Calculation of the continuum contribution to hadronic current correlation functions in a chiral quark model with confinement - art. no. 114007

A powerful technique for the calculation of hadronic properties is the appl ication of QCD sum rules in a study of correlation functions. The calculati on of hadronic current correlation functions may be carried out using the o perator-product expansion. The correlator may also be represented by hadron ic states, which include one or more discrete levels and a continuum contri bution. Comparison of the two methods of calculation of the same correlator allows for the determination of hadronic parameters after one estimates th e continuum contribution and specifies the values of the vacuum condensates . In this work we consider two types of contribution to the continuum. The first involves the radially excited states of a meson. These states appear as resonances which ultimately decay into the continuum of multimeson state s. In a second process, the multimeson continuum is reached in a direct pro cess, without the excitation of a resonance. For the resonances, we calcula te the contribution to the hadronic correlator by calculating the meson dec ay constants in the region 0<P-2 <6 GeV2, making use of our generalized Nam bu-Jona-Lasinio model, which includes a covariant model of confinement. [Ou r model provides a good fit to the decay constants of the a(0)(1450) and K- 0* (1430) mesons. Our value for the a(0)(980) is about 60% larger than the value obtained by Maltman using QCD sum rules. Also, our values for the pio n and kaon decay constants are about 35 and 10% too large, respectively. We have not performed any parameter variations to improve upon these values.] The second contribution to the correlator arises from the direct excitatio n of multimeson continuum states. For the a(0)(980) and its radial excitati ons, we calculate both the resonant and direct contributions. In the case o f the isovector pseudoscalar states we calculate the resonance contribution and parametrize the direct multimeson contribution so as to reproduce a ph enomenological expression of the quark-hadron duality model. In this case t he calculated resonance contribution is about 15% of the phenomenological r esult after a Borel transformation is made. The resonance contribution plus a quark-hadron duality model contribution with s(0) = 1.65GeV(2) yields a good fit to the phenomenological form. In this phenomenological form only t he quark-hadron duality model is used with s(0) = 1.53 GeV2. We also provid e values of the resonance contribution to the continuum strength in the cas e of the strange pseudoscalar states. In the case of the isovector scalar m esons we find significant disagreement between our microscopic calculations and the result of the quark-duality model for the continuum of the hadroni c current correlator. Indeed, the contribution of the resonances to the con tinuum is a least an order of magnitude larger than the values obtained fro m the quark-hadron duality model. That result may suggest an explanation fo r the problems encountered by some authors who have studied the isovector s calar mesons using QCD sum rules.