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.

arXiv comment17 pages

References in corpus (15)

• New features of FORM
• ππscattering
• The analytical value of the electron (g-2) at order alpha^3 in QED
• Reduze - Feynman Integral Reduction in C++
• The Mesonic Chiral Lagrangian of Order $p^6$
• Elastic $\pi \pi$ scattering to two loops
• Analytic treatment of the two loop equal mass sunrise graph
• Renormalization of chiral perturbation theory to order p^6
• The three loop on-shell renormalization of QCD and QED
• Two-point Functions at Two Loops in Three Flavour Chiral Perturbation Theory
• Charged Pion-Pair Production and Pion Polarizabilities to two Loops
• Leading Logarithms in the Massive O(N) Nonlinear Sigma Model
• 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

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• Chiral Perturbation Theory Reflections on Effective Theories of the Standard Model
• Hadronic vacuum polarization to three loops in chiral perturbation theory