Spectral Functions for Heavy-Light Currents and Form Factor Relations in HQET

Abstract

We derive relations among form factors describing the current-induced transitions: (vacuum) → B,B, Bπ,Bπ,Bρ and Bρ using heavy quark symmetry. The results are compared to corresponding form factor relations following from identities between scalar and axial vector, and pseudoscalar and vector spectral functions in the heavy quark limit. Supported in part by the Foundation for Research Development, South Africa. Supported in part by Bundesministerium für Forschung und Technologie BMFT, FRG under contract 06MZ730 and by the Humboldt Foundation. With the introduction of the heavy quark effective theory [1], (HQET ) we have witnessed dramatic developments in our understanding of the physics of hadrons containing a heavy quark Q. The systematic expansion in inverse powers of the heavy quark mass mQ accomplished in the HQET allows QCD calculations of hadronic processes to a level of rigor previously only conceivable in deep inelastic reactions. In the heavy quark limit (HQL) the effective Lagrangian exhibits a new spin-flavor symmetry [1]. This heavy quark symmetry (HQS) imposes restrictive constraints on weak decay amplitudes. Notable results are the scaling relation between decay constants [2] and the reduction of semileptonic form factors of heavy mesons and baryons to a small number of Isgur–Wise functions [1]. In this paper we will present an alternative approach to obtain relations between form factors in the heavy quark limit (HQL). Our approach is based on the observation that in this limit certain correlators of two currents comprised of a heavy and a light quark become identical (while they bear no relation to each other in the full QCD). For example, the vector-vector (VV) correlator equals the pseudoscalar-pseudoscalar (PP) one and the axial vector-axial vector (AA) correlator equals the scalar-scalar (SS) one. If we adopt the point of view that the physical spectral function is obtained from the QCD correlator by some form of analytic continuation, then identical QCD correlators imply identical physical spectral functions. We will try in this paper to exploit this form of duality as far as possible. We consider two-point functions defined (in full QCD) through Πμν(q) = i ∫

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Cite this paper

@inproceedings{Dominguez1992SpectralFF, title={Spectral Functions for Heavy-Light Currents and Form Factor Relations in HQET}, author={Cesareo A. Dominguez}, year={1992} }