The $\Upsilon(nS) \to B_{(c)}$ transition form factors and their applications to semileptonic and nonleptonic weak decays

Abstract

The semileptonic and nonleptonic decays of the $\Upsilon(nS)$ with $n=1,2,3,4$ are investigated within the covariant light-front quark model (CLFQM). Using the form factors of the transitions $\Upsilon(nS) \to B_{(c)}$ obtained from the CLFQM, we calculate the branching ratios of the decays $\Upsilon(nS)\to B_{(c)}\ell\nu_\ell$ and $\Upsilon(nS)\to B_{(c)}M$ with $\ell=e,\mu,\tau$ and $M$ referring to $\pi(\rho),K^{(*)},D^{(*)},D^{(*)}_s$. One can find that the branching ratios of the decays $\Upsilon(3S)\to B_c\ell\nu_\ell$ are the largest among those of considered semileptonic decays and can amount to $10^{-9}$; As to the nonleptonic decays, $\Upsilon(3S)\to B_c\rho$ and $\Upsilon(3S)\to B_cD^{(*)}_s$ have the largest branching ratios, which reach up to $10^{-10}$. Given the identification and detection efficiency of final states, searching for these weak decay modes should be fairly challenging in future experiments. The forward-backward asymmetry $A_{FB}$ and the longitudinal polarization fraction $f_L$ are also calculated for those semileptonic decays.