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 ${\mu }_{\chi }\simeq 1$ GeV, $<\bar{u}u>=-(230\pm 15\mathrm{MeV}{)}^3$ and $<\bar{s}s>=-(220\pm 15\mathrm{MeV}{)}^3$ 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 ${\mu }_{\chi }$. 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.

8 pages, discussion of scale dependence of quark-model parameters above the chiral symmetry breaking scale is added

References in corpus (5)

• Flavour-symmetry breaking of the quark condensate and chiral corrections to the Gell-Mann-Oakes-Renner relation
• f_B and f_B_s from QCD sum rules
• Possible evidence of extended objects inside the proton
• Relativistic instant-form approach to the structure of two-body composite systems (short version)
• Relativistic instant-form approach to the structure of two-body composite systems

Cited by in corpus (11)

• Systematic uncertainties of hadron parameters obtained with QCD sum rules
• Diquark and light four-quark states
• Can one control systematic errors of QCD sum rule predictions for bound states?
• Pion form factor at spacelike momentum transfers from local-duality QCD sum rule
• Bound-state parameters from dispersive sum rules for vacuum-to-vacuum correlators
• Quark-hadron duality and hadron properties from correlators of pseudoscalar and axial currents
• Constituent quarks, chiral symmetry, and chiral point of the constituent quark model
• Heavy-to-light form factors: sum rules on the light cone and beyond
• Strong three-meson couplings of $J/\psi$ and ${\eta }_c$
• Fall-apart decays of polyquark hadrons
• Exploration of hyperfine interaction between constituent quarks via eta productions