Publication: Isospin-breaking quark condensates in chiral perturbation theory
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2012-01
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Torres Andrés, R.
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IOP Publishing Ltd
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Abstract
We analyze the isospin-breaking corrections to quark condensates within one-loop SU(2) and SU(3) chiral perturbation theory including m(u) not equal m(d) as well as electromagnetic (EM) contributions. The explicit expressions are given and several phenomenological aspects are studied. We analyze the sensitivity of recent condensate determinations to the EM low-energy constants (LEC). If the explicit chiral symmetry breaking induced by EM terms generates a ferromagnetic-like response of the vacuum, as in the case of quark masses, the increasing of the order parameter implies constraints for the EM LEC, which we check with different estimates in the literature. In addition, we extend the sum rule relating quark condensate ratios in SU(3) to include EM corrections, which are of the same order as the m(u) not equal m(d) ones, and we use that sum rule to estimate the vacuum asymmetry within ChPT. We also discuss the matching conditions between the SU(2) and SU(3) LEC involved in the condensates, when both isospin-breaking sources are taken into account.
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© IOP Publishing Ltd.
We are grateful to J.R.Peláez and E.Ruiz Arriola for useful comments. R.T.A would like to thank Buenaventura Andrés López for invaluable advice. Work partially supported by the Spanish research contracts FPA2008-00592, FIS2008-01323, UCM-Santander 910309 GR58/08, GR35/10-A and the FPI programme (BES-2009-013672).
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