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

Ananthanarayan, B.; Bijnens, Johan LU ; Friot, Samuel and Ghosh, Shayan (2018) In Physical Review D 97(11).
Abstract

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... (More)

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.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review D
volume
97
issue
11
publisher
American Physical Society
external identifiers
  • scopus:85049805254
ISSN
2470-0010
DOI
10.1103/PhysRevD.97.114004
language
English
LU publication?
yes
id
02879b7b-23cd-42e2-8655-65c47f1c577f
date added to LUP
2018-09-10 14:32:42
date last changed
2019-06-25 08:09:00
@article{02879b7b-23cd-42e2-8655-65c47f1c577f,
  abstract     = {<p>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.</p>},
  articleno    = {114004},
  author       = {Ananthanarayan, B. and Bijnens, Johan and Friot, Samuel and Ghosh, Shayan},
  issn         = {2470-0010},
  language     = {eng},
  month        = {06},
  number       = {11},
  publisher    = {American Physical Society},
  series       = {Physical Review D},
  title        = {Analytic representations of mK, FK, mη, and Fη in two loop SU (3) chiral perturbation theory},
  url          = {http://dx.doi.org/10.1103/PhysRevD.97.114004},
  volume       = {97},
  year         = {2018},
}