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

TL;DR

This paper calculates semileptonic decay form factors and widths of the $B_c$ meson into $car c$ states using a quark model and heavy quark effective theory, revealing universal behavior of the Isgur-Wise function for certain potential parameters.

Contribution

It introduces a phenomenological Coulomb plus power potential model to compute decay form factors and explores the universality of the Isgur-Wise function across different potential indices.

Findings

Predicted branching ratios for $B_c$ decays into $ au$ and $J/ au$ mesons.

Universal behavior of the Isgur-Wise function observed for potential index $ u$ between 0.5 and 2.0.

Branching ratios estimated within specific potential parameter ranges.

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 $(CPP_\nu)$ 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 $B_c\rightarrow\eta_c\ell^+\nu_\ell$ lie 0.50 $%$ - 0.56 $%$ while that for $B_c\rightarrow J/\psi\ell^+\nu_\ell$ lie 1.8 $%$ - 2.0 $%$ for the choice of the potential index in the range $0.5\leq\nu\leq2.0$.