Search for the $B_c$ meson

In a sample of 3.02 million hadronic $Z^o$ decays collected by the DELPHI detector, 270 $J/\psi \into$ \lplm candidates have been selected. A search for fully reconstructed $B_c\upm$ mesons has yielded one $B_c\upm\to J/\psi ~\pi\upm$ candidate, no $B_c\upm \into J/\psi ~\ell\upm ~\nu_\ell$ candidates, and one $B_c\upm \into J/\psi ~\pi^+~\pi^- ~\pi\upm$ candidate, consistent with expected background in each channel. The following 90\% confidence level upper limits are determined: r(Z^o \into B_c\upm ~X) \times Br(B_c\upm \into J/\psi ~\pi\upm) (1.05~{\mathrm{to}}~0.84) \times 10^{-4} and r(Z^o \into B_c\upm ~X) \times Br(B_c\upm \into J/\psi ~\ell\upm ~\nu_\ell) (5.8~{\mathrm{to}}~5.0) \times 10^{-5}, where the ranges quoted correspond to the range of predicted $B_c\upm$ lifetimes from 0.4 to 1.4 ps, and r(Z^o \into B_c\upm ~X) \times Br(B_c\upm \into J/\psi ~\pi^+ ~\pi^- ~\pi\upm) 1.75 \times 10^{-4}, constant over the range of predicted $B_c\upm$ lifeti