Semileptonic decays of the $B_c$ meson

We study the semileptonic transitions $B_c\to {\eta }_c,J/\Psi ,D,D^{*},B,B^{*},B_s,B_s^{*}$ in the leading order in the framework of a relativistic independent quark model based on a confining potential in the equally mixed scalar-vector harmonic form. We compute relevant weak form factors as overlap integrals of the meson-wave functions obtained in the relativistic independent quark model in the whole accessible kinematical range. We predict that the semileptonic transitions of the $B_c$ meson are mostly dominated by two Cabibbo-Kobayashi-Maskawa (CKM)-favored modes, $B_c\to B_s(B_s^{\star })e\nu$, contributing about 77% of the total decay width, and its decays to vector meson final states take place in the predominantly transverse mode. Our predicted values for the total decay rates, branching ratios, polarization ratios, the forward-backward asymmetry factor, etc., are broadly in agreement with other model predictions.

Figure 1

Coordinate system for the semileptonic decay of meson $M$. (a) The $e\nu$ center-of-mass frame. (b) The vector meson helicity frame.

Figure 2

Semileptonic decay: $M\to me{\nu }_e$.

Figure 3

Form factors of $B_c\to {\eta }_c,J/\Psi$.

Figure 4

Form factors of $B_c\to D,D^{*}$.

Figure 5

Form factors of $B_c\to B_s,B_s^{*}$.

Figure 6

Form factors of $B_c\to B,B^{*}$.

Figure 7

Differential decay rate of $B_c\to {\eta }_c(J/\Psi )$ in ${10}^{-12}\mathrm{GeV}$.

Figure 8

Differential decay rate of $B_c\to D(D^{*})$ in ${10}^{-12}\mathrm{GeV}$.

Figure 9

Differential decay rate of $B_c\to B_s(B_s^{*})$ in ${10}^{-12}\mathrm{GeV}$.

Figure 10

Differential decay rate of $B_c\to B(B^{*})$ in ${10}^{-12}\mathrm{GeV}$.