https://doi.org/10.1140/epjc/s10052-017-5019-y
Regular Article - Theoretical Physics
An analytic analysis of the pion decay constant in three-flavoured chiral perturbation theory
1
Centre for High Energy Physics, Indian Institute of Science, Bangalore, Karnataka, 560012, India
2
Department of Astronomy and Theoretical Physics, Lund University, Sölvegatan 14A, 223-62, Lund, Sweden
* e-mail: shayanghosh@gmail.com
Received:
2
March
2017
Accepted:
23
June
2017
Published online:
26
July
2017
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 
and 
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.
© The Author(s), 2017
