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In the paper, we present a detailed discussion on the semi-inclusiveproduction of doubly heavy baryons ($\Xi_{bc}$ and $\Xi_{bb}$) throughtop-quark decay channel, $t\rightarrow \Xi_{bQ^{\prime}}+ \bar {Q^{\prime}} +W^+ $, within the framework of non-relativistic QCD (NRQCD). In ourcalculations, the contributions from the intermediate diquark states, $\langlebc\rangle[^{3}S_{1}]_{\mathbf{\bar 3}/ \mathbf{6}}$, $\langlebc\rangle[^{1}S_{0}]_{\mathbf{\bar 3}/ \mathbf{6}}$, $\langlebb\rangle[^{1}S_{0}]_{\mathbf{6}}$ and $\langlebb\rangle[^{3}S_{1}]_{\mathbf{\bar 3}}$, have been taken into consideration.Main uncertainties from the heavy quark mass $(m_c,~m_b~\mbox{or}~m_t)$, therenormalization scale $\mu_r$, and the nonperturbative transition probabilityhave been estimated. For a comparison, we also analyze the production of doublyheavy baryons under the approximate fragmentation function approach. Estimatedat the LHC or a High Luminosity LHC with $\mathcal{L}$=$10^{34-36}~\rm{cm}^{-2}~\rm{s}^{-1}$, there will be about$2.25\times10^{4-6}$ events of $\Xi_{bc}$ and $9.49\times10^{2-4}$ events of$\Xi_{bb}$ produced in one operation year through top-quark decays.

Production of semi-inclusive doubly heavy baryons via top-quark decays