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 $V_V(r)=-A{r}^{-\beta }+(1-\epsilon )\kappa r^{\beta }$ and $V_S(r)=\epsilon \kappa r^{\beta }+V_0;$ where $0\le \epsilon \le 1.$ We have used the shifted large-N-expansion technique (SLNET) to solve the reduced equation for the scalar $(\epsilon =1),$ equal mixture of scalar-vector $(\epsilon =1/2),$ and vector $(\epsilon =0)$ confinement interaction kernels. The energy eigenvalues are carried out up to the third order approximation.

35 pages

References in corpus (3)

• The ${\eta }_c(3654)$ and hyperfine splitting in charmonium
• Fine and Hyperfine Splittings of Charmonium and Bottomonium: An Improved Perturbative QCD Approach
• Improved Perturbative QCD Approach to the Bottomonium Spectrum

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