Semileptonic decay of $B_c$ meson into $c\bar{c}$ states in a quark model

Abstract

The exclusive semileptonic decay form factors and widths of $B_c$ meson in the $c\bar{c}({\eta }_c,J/\psi )$ states based on heavy quark effective theory are computed. The spectroscopic parameters of $B_c$ and the $c\bar{c}$ states deduced using the phenomenological coulomb plus power form of the $q-\bar{q}$ potential $(CP{P}_{\nu })$ with power index $\nu$ have been employed to compute the Isgur wise function as well as the decay form factors. The universal behaviour of the Isgur-wise function at the maximum momentum transfer has been observed for different choices of $\nu$ between 0.5 to 2.0. However, such an universality is not observed for the choice of $\nu <0.5$. Our predictions for the branching ratio $B_c\to {\eta }_c{\ell }^{+}{\nu }_{\ell }$ lie 0.50 - 0.56 while that for $B_c\to J/\psi {\ell }^{+}{\nu }_{\ell }$ lie 1.8 - 2.0 for the choice of the potential index in the range $0.5\le \nu \le 2.0$.

Comments: Due to misconception in eqn. 5 and 6