NLL resummation of the heavy-quark hadroproduction cross-section

TL;DR

This work delivers a complete NLL soft-gluon resummation for the heavy-quark hadroproduction total cross-section, implemented in Mellin space with a color-singlet/octet basis. By matching to NLO and employing a Minimal Prescription for inverse transforms, it yields NLO+NLL predictions with significantly reduced scale dependence, particularly near threshold. The results demonstrate improved perturbative stability for top, bottom, and charm production across Tevatron and LHC energies, with notable impact on near-threshold regimes. The methodology provides more reliable cross-section estimates for heavy-quark phenomenology at hadron colliders and clarifies the role of threshold logarithms in shaping high-mass production rates.

Abstract

We compute the effect of soft-gluon resummation, at the next-to-leading-logarithmic level, in the hadroproduction cross-section for heavy flavours. Applications to top, bottom and charm total cross-sections are discussed. We find in general that the corrections to the fixed next-to-leading-order results are larger for larger renormalization scales, and small, or even negative, for smaller scales. This leads to a significant reduction of the scale-dependence of the results, for most experimental configurations of interest.

Figures (15)

• Figure 1: Left (Right): the function $f_{q\bar{q}}^{(1)}(\rho)$ ($f_{gg}^{(1)}(\rho)$), plotted as a function of $\eta=(1-\rho)/\rho$. The solid line represents the exact NLO result NDEVN; the short-dashed line corresponds to the $\hbox{$O(\alpha_s^3)$}$ truncation of the resummed result defined by eqs. (\ref{['fijress']}--\ref{['fcorr']}); the dot-dashed line is obtained from this last result by setting the constant $C_{q\bar{q}}$ ($C_{gg}$) to 0; the dashed line is obtained instead by the replacement in eq. (\ref{['eq:Cshift']}), with $A=2$.
• Figure 2: Partonic cross-section for the processes $q\bar{q} \to Q \overline{Q}$ (left) and $gg \to Q \overline{Q}$ (right) (in pb, and for $m_{Q}=175$ GeV). The dashed line is the exact NLO result NDEVN; the short-dashed (solid) lines correspond to the NLO+NLL result, with the coefficient $A$ defined in eq. (\ref{['eq:Cshift']}) equal to 0 (2). The lower and upper curves correspond to inclusion or neglect of the Coulomb contribution.
• Figure 3: Contribution of gluon resummation at order $\hbox{$O(\alpha_s^4)$}$ and higher, relative to the exact NLO result, for top-pair production via $q\bar{q}$ annihilation in $p\bar{p}$ collisions. The solid (dashed) lines correspond to $A=2$ ($A=0$). The three sets of curves correspond to the choice of scale $\mu=2m_{t},\; m_{t}$ and $m_{t}/2$, in descending order, with $m_{t}=175$ GeV, and PDF set MRSR2.
• Figure 4: Same as fig. \ref{['fig:deltaqq']}, for production via $gg$ annihilation.
• Figure 5: Same as fig. \ref{['fig:deltaqq']}, for the combined production channels $gg+q\bar{q}$.