Eur. Phys. J. C (2004) 34: 201-227
https://doi.org/10.1140/epjc/s2004-01601-4

theoretical physics

Resumming QCD vacuum fluctuations in three-flavor Chiral Perturbation Theory

¹ Laboratoire de Physique Théorique, 91405, Orsay Cedex, France
² Department of Physics, Purdue University, IN 47907, West Lafayette, USA
³ European Center for Theoretical Studies in Nuclear Physics and Related Areas, Strada delle Tarabelle 286, 38050, Trento, Italy
⁴ Groupe de Physique Théorique, Institut de Physique Nucléaire, 91406, Orsay-Cedex, France

^* e-mail: descotes@th.u-psud.fr

Abstract

Due to its light mass, of order , the strange quark can play a special role in chiral symmetry breaking (SB): differences in the pattern of SB in the limits N _f = 2 (, m _s physical) and N _f = 3 () may arise due to vacuum fluctuations of pairs, related to the violation of the Zweig rule in the scalar sector and encoded in particular in the O(p ⁴) low-energy constants L ₄ and L ₆. In case of large fluctuations, we show that the customary treatment of SU(3) x SU(3) chiral expansions generates instabilities upsetting their convergence. We develop a systematic program to cure these instabilities by resumming non-perturbatively vacuum fluctuations of pairs, in order to extract information about SB from experimental observations even in the presence of large fluctuations. We advocate a Bayesian framework for treating the uncertainties due to the higher orders. As an application, we present a three-flavor analysis of the low-energy scattering and show that the recent experimental data imply a lower bound on the quark mass ratio at 95% confidence level. We outline how additional information may be incorporated to further constrain the pattern of SB in the N _f = 3 chiral limit.