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
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.
© Springer-Verlag, 2004
