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Photo of Johan Bijnens

Johan Bijnens

Professor

Photo of Johan Bijnens

Analytic representations of mK, FK, mη, and Fη in two loop SU (3) chiral perturbation theory

Author

  • B. Ananthanarayan
  • Johan Bijnens
  • Samuel Friot
  • Shayan Ghosh

Summary, in English

In this work, we consider expressions for the masses and decay constants of the pseudoscalar mesons in SU(3) chiral perturbation theory. These involve sunset diagrams and their derivatives evaluated at p2=mP2 (P=π, K, η). Recalling that there are three mass scales in this theory, mπ, mK and mη, there are instances when the finite part of the sunset diagrams do not admit an expression in terms of elementary functions, and have therefore been evaluated numerically in the past. In a recent publication, an expansion in the external momentum was performed to obtain approximate analytic expressions for mπ and Fπ, the pion mass and decay constant. We provide fully analytic exact expressions for mK and mη, the kaon and eta masses, and FK and Fη, the kaon and eta decay constants. These expressions, calculated using Mellin-Barnes methods, are in the form of double series in terms of two mass ratios. A numerical analysis of the results to evaluate the relative size of contributions coming from loops, chiral logarithms as well as phenomenological low-energy constants is presented. We also present a set of approximate analytic expressions for mK, FK, mη and Fη that facilitate comparisons with lattice results. Finally, we show how exact analytic expressions for mπ and Fπ may be obtained, the latter having been used in conjunction with the results for FK to produce a recently published analytic representation of FK/Fπ.

Department/s

  • Theoretical Particle Physics
  • Department of Astronomy and Theoretical Physics

Publishing year

2018-06-06

Language

English

Publication/Series

Physical Review D

Volume

97

Issue

11

Document type

Journal article

Publisher

American Physical Society

Topic

  • Subatomic Physics

Status

Published

ISBN/ISSN/Other

  • ISSN: 2470-0010