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

We investigate the inclusive weak decay $\Xi_{bcq} \to \Xi_{ccq} + X$ ($q=u,d,s$) within the framework of the non-relativistic potential quark model. Treating the heavy diquarks $\Phi_{bc}$ and $\Phi_{cc}$ as compact color anti-triplet bound states, we calculate the transition form factors via the overlap integral of Schr\"odinger wave functions derived from the Cornell potential. The decay rates for four dominant channels-$\Phi_{bc} \to \Phi_{cc} + \bar{c}s$, $\Phi_{bc} \to \Phi_{cc} + \bar{u}s$, $\Phi_{bc} \to \Phi_{cc} + e/\mu + \bar{\nu}$, and $\Phi_{bc} \to \Phi_{cc} + \tau + \bar{\nu}_{\tau}$-are computed, yielding a total inclusive decay width of $\Gamma(\Xi_{bcq} \to \Xi_{ccq} + X) \approx 4.1 \times 10^{-13}$ GeV. We also evaluate the potential background from $B_c^- \to \Xi_{cc} + X$ 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 $\Xi_{bc} \to \Xi_{cc} + X$ , followed by the well-established $\Xi_{cc}$ decay chains, provides a viable discovery channel for the doubly heavy baryon $\Xi_{bc}$ at the LHC.