Inclusive beauty-charmed baryons decay $Ξ_{bcq} \to Ξ_{ccq} +X$

We investigate the inclusive weak decay $Ξ_{bcq} \to Ξ_{ccq} + X$ ($q=u,d,s$) within the framework of the non-relativistic potential quark model. Treating the heavy diquarks $Φ_{bc}$ and $Φ_{cc}$ as compact color anti-triplet bound states, we calculate the transition form factors via the overlap integral of Schrödinger wave functions derived from the Cornell potential. The decay rates for four dominant channels-$Φ_{bc} \to Φ_{cc} + \bar{c}s$, $Φ_{bc} \to Φ_{cc} + \bar{u}s$, $Φ_{bc} \to Φ_{cc} + e/μ+ \barν$, and $Φ_{bc} \to Φ_{cc} + τ+ \barν_τ$-are computed, yielding a total inclusive decay width of $Γ(Ξ_{bcq} \to Ξ_{ccq} + X) \approx 4.1 \times 10^{-13}$ GeV. We also evaluate the potential background from $B_c^- \to Ξ_{cc} + X$ decays, finding a rate of approximately $ 3.0 \times 10^{-14}$ GeV, which is roughly one order of magnitude smaller than the signal process. Our results suggest that the inclusive decay $Ξ_{bc} \to Ξ_{cc} + X$ , followed by the well-established $Ξ_{cc}$ decay chains, provides a viable discovery channel for the doubly heavy baryon $Ξ_{bc}$ at the LHC.