Solutions of a Dirac hydrogenlike mesons and scalar confinement in low orbital angular momentum states

Abstract

Wavefunctions of a relativistic heavy quark-light quark $(Q,q)$ system described by a Dirac hamiltonian are analyzed. By assuming that the confinement potential is a Lorentz scalar (S), the slope of the Isgur-Wise function is calculated at zero recoil point. The result obtained is ${\xi }^{\prime }(1)=-0.93\pm \mathrm{0.05.}$ This means that the solutions are perfectly consistent. If relativistic corrections in the light quark wave functions are included the result is ${\xi }^{\prime }(1)=-1.01\pm \mathrm{0.04.}$ From heavy-light data this suggest that if relativistic effects are considered, scalar confinement is reliable in low orbital angular momentum states.

Comments: 11 pages, Latex, 2 figures, Corrected Version