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We present a detailed discussion on the doubly charmed baryon $\Xi_{cc}$production at the RHIC and LHC via the proton-nucleus ($p$-N) andnucleus-nucleus (N-N) collision modes. The extrinsic charm mechanism via thesubprocesses $g+c\to (cc)[n]+\bar{c}$ and $c+c\to (cc)[n]+g$ together with thegluon-gluon fusion mechanism via the subprocess $g+g\to(cc)[n]+\bar{c}+\bar{c}$have been taken into consideration, where the intermediate diquark is in$[n]=[^1S_0]_{\bf 6}$-state or $[^3S_1]_{\bar{\bf 3}}$-state, respectively.Total and differential cross sections have been discussed under variouscollision energies. To compare with the $\Xi_{cc}$ production via proton-protoncollision mode at the LHC, we observe that sizable $\Xi_{cc}$ events can alsobe generated via $p$-N and N-N collision modes at the RHIC and LHC. Forexamples, about $8.1\times10^7$ and $6.7\times10^7$ $\Xi_{cc}$ events can beaccumulated in $p$-Pb and Pb-Pb collision modes at the LHC within one operationyear.

Hadronic production of the doubly charmed baryon via the proton-nucleus and the nucleus-nucleus collisions at the RHIC and LHC