The Resummation of Soft Gluon in Hadronic Collisions

TL;DR

This work tackles the problem of resumming soft-gluon emissions near partonic threshold in hadronic collisions. It identifies that naive x-space implementations produce spurious factorial growth due to improper handling of subleading terms and Landau-pole effects, and introduces the Minimal Prescription to perform resummation in Mellin space without such pathologies. The authors apply the method to Drell-Yan, heavy-flavour production, and dijet production, finding resummation effects are typically modest except near threshold; heavy-flavour corrections are small in current experiments, and jet data are unlikely to be explained by resummation alone. The work also provides both theoretical justification and practical numerical prescriptions (and appendices) for implementing the MP approach and understanding its asymptotic behavior.

Abstract

We compute the effects of soft gluon resummation for the production of high mass systems in hadronic collisions. We carefully analyse the growth of the perturbative expansion coefficients of the resummation formula. We propose an expression consistent with the known leading and next-to-leading resummation results, in which the coefficients grow much less than factorially. We apply our formula to Drell--Yan pair production, heavy flavour production, and the production of high invariant mass jet pairs in hadronic collisions. We find that, with our formula, resummation effects become important only fairly close to the threshold region. In the case of heavy flavour production we find that resummation effects are small in the experimental configurations of practical interest.

Figures (10)

• Figure 1: Integration contour for $N$ for the determination of asymptotic properties.
• Figure 2: Drell--Yan pair production cross section in $p\bar{p}$ collisions, normalized to the Born result.
• Figure 3: Partonic cross section for the production of a 175 GeV heavy quark pair. $q\bar{q}$ initial state (left) and $gg$ initial state (right). The dotted lines are the Born result, the dashed lines the NLO result and the solid line the resummed result. _5^MS$\Lambda_5^{\rm \overline{MS}}$ =152 MeV.
• Figure 4: Contribution of gluon resummation at order $\alpha_S^4$ and higher, relative to the NLO result, for the individual channels and for the total, for bottom production as a function of the CM energy in $pp$ collisions.
• Figure 5: Contribution of gluon resummation at order $\alpha_S^4$ and higher, relative to the NLO result, for the individual subprocesses and for the total, as a function of the top mass in $p\bar{p}$ collisions at 1.8 TeV.