Hadronic Production of $B_c(B^*_c)$ Meson Induced by the Heavy Quarks inside the Collision Hadrons

In general-mass variable-flavor-number (GM-VFN) scheme, the `heavy quark mechanisms' of $B_c(B_c^*)$ meson hadroproduction via the sub-processes $g+c\to B_c(B_c^*)+...$ and $g+\bar{b}\to B_c(B_c^*)+...$ are investigated. In the scheme, possible double counting from these mechanisms and the `light mechanisms' (the gluon-gluon fusion and quark-antiquark annihilation mechanisms) is subtracted properly. The numerical results show that the transverse momentum, $p_t$, distribution of the produced $B_c(B_c^*)$ from the `intrinsic heavy quark mechanisms' (i.e. the heavy quark mechanisms in which the double counting components have been subtracted accordingly) declines faster with the increment of the $p_t$ than that from the `light mechanisms', and only in small $p_t$ region ($p_t\lesssim 7.0$ GeV) the `intrinsic heavy quark mechanisms' themselves may make remarkable contributions. The combined contributions from the `intrinsic heavy quark mechanisms' and the `light mechanisms' to the production are compared with that obtained by the most calculations in literature, which in some sense are within the fixed flavor number (FFN) scheme at leading order, and we find that the production by virtue of the GM-VFN scheme is more or less the same as the one in literature, except in the small $p_t$ region.