Further study on the production of P-wave doubly heavy baryons from Z-boson decays

In this paper, we carried out a systematic investigation for the excited doubly heavy baryons production in $Z$-boson decays within the NRQCD factorization approach. Our investigation accounts for all the $P$-wave intermediate diquark states, {\it i.e.} $⟨cc⟩{[}^1{P}_1{]}_{\bar{3}}$, $⟨cc⟩{[}^3{P}_J{]}_6$, $⟨bc⟩{[}^1{P}_1{]}_{\bar{3}\mathrm{/}6}$, $⟨bc⟩{[}^3{P}_J{]}_{\bar{3}\mathrm{/}6}$, $⟨bb⟩{[}^1{P}_1{]}_{\bar{3}}$, and $⟨bb⟩{[}^3{P}_J{]}_6$ with $J=(0,1,2)$. The results show that contributions from all diquark states in $P$-wave were $7\mathrm{\%}$, $8\mathrm{\%}$, and $3\mathrm{\%}$ in comparing with $S$-wave for the production of ${\mathrm{\Xi }}_{cc}$, ${\mathrm{\Xi }}_{bc}$ and ${\mathrm{\Xi }}_{bb}$ via $Z$-boson decay, respectively. Based on these results, we predicted about $0.539\times {10}^3({10}^6)$ events for ${\mathrm{\Xi }}_{cc}$, $1.827\times {10}^3({10}^6)$ events for ${\mathrm{\Xi }}_{bc}$, and $0.036\times {10}^3({10}^6)$ events for ${\mathrm{\Xi }}_{bb}$ can be produced annually at the LHC (CEPC). Additionally, we plot the differential decay widths of ${\mathrm{\Xi }}_{cc}$, ${\mathrm{\Xi }}_{bc}$ and ${\mathrm{\Xi }}_{bb}$ as a function of the invariant mass $s_{23}$ and energy function $z$ distributions, and analyze the theoretical uncertainties in decay width arising from the mass parameters of heavy quark.