Uncertainties in Estimating Hadronic Production of the Meson B_c and Comparisons between TEVATRON and LHC

The uncertainties in estimating the hadronic production of the $B_c$ meson are studied under the framework of the complete $\alpha_s^4$ approach of the perturbative QCD and the gluon-gluon fusion mechanism. Quantitative comparisons on the production at TEVATRON and LHC are made. Considering the detectors at TEVATRON and LHC, we have also estimated the production with proper kinematic cuts. Based on the results, we conclude that the experimental studies of the $B_c$ meson at the two colliders will be complimentary and stimulative. We find that as c.m. energy is increasing from RUN-I to RUN-II at TEVATRON, the production cross-section increases about 20%.