Branching fraction of $Ξ_{bc}^+\to Ξ_{c}^+ J/ψ$ in the final-state-interaction approach

TL;DR

The paper addresses the branching fraction of ${\Xi}_{bc}^{+}\to{\Xi}_{c}^{+}J/\psi$, a color-suppressed decay sensitive to nonfactorizable dynamics, by combining short-distance factorization with long-distance final-state interactions (FSI) via hadronic rescattering triangles. The short-distance piece uses the effective Hamiltonian with operators $O_1$ and $O_2$ and the coefficient $a_2$, while the long-distance part employs a triangle-diagram rescattering mechanism regulated by Pauli-Villars factors and regulated by $\eta$, which is fixed using ${\Lambda}_{b}\to{\Lambda}J/\psi$ data. Using LFQM form factors and known decay constants, the authors predict ${\mathcal B}(\Xi_{bc}^{+}\to{\Xi}_{c}^{+}J/\psi)=(1.55_{-0.42}^{+0.50})\times10^{-4}$ and discuss its relative size to similar decays, CKM scaling, and experimental observability. They further estimate potential signal yields at LHCb for future runs, concluding that observation of the bottom-charm baryon in this channel is feasible with larger data sets. Overall, the work provides a quantitative framework for understanding nonfactorizable contributions in heavy-baryon decays and guides experimental searches for the yet-unobserved bottom-charm baryons.

Abstract

The process of $Ξ_{bc}^{+}\to Ξ_{c}^{+}J/ψ$ is among the most favored modes for searching for bottom-charm baryons. However, its branching fraction has never been studied in theory. In this work, we investigate the branching fraction of $Ξ_{bc}^{+}\to Ξ_{c}^{+}J/ψ$ in the final-state-interaction approach, as it is dominated by the color-suppressed non-factorizable contributions. A similar process, $Λ_{b}^{0}\to Λ^0 J/ψ$, is used as a control mode to fix the model parameter. Consequently, the branching fraction of $Ξ_{bc}^{+}\to Ξ_{c}^{+}J/ψ$ is predicted to be $(1.55_{-0.42}^{+0.50})\times10^{-4}$. With the production rate of bottom-charm baryons and the detection efficiencies of the final states, it is expected for considerable signal events to observe $Ξ_{bc}^+$ in the near future.

Figures (5)

• Figure 1: The leading-order Feynman diagram for the decay ${\Xi}_{bc}^{+}\to{\Xi}_{c}^{+}J/\psi$. C: the color-suppressed internal W-emission diagram; E: the W-exchange diagram.
• Figure 2: The triangle diagram at the hadron level for the decay ${\Xi}_{bc}^{+}\to{\Xi}_{c}^{+}J/\psi$.
• Figure 3: The leading-order Feynman diagram for the decay $\Lambda_b \rightarrow \Lambda J/\psi$.
• Figure 4: The value of $\eta$ determined by the branching ratio of the decay $\Lambda_{b} \to\Lambda J/\psi$.
• Figure 5: (a):The branching ratio of the decay $\Xi_{bc}^{+}\to\Xi_{c}^{+}J/\psi$; (b):The dependence of the ratio ${\cal B}(\Xi_{bc}^{+}\to\Xi_{c}^{+}J/\psi)/{\cal B}(\Lambda_{b}\to\Lambda J/\psi)$ on the parameter $\eta$.