Correspondence between QCD sum rules and constituent quark models

Abstract

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 hadron observables with an important difference that 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 a similarity of the smearing function in sum rules 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 $μ_χ\simeq 1$ GeV, $<\bar u u > = - (230 \pm 15 {\rm MeV})^3$ and $<\bar s s > = - (220 \pm 15 {\rm MeV})^3$ correspond to constituent quark masses $m_u\simeq 220$ MeV and $m_s \simeq 350$ MeV, respectively. We also obtain the running of the quark model parameters above the chiral scale $μ_χ$. The observed correspondence between constituent quark models and QCD sum rules allows 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.