Heavy Quark Production in Parton Model and in QCD

TL;DR

This paper addresses heavy quark production at high energies by incorporating gluon virtuality and transverse momentum through unintegrated gluon densities in photoproduction, electroproduction, and hadroproduction. It derives cross sections with explicit $q_T$-dependent structure and gluon polarization, using two gluon distributions (MT(S-DIS) and a shadowed version) and computes Born-order matrix elements for $gg \to Q\overline{Q}$ and $\gamma g \to Q\overline{Q}$. The findings show faster energy growth and smoother $p_T$ spectra compared to LO parton-model predictions, with screening corrections moderating the rise—most notably for charm at LHC energies—and generally good agreement with $b$-quark data at the Tevatron. The study demonstrates the tangible impact of small-$x$ semihard dynamics and provides a framework for employing unintegrated gluon densities in heavy-flavor production, while noting that higher-order effects can be effectively incorporated via a $K$-factor.

Abstract

The cross sections of heavy quark production in $pp$ collision and for their photo- and electroproduction are calculated in the framework of QCD. The virtual nature of the interacting gluons as well as their transverse motion and different polarizations are taken into account. The obtained cross sections exhibit more rapid growth with the initial energy than the parton model predictions and the $p_T$ distributions of produced heavy quarks are more smooth.