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The p_T Spectrum in Heavy-Flavour Hadroproduction

M. Cacciari, M. Greco, P. Nason

TL;DR

The paper develops a systematic framework (FONLL) to predict heavy-flavour transverse-momentum spectra by merging exact fixed-order massive calculations with next-to-leading-log resummation of $\log(p_T/m)$. It introduces a scheme-consistent matching strategy, analyzes power-suppressed mass effects, and explores LL and DL fragmentation-scheme variants to optimize cancellation near threshold. Numerical results for $b$ production at the Tevatron show a mild enhancement at intermediate $p_T$ with controlled uncertainties, underscoring the importance of including mass effects and non-perturbative fragmentation for accurate predictions. The work provides a practical, extensible approach for combining FO and RS components across the $p_T$ spectrum and clarifies the role of scheme choices in heavy-quark production calculations.

Abstract

We consider the transverse-momentum distribution of heavy flavours in hadronic collisions. We present a formalism in which large transverse-momentum logarithms are resummed at the next-to-leading level, and mass effects are included exactly up to order α_strong^3, so as to retain predictivity at both small and large transverse momenta. As an example, we apply our formalism to b production at the Tevatron.

The p_T Spectrum in Heavy-Flavour Hadroproduction

TL;DR

The paper develops a systematic framework (FONLL) to predict heavy-flavour transverse-momentum spectra by merging exact fixed-order massive calculations with next-to-leading-log resummation of . It introduces a scheme-consistent matching strategy, analyzes power-suppressed mass effects, and explores LL and DL fragmentation-scheme variants to optimize cancellation near threshold. Numerical results for production at the Tevatron show a mild enhancement at intermediate with controlled uncertainties, underscoring the importance of including mass effects and non-perturbative fragmentation for accurate predictions. The work provides a practical, extensible approach for combining FO and RS components across the spectrum and clarifies the role of scheme choices in heavy-quark production calculations.

Abstract

We consider the transverse-momentum distribution of heavy flavours in hadronic collisions. We present a formalism in which large transverse-momentum logarithms are resummed at the next-to-leading level, and mass effects are included exactly up to order α_strong^3, so as to retain predictivity at both small and large transverse momenta. As an example, we apply our formalism to b production at the Tevatron.

Paper Structure

This paper contains 12 sections, 73 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Review of the resummation formalism
  3. The change of scheme
  4. Massless limit of the fixed-order calculation
  5. Matching
  6. Power effects in the RS and FOM0 calculations
  7. An LL implementation of the matching procedure
  8. Alternative choice of fragmentation scheme
  9. Some numerical NLL results
  10. Conclusions
  11. Perturbative expansion of the heavy-quark parton density
  12. The DL scheme

Figures (11)

  • Figure 1: Comparison of the FO and FOM0 differential cross sections as a function of the logarithm of the mass, at $p_{\rm T}=5$ GeV.
  • Figure 2: Comparison of the FO and FOM0 differential cross sections as a function of the logarithm of the mass, at $p_{\rm T}=50$ GeV.
  • Figure 3: Matching of the FOM0 and RS computations for small $\alpha_{\rm s}$, for $p_{\rm T}=40\;$GeV and $y=0$. The colliding hadrons are $p\bar{p}$ at $\sqrt{S}=1.8\;$TeV. The triangles represent the RS computation, the full circles the RSA, and the empty circles the FOM0.
  • Figure 4: FO versus FOM0 at Born and full ${\cal O}(\alpha_{\rm s}^3)$ level, plotted as a function of the mass and at fixed transverse mass (left figure) or fixed transverse momenta (right figure).
  • Figure 5: Illustration of the FOLL result for the central values of the scales $\hbox{$\mu_{\rm {F}}$}=\hbox{$\mu_{\rm {R}}$}=m{\rm T}$m_ T$$.
  • ...and 6 more figures