Heavy Quark Hadroproduction in Perturbative QCD

TL;DR

The paper develops a general-mas s variable-flavor-number framework (ACOT) for heavy-quark hadroproduction, retaining full $m_H$ dependence and resumming mass logarithms into heavy-quark PDFs and fragmentation functions. It demonstrates that this GM-VFN approach naturally reduces to both the fixed-flavor-number scheme near threshold and the zero-mass parton picture at high energy, enabling αs^3 precision for bottom production at colliders. Numerical results show reduced scale dependence and cross sections larger than NLO FFN, with the bulk of the NLO FFN contribution captured by the resummed heavy-flavor excitation term. The work provides a consistent, energy-spanning description of heavy-quark production and identifies higher-order and small-$x$ effects as avenues for further refinement.

Abstract

Existing calculations of heavy quark hadroproduction in perturbative QCD are either based on the approximate conventional zero-mass perturbative QCD theory or on next-to-leading order (NLO) fixed-flavor-number (FFN) scheme which is inadequate at high energies. 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 NLO FFN scheme, we obtain more complete results on bottom production in the general scheme to order α_s^3 both for current accelerator energies and for LHC. The scale dependence of the cross-section is reduced, and the magnitude is increased with respect to the NLO FFN results. It is shown that the bulk of the large NLO FFN contribution to the single heavy-quark inclusive cross-section is already contained in the (resummed) order α_s^2 ``heavy flavor excitation'' term in the general scheme.

Figures (16)

• Figure 1: Graphical representation of the leading terms in the factorization formula which correspond to the various production mechanisms. The initial state hadron line for the parton distributions are uniformly suppressed.
• Figure 2: PDFs vs. $x$ for $\mu$ = 10 and 100 GeV. The gluon PDF is scaled by 1/5.
• Figure 3: Graphical representation of the terms in the right-hand-side of Eq. \ref{['nloIRSxsec']}. Collinear singularities due to light partons have already been subtracted. The vertices represented by a dot are the heavy quark parts of the perturbative distribution and fragmentation functions, as in Eqs. \ref{['pertpdf']} and \ref{['pertfrg']}.
• Figure 4: Graphical representation of the physical cross-section, Eq. \ref{['HadXsec1']} and Fig. \ref{['fig:HadXsecA']}, written in terms of the intermediate partonic cross-sections $^n\tilde{\sigma}$'s and the attendant heavy quark mass subtraction terms which represent the overlap between the 2$\rightarrow$2 and 2$\rightarrow$3 cross-sections. Initial state parton distribution function factors are uniformly suppressed.
• Figure 5: Comparison of the evolved PDFs, $f^H(x,\mu)$ (labeled PDF), and perturbative PDFs, $^1f^H(x,\mu)$ (labeled SUB), as a function of the renormalization scale $\mu$ for charm at $x=0.1$ (a) and $x=0.01$ (b), and for bottom at $x=0.1$ (c) and $x=0.01$ (d). This shows the compensation between fully evolved heavy quark parton distribution and the first order perturbative contribution (which is the only part contained in the FFN scheme calculation).