Large $\pt$ Hadroproduction of Heavy Quarks

TL;DR

Problem: heavy-quark production at large transverse momentum suffers from large logarithms $\log(p_\bot/m)$ and sizable scale uncertainties in fixed-order $O(\alpha_s^3)$ QCD calculations. Approach: the authors adopt a perturbative fragmentation function (PFF) framework, computing heavy-quark fragmentation functions at $\mu_0 \sim m$ and evolving to $\mu_F \sim p_\bot$ to resum the large logs via a factorized cross section with massless kernels for the hard scattering. Findings: the PFF approach substantially decreases the renormalization/factorization scale sensitivity and reduces PDF dependence at large $p_\bot$ for $b$-quark production, though it does not easily reproduce the region $p_\bot \lesssim m$ and charm production requires separate treatment. Scope: detailed numerical comparisons with the full $O(\alpha_s^3)$ results demonstrate improved theoretical stability, providing a more reliable framework for high-$p_\bot$ heavy-quark hadroproduction and guiding comparisons with collider data. Significance: this method offers enhanced predictive power for heavy-quark production at high energies and sets the stage for improved interpretation of experimental measurements in hadron colliders.

Abstract

The production of heavy quarks at large $\pt$ ($\pt\gg m$) in hadronic collisions is considered. The analysis is carried out in the framework of perturbative fragmentation functions, thereby allowing a resummation at the NLO level of final state large mass logarithms of the kind $\log(\pt/m)$. The case of $b$-quark production is considered in detail. The resulting theoretical uncertainty from factorization/renormalization scales at large $\pt$ is found to be much smaller than that shown by the full $O(\as^3)$ perturbative calculation.

Figures (15)

• Figure 1: Bottom distributions in hadrons according to HMRS-B (solid line), MT-B2 (dashed) and CTEQ1M (dotted) sets, at different values of the factorization scale.
• Figure 2: Bottom fragmentation functions at $Q = 91$ GeV.
• Figure 3: Results from the PFF approach compared to the perturbative prediction of NDE at 1800 GeV.
• Figure 4: Results from the PFF approach compared to the perturbative prediction of NDE, with the MT-B2 and the HMRS-B sets, at 630 GeV and 16 TeV.
• Figure 5: Results from the PFF approach compared to the perturbative prediction of NDE, with the MT-B2 and CTEQ1M sets, at 1800 GeV and 16 TeV.