\(N_f\) dependence of the quark condensate from a chiral sum rule
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How fast does the quark condensate in QCD-like theories vary as a function of \(N_f\) is inferred from real QCD using chiral perturbation theory at order one loop. A sum rule is derived for the single relevant chiral coupling constant, \(L_6\). A model independent lower bound is obtained. The spectral function satisfies a Weinberg-type superconvergence relation. It is discussed how this, together with chiral constraints, allows a solid evaluation of \(L_6\), based on experimental \(\pi\pi\)–\(K\bar K\)S-wave T-matrix input. The resulting value of \(L_6\) is compatible with a strong \(N_f\) dependence possibly suggestive of the proximity of a chiral phase transition.
KeywordsPerturbation Theory Phase Transition Strong Dependence Spectral Function Chiral Perturbation Theory
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