Correspondence between QCD sum rules and constituent quark models
Institut für Theoretische Physik, Philosophenweg 16, 69120, Heidelberg, Germany
2 Nuclear Physics Institute, Moscow State University, 119991, Moscow, Russia
3 Sezione di Roma III, INFN, Via della Vasca Navale 84, 00146, Roma, Italy
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We compare two widely used approaches to the description of hadron properties: QCD sum rules and constituent quark models. Making use of the dispersion formulation of the quark model, we show that both approaches lead to similar spectral representations for the hadron observables with the important difference that the quark model is based on Feynman diagrams with massive quarks, whereas QCD sum rules are based on the same Feynman diagrams for current quarks with the additional condensate contributions for light quarks and gluons. We give arguments for the similarity of the smearing function in the sum rule case and the hadron wave function of the quark model. Analyzing the sum rule for the leptonic decay constant of the heavy pseudoscalar meson containing a light u or s quark, we find that the quark condensates at the chiral symmetry-breaking scale GeV, and correspond to constituent quark masses of MeV and MeV, respectively. We also obtain the running of the quark-model parameters above the chiral scale . The observed correspondence between constituent quark models and QCD sum rules allows for a deeper understanding of both methods and their parameters. It also provides a QCD basis for constituent quark models, extending their applicability above the scale of chiral symmetry breaking.
© Springer-Verlag, 2004