An-Najah Staff

We present bound state masses of the self-conjugate and non-self-conjugate mesons in the context of the Schrödinger equation taking into account the relativistic kinematics and the quark spins. We apply the usual interaction by adding the spin dependent correction. The hyperfine splittings for the 2S charmonium and 1S bottomonium are calculated. The pseudoscalar and vector decay constants of the B_c meson and the unperturbed radial wave function at the origin are also calculated. We have obtained a local equation with a complete relativistic corrections to a class of three attractive static interaction potentials of the general form V(r) = -Ar^-β+κr^β+V₀, with β = 1, 1/2, 3/4 which can also be decomposed into scalar and vector parts in the form V_V(r) = -Ar^-β+(1-ɛ)κr^β and V_S(r) = ɛκr^β+V₀ where 0≤ɛ≤1. The energy eigenvalues are carried out up to the third order approximation using the shifted large-N-expansion technique.

In the framework of potential models for heavy quarkonium, we compute the mass spectrum of the bottom-charmed B_c meson system and spin-dependent splittings from the Schrödinger equation using the shifted-large-N expansion technique. The masses of the lightest vector B_c^* and pseudoscalar B_c states as well as the higher states below the threshold are estimated. Our predicted result for the ground state energy is 6253_-6⁺¹⁵ MeV and are generally in exact agreement with earlier calculations. Calculations of the Schrödinger energy eigenvalues are carried out up to the third order of the energy series. The parameters of each potential are adjusted to obtain best agreement with the experimental spin-averaged data (SAD). Our findings are compared with the observed data and with the numerical results obtained by other numerical methods.