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An analytic analysis of the pion decay constant in three-flavoured chiral perturbation theory

Ananthanarayan, B.; Bijnens, Johan LU and Ghosh, Shayan (2017) In European Physical Journal C 77(7).
Abstract

A representation of the two-loop contribution to the pion decay constant in SU(3) chiral perturbation theory is presented. The result is analytic up to the contribution of the three (different) mass sunset integrals, for which an expansion in their external momentum has been taken. We also give an analytic expression for the two-loop contribution to the pion mass based on a renormalized representation and in terms of the physical eta mass. We find an expansion of Fπ and Mπ2 in the strange-quark mass in the isospin limit, and we perform the matching of the chiral SU(2) and SU(3) low-energy constants. A numerical analysis demonstrates the high accuracy of our representation, and the strong dependence of the pion decay constant... (More)

A representation of the two-loop contribution to the pion decay constant in SU(3) chiral perturbation theory is presented. The result is analytic up to the contribution of the three (different) mass sunset integrals, for which an expansion in their external momentum has been taken. We also give an analytic expression for the two-loop contribution to the pion mass based on a renormalized representation and in terms of the physical eta mass. We find an expansion of Fπ and Mπ2 in the strange-quark mass in the isospin limit, and we perform the matching of the chiral SU(2) and SU(3) low-energy constants. A numerical analysis demonstrates the high accuracy of our representation, and the strong dependence of the pion decay constant upon the values of the low-energy constants, especially in the chiral limit. Finally, we present a simplified representation that is particularly suitable for fitting with available lattice data.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
European Physical Journal C
volume
77
issue
7
publisher
Springer
external identifiers
  • scopus:85026675596
  • wos:000406425400001
ISSN
1434-6044
DOI
10.1140/epjc/s10052-017-5019-y
language
English
LU publication?
yes
id
5d190fb0-9ecf-4c22-ac7d-dd06b5490482
date added to LUP
2017-08-31 15:18:07
date last changed
2018-03-27 13:32:20
@article{5d190fb0-9ecf-4c22-ac7d-dd06b5490482,
  abstract     = {<p>A representation of the two-loop contribution to the pion decay constant in SU(3) chiral perturbation theory is presented. The result is analytic up to the contribution of the three (different) mass sunset integrals, for which an expansion in their external momentum has been taken. We also give an analytic expression for the two-loop contribution to the pion mass based on a renormalized representation and in terms of the physical eta mass. We find an expansion of F<sub>π</sub> and Mπ2 in the strange-quark mass in the isospin limit, and we perform the matching of the chiral SU(2) and SU(3) low-energy constants. A numerical analysis demonstrates the high accuracy of our representation, and the strong dependence of the pion decay constant upon the values of the low-energy constants, especially in the chiral limit. Finally, we present a simplified representation that is particularly suitable for fitting with available lattice data.</p>},
  articleno    = {497},
  author       = {Ananthanarayan, B. and Bijnens, Johan and Ghosh, Shayan},
  issn         = {1434-6044},
  language     = {eng},
  month        = {07},
  number       = {7},
  publisher    = {Springer},
  series       = {European Physical Journal C},
  title        = {An analytic analysis of the pion decay constant in three-flavoured chiral perturbation theory},
  url          = {http://dx.doi.org/10.1140/epjc/s10052-017-5019-y},
  volume       = {77},
  year         = {2017},
}