Comparative study of the hadronic production ofBcmesons

A comparative study of the full ${\alpha }_s^4$ perturbative QCD calculation of the hadronic production of the $B_c$ and $B_c^{*}$ mesons and the fragmentation approximation is presented. We examined the various subprocesses in detail and the distribution $C\left(z\right)\mathrm{}$, where $z$ is twice the fraction of the $B_c$ or $B_c^{*}$ meson energy in the center of mass of the subprocess, which proved insightful and revealed the importance of certain nonfragmentation contributions. We concluded that the condition for the applicability of the fragmentation approximation in hadronic collisions is that the transverse momentum $P_T$ of the produced $B_c$ and $B_c^{*}$ be much larger than the mass of the $B_c$ meson: i.e., $P_T\gg M_{B_c}$. Numerical results for the cross sections at the Fermilab Tevatron are also presented using updated parton distribution functions with various kinematic cuts.