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Analytic representations of m(K), F-K, m(eta), and F-eta in two loop SU(3) chiral perturbation theory

Ananthanarayan, B and Bijnens, Johan and Friot, Samuel and Ghosh, Shayan (2018) Analytic representations of m(K), F-K, m(eta), and F-eta in two loop SU(3) chiral perturbation theory. In: PHYSICAL REVIEW D, 97 (11).

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Official URL: https://dx.doi.org/ 10.1103/PhysRevD.97.114004


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 p(2) = m(P)(2) (P = pi, K, eta). Recalling that there are three mass scales in this theory, m(pi), m(K) and m(eta), 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 m(pi) and F-pi, the pion mass and decay constant. We provide fully analytic exact expressions for m(K) and m(eta), the kaon and eta masses, and F-K and F-eta, 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 lowenergy constants is presented. We also present a set of approximate analytic expressions for m(K), F-K, m(eta) and F-eta that facilitate comparisons with lattice results. Finally, we show how exact analytic expressions for m(pi) and F-pi may be obtained, the latter having been used in conjunction with the results for F-K to produce a recently published analytic representation of F-K= F-pi.

Item Type: Journal Article
Additional Information: Copy right of this article belong to AMER PHYSICAL SOC, ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Depositing User: Id for Latest eprints
Date Deposited: 25 Jun 2018 15:52
Last Modified: 25 Jun 2018 15:52
URI: http://eprints.iisc.ac.in/id/eprint/60082

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