Relations among zero momentum correlators for heavy-light systems in QCD.

Relations connecting various zero momentum correlators of interpolating fields for pseudoscalar and scalar channel, containing one heavy and one light quark field, are derived from the Euclidean space formulation of the QCD functional integral. These relations may serve as constraints on the phenomenological models or approaches motivated from QCD, and suggest a method to extract the chiral quark condensates. It is also found that the correlator for pseudoscalar channel differs from that for scalar channel even in the large heavy quark mass limit. PACS numbers: 11.15.Tk, 12.38.Aw Typeset using REVTEX 1 Heavy-light systems made of one heavy and one light quark have been attracting attentions, motivated by the observation of heavy quark symmetry in the infinite heavy quark mass limit [1]. The basis of this symmetry is a separation between the scale of the heavy quark mass and all other dynamical scales in the problem. The properties of heavy-light systems have been investigated using various phenomenological approaches such as QCD sum-rule method [2–5] and numerical simulations on a lattice [6–10], based on the analytic properties of two-point correlators of interpolating fields, carrying the quantum numbers of the system under study, and on asymptotic freedom. In these approaches, hadronic spectral properties (e.g., masses, coupling constants, etc.) are related via dispersion relations to the correlators evaluated in terms of quark and gluon degrees of freedom. In practical applications, one needs to parametrize the spectral functions and to evaluate the correlators approximately. The success of such approaches depends on correct understanding of the qualitative features of the spectral functions and accurate evaluation of the correlators from QCD. In this paper, we show, within the Euclidean formulation of the QCD functional integral, that the two-point zero momentum correlators of interpolating fields for both pseudoscalar and scalar channel containing one heavy and one light flavor can be expressed as combinations of quark condensates. We then derive relations which connect various correlators. These relations can be regarded as constraints on phenomenological descriptions of the correlators. We find that the correlators for pseudoscalar and scalar channel are different even in the large heavy quark mass limit, suggesting differences between positiveand negativeparity states. To evaluate various two-point correlators from QCD, it is necessary to know the properties of the QCD vacuum. This is, however, difficult due to the nonperturbative features of QCD at large distances, which lead to complicated properties of the QCD vacuum such as the formation of the gluon condensate 〈0|(αs/π)G |0〉 and the quark condensate 〈0|qq|0〉. The latter is of particular importance as it signals spontaneous breaking of the chiral symmetry