Soft-gluon resummation for Higgs boson production at hadron colliders

TL;DR

The paper develops soft-gluon resummation for Higgs production via gluon fusion, achieving NNLL accuracy and combining it with fixed-order NNLO results. It formulates the resummation in Mellin space, derives the LL, NLL and NNLL components, and assesses soft-virtual approximations against exact fixed-order results. Phenomenological studies for the LHC and Tevatron show modest NNLL enhancements for a light Higgs at the LHC and larger effects at the Tevatron, with overall perturbative uncertainties around 8–10% when PDFs are considered. The work also demonstrates the superiority of the N-space formulation over x-space for stability and reliability of the resummed predictions, highlighting PDFs as a key source of residual uncertainty.

Abstract

We consider QCD corrections to Higgs boson production through gluon--gluon fusion in hadron collisions. We compute the cross section, performing the all-order resummation of multiple soft-gluon emission at next-to-next-to-leading logarithmic level. Known fixed-order results (up to next-to-next-to-leading order) are consistently included in our calculation. We give phenomenological predictions for Higgs boson production at the Tevatron and at the LHC. We estimate the residual theoretical uncertainty from perturbative QCD contributions. We also quantify the differences obtained by using the presently available sets of parton distributions.

Figures (14)

• Figure 1: The SV (dotted lines) and SVC (dashed lines) approximations in $N$-space versus the exact results (solid lines) at the LHC (${\sqrt s}=14$ TeV).
• Figure 2: The SV (dotted lines) and SVC (dashed lines) approximations in $N$-space versus the exact results (solid lines) at the Tevatron (${\sqrt s}=1.96$ TeV).
• Figure 3: The SV-$x$ (dotted lines) and SVC-$x$ (dashed lines) approximations versus the exact results (solid lines) at the LHC (${\sqrt s}=14$ TeV).
• Figure 4: The SV-$x$ (dotted lines) and SVC-$x$ (dashed lines) approximations versus the exact results (solid lines) at the Tevatron (${\sqrt s}=1.96$ TeV).
• Figure 5: $N$-dependence of resummed (left-hand side) and fixed-order (right-hand side) gluon coefficient functions for Higgs production ($M_H=150$ GeV) with fixed coupling constant $\alpha_{\mathrm{S}}=0.1$.