Decays of the Meson $B_c$ to a $P$-Wave Charmonium State ${\chi }_c$ or $h_c$

Abstract

The semileptonic decays, $B_c⟶{\chi }_c(h_c)+\ell +{\nu }_{\ell }$, and the two-body nonleptonic decays, $B_c⟶{\chi }_c(h_c)+h$, (here ${\chi }_c$ and $h_c$ denote $(c\bar{c}{[}^3{P}_J])$ and $(c\bar{c}{[}^1{P}_1])$ respectively, and $h$ indicates a meson) were computed. All of the form factors appearing in the relevant weak-current matrix elements with $B_c$ as its initial state and a $P$-wave charmonium state as its final state for the decays were precisely formulated in terms of two independent overlapping-integrations of the wave-functions of $B_c$ and the $P$-wave charmonium and with proper kinematics factors being `accompanied'. We found that the decays are quite sizable, so they may be accessible in Run-II at Tevatron and in the foreseen future at LHC, particularly, when BTeV and LHCB, the special detectors for B-physics, are borne in mind. In addition, we also pointed out that the decays $B_c\to h_c+...$ may potentially be used as a fresh window to look for the $h_c$ charmonium state, and the cascade decays, $B_c\to {\chi }_c{[}^3{P}_{1,2}]+l+{\nu }_l$ ($B_c\to {\chi }_c{[}^3{P}_{1,2}]+h$) with one of the radiative decays ${\chi }_c{[}^3{P}_{1,2}]\to J/\psi +\gamma$ being followed accordingly, may affect the observations of $B_c$ meson through the decays $B_c\to J/\psi +l+{\nu }_l$ ($B_c\to J/\psi +h$) substantially.

Comments: 24 pages, 3 figures, the replacement for improving the presentation and adding references