Isospin-Breaking quark condensates in Chiral Perturbation Theory

Abstract

We analyze the isospin-breaking corrections to quark condensates within one-loop SU(2) and SU(3) Chiral Perturbation Theory including $m_u\ne m_d$ 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 $m_u\ne m_d$ 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.

16 pages, 1 figure, final version accepted for publication in Journal of Physics G

References in corpus (6)

• Equation of State for physical quark masses
• The chiral condensate in a constant electromagnetic field
• Isospin breaking in Kl4 decays
• Investigation of a0-f0 mixing
• Electromagnetic low-energy constants in ChPT
• Isospin Breaking and chiral symmetry restoration

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• The ${\pi }^0-\eta -{\eta }^{\prime }$ mixing in a generalized multi-quark interaction scheme
• Scalar susceptibilities and Electromagnetic thermal mass differences in Chiral Perturbation Theory
• Contribution of the Weinberg-type Operator to atomic and nuclear electric dipole moments