Estimate of the Hadronic Production of the Doubly Charmed Baryon $\Xi_{cc}$ under GM-VFN Scheme

Hadronic production of the doubly charmed baryon $\Xi_{cc}$ ($\Xi^{++}_{cc}$ and $\Xi^{+}_{cc}$) is investigated under the general-mass variable-flavor-number (GM-VFN) scheme. The gluon-gluon fusion mechanism and the intrinsic charm mechanisms, i.e. via the sub-processes $g+g\to(cc)[^3S_1]_{\bar 3}+\bar{c}+\bar{c}$, $g+g\to(cc)[^1S_0]_6+\bar{c}+\bar{c}$; $g+c\to (cc)[^3S_1]_{\bar 3}+\bar{c}$, $g+c\to (cc)[^1S_0]_6+\bar{c}$ and $c+c\to (cc)[^3S_1]_{\bar 3}+g$, $c+c\to (cc)[^1S_0]_6+g$, are taken into account in the investigation, where $(cc)[^3S_1]_{\bar 3}$ (in color {\bf $\bar 3$}) and $(cc)[^1S_0]_6$ (in color {\bf 6}) are two possible $S$-wave configurations of the doubly charmed diquark pair $(cc)$ inside the baryon $\Xi_{cc}$. Numerical results for the production at hadornic colliders LHC and TEVATRON show that both the contributions from the doubly charmed diquark pairs $(cc)[^1S_0]_6$ and $(cc)[^3S_1]_{\bar 3}$ are sizable with the assumption that the two NRQCD matrix elements are equal, and the total contributions from the `intrinsic' charm mechanisms are bigger than those of the gluon-gluon fusion mechanism. For the production in the region of small transverse-momentum $p_t$, the intrinsic mechanisms are dominant over the gluon-gluon fusion mechanism and they can raise the theoretical prediction of the $\Xi_{cc}$ by almost one order.