Estimation of semileptonic decays ofBcmeson toS-wave charmonia with nonrelativistic QCD

Abstract

We study the semileptonic differential decay rates of the ${B}_{c}$ meson to S-wave charmonia, ${\ensuremath{\eta}}_{c}$, and $J/\ensuremath{\Psi}$ at next-to-leading order accuracy in the framework of nonrelativistic QCD. In the heavy quark limit, ${m}_{b}\ensuremath{\rightarrow}\ensuremath{\infty}$, we obtain analytically the asymptotic expression for the ratio of the next-to-leading order form factor to the leading-order form factor. Numerical results show that the convergence of the ratio is perfect. At the maximum recoil region, we analyze the differential decay rates in detail with various input parameters and polarizations of $J/\ensuremath{\psi}$, which can now be checked in the LHCb experiment. Phenomenologically, the form factors are extrapolated to the minimal recoil region, and then the ${B}_{c}$-to-charmonium semileptonic decay rates are estimated.