Resumming QCD vacuum fluctuations in three-flavour Chiral Perturbation Theory
Abstract
Due to its light mass of order LambdaQCD, the strange quark can play a special role in Chiral Symmetry Breaking (ChSB): differences in the pattern of ChSB 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-bar 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)xSU(3) chiral expansions generate instabilities upsetting their convergence. We develop a systematic program to cure these instabilities by resumming nonperturbatively vacuum fluctuations of s-bar s pairs, in order to extract information about ChSB 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-flavour analysis of the low-energy pi-pi 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 ChSB in the Nf=3 chiral limit.
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