Bcmeson weak decays andCPviolation

Abstract

The form factors for ${B}_{c}$ transitions are calculated with a relativistic constituent quark model based on the Bethe-Salpeter formalism. The rates for some semileptonic and nonleptonic ${B}_{c}$ weak decays and $\mathrm{CP}$-violating asymmetries for two-body hardonic ${B}_{c}$ decays are estimated as well. The calculated widths are compared with those predicted in other quark models of mesons. For the most promising signatures for the discovery of ${B}_{c}:$ ${B}_{c}\ensuremath{\rightarrow}\ensuremath{\psi}l\ensuremath{\nu}\ensuremath{\rightarrow}{(l}^{\ensuremath{'}+}{l}^{\ensuremath{'}\ensuremath{-}})l\ensuremath{\nu}$ and ${B}_{c}\ensuremath{\rightarrow}\ensuremath{\psi}\ensuremath{\pi}\ensuremath{\rightarrow}{(l}^{\ensuremath{'}+}{l}^{\ensuremath{'}\ensuremath{-}})\ensuremath{\pi}$ (with ${l}^{\ensuremath{'}}=e$ or $\ensuremath{\mu})$, the combined branching ratios are, respectively, estimated to be $1.06\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and ${4.8a}_{1}^{2}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ for ${\ensuremath{\tau}}_{{B}_{c}}=0.5$ ps and as large as $2.56\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and ${1.15a}_{1}^{2}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ for ${\ensuremath{\tau}}_{{B}_{c}}=1.2$ ps. There are large $\mathrm{CP}$-violating effects in some ${B}_{c}$ decay modes, and the rates for some of these (e.g., ${B}_{c}\ensuremath{\rightarrow}\ensuremath{\psi}{D}^{*},{\ensuremath{\eta}}_{c}D$, and ${\ensuremath{\eta}}_{c}{D}^{*}$, etc.) are large too.