay constant in two-flavour chiral perturbation theory, providing higher-order precision and consistency checks with known coefficients.

Contribution

It provides the first three-loop (NNNLO) calculation of pion mass and decay constant in two-flavour chiral perturbation theory with multiple parameterization cross-checks.

Findings

Good agreement with lower order results at physical quark masses

Validation of results through different parameterizations and known coefficients

Enhanced understanding of quark mass dependence at higher orders

Abstract

A calculation of the pion mass and decay constant at NNNLO in two-flavour chiral perturbation theory is presented. The results are cross-checked by using both the exponential and square root parameterizations of the Goldstone matrix field, as well as by comparing to the known leading log coefficients of the two quantities. A small numerical study of the quark mass dependence is performed, and for a physical quark mass there is good agreement with lower order results.