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

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.

17 pages

References in corpus (3)

• The Massive O(N) Non-linear Sigma Model at High Orders
• Vector Formfactors in Hard Pion Chiral Perturbation Theory
• On the factorization of chiral logarithms in the pion form factors

Cited by in corpus (4)

• Higher-order tree-level amplitudes in the nonlinear sigma model
• Spectroscopic parameters and electromagnetic form factor of kaon in vacuum and a dense medium
• Chiral Perturbation Theory Reflections on Effective Theories of the Standard Model
• Hadronic vacuum polarization to three loops in chiral perturbation theory