Investigation for $Z$-boson decay into ${\Xi }_{bc}$ and ${\Xi }_{bb}$ baryon with the NRQCD factorizations approach

Abstract

The $Z$-boson decay provides good opportunities for the research on ${\Xi }_{b{Q}^{\prime }}$ baryon due to large quantity of $Z$ events that can be collected at the high-energy colliders. We performed a completed investigation of the indirect production of the ${\Xi }_{bc}$ and ${\Xi }_{bb}$ baryon via $Z$-boson decay $Z\to {\Xi }_{b{Q}^{\prime }}+\bar{b}+{\bar{Q}}^{\prime }$ with $Q^{\prime }=(c,b)$ quark according to NRQCD factorizations approach. After considering the contribution of the diquark states $⟨bc⟩{[}^3{S}_1{]}_{\bar{3}/6}$, $⟨bc⟩{[}^1{S}_0{]}_{\bar{3}/6}$, $⟨bb⟩{[}^1{S}_0{]}_6$ and $⟨bb⟩{[}^3{S}_1{]}_{\bar{3}}$, the calculated branching ratio for $Z\to {\Xi }_{b{Q}^{\prime }}+X$ are $\mathcal{B}(Z\to {\Xi }_{bc}+X)=3.595\times 10^{-5}$ and $\mathcal{B}(Z\to {\Xi }_{bc}+X)=1.213\times 10^{-6}$. Moreover, the ${\Xi }_{bc}$ events produced are predicted to be of the $10^4(10^7)$ order at the LHC(CEPC), while the ${\Xi }_{bb}$ events produced are forecasted to be of the $10^3(10^6)$ order. Furthermore, we have estimated the production ratio $\mathcal{R}(Z_Q\to {\Xi }_{bc}^{+,0})$ with four $Z$-boson decay channels. The $\mathcal{R}(Z_Q\to {\Xi }_{bc}^{+,0})$ up to $10^{-6}$ for $Z\to c\bar{c}$ channel and $10^{-5}$ for $Z\to b\bar{b}$ channel, respectively. Finally, we present the differential decay widths of ${\Xi }_{bc}({\Xi }_{bb})$ with respect to $s_{23}$ and $z$ distributions, and analysis the uncertainties.

Comments: 9 pages, 4 figures. Some ambiguous sentences have been modified and discussion extended