Heavy quark hadroproduction in perturbative QCD

Abstract

Existing calculations of heavy quark hadroproduction in perturbative QCD are either based on the conventional zero-mass perturbative QCD theory, valid for energy scales much higher than the quark mass, or on a next-to-leading order (NLO) fixed-flavor-number (FFN) scheme which is appropriate for energy scales comparable to the quark mass. We formulate this problem in the general mass variable-flavor-number scheme which incorporates initial (final) state heavy quark parton distribution (fragmentation) functions as well as exact mass dependence in the hard cross section. This formalism has the built-in feature of reducing to the FFN scheme near threshold and to the conventional zero-mass parton picture in the very high energy limit. Making use of existing calculations in the NLO FFN scheme, we obtain more complete results on bottom quark production in the general scheme to order ${\ensuremath{\alpha}}_{s}^{3}$ both for current accelerator energies and for CERN LHC. Modest improvement over the FFN results is observed in the reduced scale dependence of the cross section and in the increased magnitude of the cross section, in the direction of experimental measurement. It is shown that the general scheme represents a more efficient way of organizing the perturbation series, since the bulk of the large NLO $({\ensuremath{\alpha}}_{s}^{3})$ FFN contribution to the single heavy-quark inclusive cross section is already contained in the (resummed) order ${\ensuremath{\alpha}}_{s}^{2}$ ``heavy flavor excitation'' term in this scheme. Remaining limitations of the present calculation and possible improvements are discussed.