Analytic representation of $F_K/F_{\pi }$ in two loop chiral perturbation theory

Abstract

We present an analytic representation of $F_K/F_{\pi }$ as calculated in three-flavour two-loop chiral perturbation theory, which involves expressing three mass scale sunsets in terms of Kampé de Fériet series. We demonstrate how approximations may be made to obtain relatively compact analytic representations. An illustrative set of fits using lattice data is also presented, which shows good agreement with existing fits.

Comments: v.2, version accepted for publication in Physical Review D as Rapid Communication; 8 pages, 5 figures; figure 1 replaced, full results for sunsets included, updated lattice fitting section, references added, clarifications introduced