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Spectroscopy of $B_{c}$ meson in a semi-relativistic quark model using the shifted large-N expansion method

We calculate the $c\bar{b}$ mass spectrum, the splitting values and some other properties in the framework of the semi-relativistic equation by applying the shifted large-N expansion technique. We use seven different central potentials together with an improved QCD-motivated interquark potentials calculated to two loops in the modified minimal-subtraction $% (\bar{MS}) $ scheme. The parameters of these potentials are fitted to generate the semi-relativistic bound states of $ c\bar{b}$ quarkonium system in close conformity with the experimental and the present available calculated center-of-gravity (c.o.g.) data. Calculations of the energy bound states are carried out up to third order. Our results are in excellent fit with the results of the other works.