2011/04/04 by V. Yu. Lazur, O. K. Reity, Василь Васильович Рубіш +1
Physics and Astronomy · #Coupling constant #Dirac equation #Lambda #Lorentz transformation #Mathematical physics #Meson #Particle physics #Particle physics theoretical and experimental studies #Physics #Physics of Superconductivity and Magnetism #Pseudovector #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Quark #Quark model #Quarkonium #Scalar (mathematics) #hep-ph
paper · pdf · doi:10.1103/physrevd.83.076003
published as Phys.Rev.D83:076003,2011 · 22 pages, 6 figures
openalex publication_date 2011/04/04 · arxiv created 2011/04/06 · arxiv updated 2015/03/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We construct a relativistic potential quark model of D, Ds, B, and Bs mesons in which the light quark motion is described by the Dirac equation with a scalar-vector interaction and the heavy quark is considered a local source of the gluon field. The effective interquark interaction is described by a combination of the perturbative one-gluon exchange potential VCoul(r)=\ensuremath-\ensuremathξ/r and the long-range Lorentz-scalar and Lorentz-vector linear potentials Sl.r.(r)=(1\ensuremath-\ensuremathλ)(\ensuremathσr+V0) and Vl.r.(r)=\ensuremathλ(\ensuremathσr+V0), where 0\ensuremath≤\ensuremathλ<1/2. Within the quasiclassical approximation, we obtain simple asymptotic formulas for the energy and mass spectra and for the mean radii of D, Ds, B, and Bs mesons, which ensure a high accuracy of calculations even for states with the radial quantum number nr\ensuremath∼1. We show that the fine structure of P-wave states in heavy-light mesons is primarily sensitive to the choice of two parameters: the strong-coupling constant \ensuremathαs and the coefficient \ensuremathλ of mixing of the long-range scalar and vector potentials Sl.r.(r) and Vl.r.(r). The quasiclassical formulas for asymptotic coefficients of wave functions at zero and infinity are obtained.