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arxiv: hep-ph/9909292 · v2 · submitted 1999-09-08 · ✦ hep-ph

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N_f Dependence of the Quark Condensate from a Chiral Sum Rule

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classification ✦ hep-ph
keywords chiralcondensatedependencefunctionquarkruleallowsbound
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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

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