Heavy-quark Binding and Kinetic Energies in Heavy-light Mesons and the Constituent Quark Model

The spin-averaged binding energy and the hyperfine mass splitting of heavy-light mesons are investigated within the constituent quark model as a function of the inverse heavy-quark mass. It is shown that the so-called heavy-quark kinetic energy, −λ1/2mQ, may differ remarkably from the non-relativistic expectation 〈p〉/2mQ, thanks to relativistic effects in the effective interquark potential for heavy-light mesons, which may yield substantial 1/mQ corrections to the heavy-quark static limit. The determination of the difference of the hadronic parameter λ1 in the Bu(d) and Bc mesons can provide information about the strength of relativistic effects in the interquark interaction. PACS numbers: 12.39.Ki; 12.39.Pn; 12.39.Hg To appear in Physics Letters B. The Heavy Quark Effective Theory (HQET ) [1] is widely recognized as a powerful tool to investigate the properties of hadrons containing a heavy quark. This theory is based on an effective Lagrangian, written in terms of effective fields, which in the limit of infinite heavy-quark masses (μQ → ∞) exhibits a spin-flavour symmetry, the so-called Heavy Quark Symmetry (HQS). Such a symmetry is shared by, but not manifest in QCD and it is only softly broken by terms of order ΛQCD/μQ [2], where ΛQCD is the QCD scale parameter. The HQS allows to derive several exact relations among hadronic properties in the heavyquark limit, while at finite values of μQ the HQET allows to represent physical quantities as a systematic expansion in terms of powers of the inverse heavy-quark mass, 1/μQ, i.e. it organizes the structure of the power corrections to the HQS limit. However, neither the HQS nor the HQET can help to predict all the properties of heavy hadrons, because the calculation of the matrix elements of the relevant operators requires the knowledge of the non-perturbative structure of heavy hadrons. In this letter, we will focus on some of the relevant HQET matrix elements, particularly the hadronic parameters Λ̄, λ1 and λ2, defined as