Mass Spectra of Heavy Quarkonia and B_{c} Decay Constant for Static Scalar-Vector Interactions with Relativistic Kinematics

Abstract

We reproduce masses of the self-conjugate and non-self-conjugate mesons in the context of the spinless Salpeter equation taking into account the relativistic kinematics and the quark spins. The hyperfine splittings for the $2S$ charmonium and $1S$ bottomonium are also calculated. Further, 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 $V(r)=-A{r}^{-\beta }+\kappa r^{\beta }+V_0,$ with $\beta =1,1/2,3/4$ decomposed into scalar and vector parts in the form $V_V(r)=-A{r}^{-\beta }+(1-ϵ)\kappa r^{\beta }$ and $V_S(r)=ϵ\kappa r^{\beta }+V_0;$ where $0\le ϵ\le 1.$ We have used the shifted large-N-expansion technique (SLNET) to solve the reduced equation for the scalar $(ϵ=1),$ equal mixture of scalar-vector $(ϵ=1/2),$ and vector $(ϵ=0)$ confinement interaction kernels. The energy eigenvalues are carried out up to the third order approximation.

Comments: 35 pages