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Doubly-charmed baryon production in $Z$ boson decay

In this paper, we carry out a detailed study of doubly-charmed baryon production in $Z$ boson decay, on the basis of the nonrelativistic QCD factorization. With the inclusion of the di-quark states $(cc)[^3S_1]_{\bar{\textbf{3}}}$ and $(cc)[^1S_0]_{\textbf{6}}$, the branching ratio of $\mathcal{B}_{Z \to Ξ_{cc}+X}$ is predicted to be of the $10^{-5}$ order, indicating its experimental measurability. By comparing to the $Λ^{+}_{c}$ yield in $Z$ decay, we predict $\mathcal{R}_{Ξ_{cc}^{+}}(=\frac{Γ(Z \to Ξ^{+}_{cc}) \times \mathcal{B}(Ξ^{+}_{cc} \to Λ_c^{+}K^{-}π^{+})}{Γ(Z \to Λ_c^{+})})=(0.85^{+0.10}_{-0.07}) \times 10^{-4}$ and $\mathcal{R}_{Ξ_{cc}^{++}}(=\frac{Γ(Z \to Ξ^{++}_{cc}) \times \mathcal{B}(Ξ^{++}_{cc} \to Λ_c^{+}K^{-}π^{+}π^{+})}{Γ(Z \to Λ_c^{+})})=(1.70^{+0.20}_{-0.14}) \times 10^{-4}$, which are at clear variance with the SELEX measurements but comparable with the values given by the LHCb and Belle collaborations.