Inclusive approach to hunt for the beauty-charmed baryons $\Xi_{bc}$

With a distinctive internal structure from all established hadrons, the beauty-charmed baryons $\Xi_{bc}$ can provide us with new points of view to decipher the strong interaction. In this work, we point out that the inclusive $\Xi_{bc} \to \Xi_{cc}^{++}+X$ decay is a golden channel for the experimental discovery of $\Xi_{bc}$ at the LHC. A unique feature of this process is that the $\Xi_{cc}^{++}$ is displaced, which greatly reduces the combinatorial background. A feasibility analysis is performed on the $\Xi_{bc}^+$ search, which is expected to have a longer lifetime than $\Xi_{bc}^0$ and thus a better displacement resolution. The $\Xi_{bc}^+ \to \Xi_{cc}^{++}+X$ branching ratio is calculated within the heavy diquark effective theory. Combining the $\Xi_{bc}$ production rate and the $\Xi_{cc}^{++}$ detection efficiency, we anticipate that hundreds of signal events will be collected during LHCb Run 3.