TY - JOUR

T1 - An analytic analysis of the pion decay constant in three-flavoured chiral perturbation theory

AU - Ananthanarayan, B.

AU - Bijnens, Johan

AU - Ghosh, Shayan

PY - 2017/7/1

Y1 - 2017/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85026675596&partnerID=8YFLogxK

U2 - 10.1140/epjc/s10052-017-5019-y

DO - 10.1140/epjc/s10052-017-5019-y

M3 - Article

C2 - 28943799

AN - SCOPUS:85026675596

VL - 77

JO - European Physical Journal C. Particles and Fields

JF - European Physical Journal C. Particles and Fields

SN - 1434-6044

IS - 7

M1 - 497

ER -