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After the discovery of the double-charm baryon $\Xi_{cc}^{++}$ by LHCb, oneof the most important topics is to search for the bottom-charm baryons whichcontain a $b$ quark, a $c$ quark and a light quark. In this work, we study thetwo-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-distancecontributions calculated under the factorization hypothesis and thelong-distance contributions considering the final-state-interaction effects.The branching fractions of all fifty-seven decay channels are estimated. Theresults indicate that $\Xi_{bc}^+\to\Xi_b^0\pi^+$,$\Xi_{bc}^{0}\to\Xi_{b}^{-}\pi^+$ and $\Omega_{bc}^0\to\Omega_b^-\pi^+$ decaymodes have relatively large decay rates and thus could be used toexperimentally search for the bottom-charm baryons. The topological diagramsand the SU(3) symmetry of bottom-charm baryon decays are discussed.

Weak decays of bottom-charm baryons: $\mathcal{B}_{bc}\to\mathcal{B}_bP$