2015/10/31 by A. Le Yaouanc, L. Oliver, J.‐C. Raynal +1 · 4 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Covariant transformation #Hadron #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Meson #Particle physics #Particle physics theoretical and experimental studies #Physics #QCD sum rules #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quark #Quark model #Quarkonium #Sum rule in quantum mechanics #hep-ph
paper · pdf · doi:10.1103/physrevd.93.114020
published in Physical review. D/Physical review. D. 93(11) (American Physical Society)
arxiv created 2016/04/17 · openalex publication_date 2016/06/20 · openalex created_date 2016/06/24 · arxiv updated 2016/06/29 · openalex updated_date 2026/08/05
The Bakamjian-Thomas relativistic quark model, describing hadrons with a fixed number of constituents, yields in the heavy quark limit of QCD covariant Isgur-Wise functions and satisfies the whole tower of lowest moment sum rules (Bjorken-Uraltsev type sum rules). We first recall, as well as earlier results, the new formalism presented in our recent papers on Lorentz representations, which provides an elegant framework for the analysis of this model in the heavy quark limit and stress the results which have been already obtained in this direction. Then, we give some very explicit demonstrations of the fact that the Bakamjian-Thomas framework satisfies the sum rules by considering simple cases of Isgur-Wise functions. In addition to the specific Bjorken and Uraltsev sum rules, an important sum rule that involves only heavy mesons with light cloud jP=(1)/(2)^\ensuremath- and their radial excitations is demonstrated. This latter sum rule is phenomenologically interesting because it constrains the derivatives of the radially excited Isgur-Wise functions at zero recoil. On the other hand, we recall the limitations of the Bakamjian-Thomas scheme. At finite mass, current matrix elements with the current coupled to the heavy quark are no longer covariant, and higher moment sum rules that hold in the heavy quark limit of QCD are not satisfied.