Correspondence between QCD sum rules and constituent quark models

Abstract

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 µχ ≃ 1 GeV, ūu = −(230 ± 15 MeV) 3 and ss = −(220 ± 15 MeV) 3 correspond to constituent quark masses mu ≃ 220 MeV and ms ≃ 350 MeV, respectively. We also obtain the running of the quark model parameters above the chiral scale µχ. 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.

StrongD*→DπandB*→Bπcouplings

“…[10], loop corrections in D-meson effective field theory have been used to constrain extrapolation of the D * Dπ coupling to physical momenta [11]. The simultaneous computation of both couplings has been completed in a dispersive quark model [12]. However, this approach makes no qualitative distinction between light-and heavy-quarks.…”

Heavy-to-light form factors: Sum rules on the light cone and beyond

“…We therefore make use of the constituent quark mass evaluated at this scale. Employing the results from [18], we find the relevant value of the constituent mass of the light quark m = 150 MeV for beauty-meson decay, and m = 200 MeV for charm-meson decay. These values of the quark masses will be used in numerical estimates below.…”

Systematic uncertainties of hadron parameters obtained with QCD sum rules

“…Expanding this expression in inverse powers of µ, we get the OPE series for Π(µ): 10) and higher coefficients may be obtained from (2.9). Each term of this expansion may be also calculated from (2.2) and (2.5), with Π 0 corresponding to G 0 :…”