Weak decays of bottom-charm baryons: $\mathcal{B}_{bc}\to\mathcal{B}_bP$
After the discovery of the double-charm baryon $Ξ_{cc}^{++}$ by LHCb, one of the most important topics is to search for the bottom-charm baryons which contain a $b$ quark, a $c$ quark and a light quark. In this work, we study the two-body non-leptonic weak decays of a bottom-charm baryon into a spin-$1/2$ bottomed baryon and a light pseudoscalar meson with the short-distance contributions calculated under the factorization hypothesis and the long-distance contributions considering the final-state-interaction effects. The branching fractions of all fifty-seven decay channels are estimated. The results indicate that $Ξ_{bc}^+\toΞ_b^0π^+$, $Ξ_{bc}^{0}\toΞ_{b}^{-}π^+$ and $Ω_{bc}^0\toΩ_b^-π^+$ decay modes have relatively large decay rates and thus could be used to experimentally search for the bottom-charm baryons. The topological diagrams and the SU(3) symmetry of bottom-charm baryon decays are discussed.