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Adopting the complete $\alpha_s^4$ approach of the perturbative QCD (pQCD)and updated parton distribution functions, we have estimated the hadronicproduction of $P$-wave excited $B_c$-states ($B_{cJ,L=1}^*$). In the estimate,special care on the relation of the production amplitude to the derivative ofwave function at origin of the potential model is payed. For experimentalreferences, main uncertainties are discussed, and the total cross sections andthe distributions of the production with reasonable cuts at the energies ofTevatron and LHC are computed and presented. The results show that $P$-waveproduction may contribute to the $B_c$-meson production indirectly by a factorabout 0.5 of the direct production, and with such a big cross section, it isworth further to study the possibility to observe the $P$-wave productionitself experimentally.Comment: 23 pages, 9 figures, to replace for revising the misprints ec

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Hadronic production of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>P</mml:mi></mml:math>-wave excited<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>B</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math>states (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>B</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>J</mml:mi><mml:mo>,</mml:mo><mml:mi>L</mml:mi><mml:mo>=</mml:mo><…

Hadronic production of theP-wave excitedBcstates (BcJ,L=<…