\(N_f\) dependence of the quark condensate from a chiral sum rule

  • B. Moussallam
Theoretical physics


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.


Perturbation Theory Phase Transition Strong Dependence Spectral Function Chiral Perturbation Theory 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • B. Moussallam
    • 1
  1. 1.I.P.N., Groupe de Physique Théorique, Université Paris-Sud, 91406 Orsay Cédex, France FR

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