  Through the interaction of Higgs with heavy quarks in standard model, we have
systematically studied and predicted the production of excited doubly heavy
baryons based on non-relativistic QCD theory. The decay widths, differential
distributions, and major theoretical uncertainties of the excited doubly heavy
baryons via the process $H \rightarrow \langle QQ'\rangle[n] \rightarrow
\Xi_{QQ'}+ \bar {Q'} + \bar {Q}$ are discussed in detail. The spin and color
quantum number of the intermediate $P$-wave diquark state $\langle
QQ'\rangle[n]$ can be $\langle cc\rangle[^{1}P_{1}]_{\mathbf{\bar 3}}$,
$\langle cc\rangle[^{3}P_{J}]_{\mathbf{6}}$, $\langle
bc\rangle[^{1}P_{1}]_{\mathbf{\bar 3}/ \mathbf{6}}$, $\langle
bc\rangle[^{3}P_{J}]_{\mathbf{\bar 3}/ \mathbf{6}}$, $\langle bb
\rangle[^{1}P_{1}]_{\mathbf{\bar 3}}$ and $\langle
bb\rangle[^{3}P_{J}]_{\mathbf{6}}$, with $J=0, 1, 2$. The contributions from
all summed $P$-wave states can be about $3.05\%$, $3.23\%$ and $2.19\%$ of the
$S$-wave states for the production of $\Xi_{cc}$, $\Xi_{bc}$ and $\Xi_{bb}$,
accordingly. Therefore, there will be about 0.41$\times10^4$ events of
$\Xi_{cc}$, 6.35$\times10^4$ events of $\Xi_{bc}$ and 0.28$\times10^4$ events
of $\Xi_{bb}$ produced per year at the HL-LHC, and a smaller number of events
would be produced at the CEPC or ILC but with a cleaner background to be
measured by the experiments.
