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.} $\langle cc\rangle[^1P_1]_{\bar 3}$, $\langle cc\rangle[^3P_J]_{6}$, $\langle bc\rangle[^1P_1]_{\bar 3/6}$, $\langle bc\rangle[^3P_J]_{\bar 3/6}$, $\langle bb\rangle[^1P_1]_{\bar 3}$, and $\langle bb\rangle[^3P_J]_{6}$ with $J = (0, 1, 2)$. The results show that contributions from all diquark states in $P$-wave were $7\%$, $8\%$, and $3\%$ in comparing with $S$-wave for the production of $\Xi_{cc}$, $\Xi_{bc}$ and $\Xi_{bb}$ via $Z$-boson decay, respectively. Based on these results, we predicted about $0.539\times 10^3(10^6)$ events for $\Xi_{cc}$, $1.827\times 10^3(10^6)$ events for $\Xi_{bc}$, and $0.036\times 10^3(10^6)$ events for $\Xi_{bb}$ can be produced annually at the LHC (CEPC). Additionally, we plot the differential decay widths of $\Xi_{cc}$, $\Xi_{bc}$ and $\Xi_{bb}$ 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.