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

TL;DR

The paper addresses the inclusive weak decay $Ξ_{bcq} \to Ξ_{ccq} + X$ in a non-relativistic potential quark framework, using a heavy-diquark picture with $Φ_{bc}$ and $Φ_{cc}$ as compact color anti-triplets. It derives the decay structure from the underlying $b \to c$ transition via an effective Hamiltonian with a single form-factor overlap $\mathcal{I}(k)$ between Coulomb-like bound-state wave functions, and computes four channels contributing to the total width. The authors obtain a total inclusive width of $Γ(Ξ_{bcq} \to Ξ_{ccq} + X) \approx 4.1\times 10^{-13}$ GeV, with the dominant nonleptonic and semileptonic modes and a background from $B_c^- \to Ξ_{cc} + X$ at about $3.0\times 10^{-14}$ GeV. The results support using the inclusive $Ξ_{bc} \to Ξ_{cc} + X$ pathway, followed by known $Ξ_{cc}$ decays, as a viable discovery channel at the LHC, while acknowledging uncertainties from non-relativistic approximations and potential relativistic and excited-state effects.

Abstract

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.

Figures (1)

• Figure 1: The form factor $\mathcal{I}(k)$ , defined in Eq.(\ref{['Ik']}), is evaluated using both the numerical ground-state wave function (blue) and the approximate form given in Eq.(\ref{['bccc']}) (yellow).