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 $(cc){[}^3{S}_1{]}_{\overline{\mathbf{\text{3}}}}$ and $(cc){[}^1{S}_0{]}_{\mathbf{\text{6}}}$, the branching ratio of ${\mathcal{B}}_{Z\to {\mathrm{\Xi }}_{cc}+X}$ is predicted to be of the ${10}^{-5}$ order, indicating its experimental measurability. By comparing to the ${\mathrm{\Lambda }}_c^{+}$ yield in $Z$ decay, we predict ${\mathcal{R}}_{{\mathrm{\Xi }}_{cc}^{+}}(=\frac{\mathrm{\Gamma }(Z\to {\mathrm{\Xi }}_{cc}^{+})\times \mathcal{B}({\mathrm{\Xi }}_{cc}^{+}\to {\mathrm{\Lambda }}_c^{+}{K}^{-}{\pi }^{+})}{\mathrm{\Gamma }(Z\to {\mathrm{\Lambda }}_c^{+})})=(0.85_{-0.07}^{+0.10})\times {10}^{-4}$ and ${\mathcal{R}}_{{\mathrm{\Xi }}_{cc}^{++}}(=\frac{\mathrm{\Gamma }(Z\to {\mathrm{\Xi }}_{cc}^{++})\times \mathcal{B}({\mathrm{\Xi }}_{cc}^{++}\to {\mathrm{\Lambda }}_c^{+}{K}^{-}{\pi }^{+}{\pi }^{+})}{\mathrm{\Gamma }(Z\to {\mathrm{\Lambda }}_c^{+})})=(1.70_{-0.14}^{+0.20})\times {10}^{-4}$, which are at clear variance with the SELEX measurements but comparable with the values given by the LHCb and Belle collaborations.