Resumming QCD vacuum fluctuations in three-flavor Chiral Perturbation Theory

Due to its light mass, of order ΛQCD, the strange quark can play a special role in chiral symmetry breaking (χSB): differences in the pattern of χSB in the limits Nf=2 (mu,md→0, ms physical) and Nf=3 (mu,md,ms→0) may arise due to vacuum fluctuations of s anti s pairs, related to the violation of the Zweig rule in the scalar sector and encoded in particular in the O(p4) low-energy constants L4 and L6. 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 s anti s pairs, in order to extract information about χSB 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 ππ scattering and show that the recent experimental data imply a lower bound on the quark mass ratio 2ms/(mu + md)≥14 at 95% confidence level. We outline how additional information may be incorporated to further constrain the pattern of χSB in the Nf=3 chiral limit. (orig.)