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

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 ${\rm 2S}$ charmonium and ${\rm 1S}$ 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 $V(r)=-Ar^{-β}+κr^β+V_{0},$ with $β=1,1/2,~3/4$ decomposed into scalar and vector parts in the form $V_{V}(r)=-Ar^{-β}+(1-ε)κr^β$ and $V_{S}(r)=εκr^{β}+V_{0};$ where $0\leq ε\leq 1.$ 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.