Search for $B_c$ Mesons Using the $B_c \rightarrow B^0_s X$ Decay Channel at CDF

To date, the $B_c$ meson has only been observed in $B_c \rightarrow J/\psi$~$\pi$ and $J/\psi\ell X$ final states, while the dominant decay modes are expected to be in the $B_c \rightarrow B^0_s X$ channel. We present the results of a first search for the $B_c$~meson through $B_c \rightarrow B^0_s X$. The measurement uses 3~fb$^{-1}$ of data collected with the CDF\,II detector during Run\,II of the Fermilab Tevatron in $p\bar{p}$ collisions at $\sqrt{s} = 1.96$~TeV. The analysis is based on a neural network selection and combines the $B^0_s$ decay modes into $J/\psi\phi$, $D_s^{\pm}\pi$, and $D_s^{\pm}3\pi$.