Soft and virtual corrections to pp -> H + X at NNLO

TL;DR

This paper computes the soft and virtual NNLO corrections to inclusive Higgs production in pp collisions within the heavy-top effective theory, demonstrating favorable perturbative convergence and moderate NNLO enhancements relative to NLO. By structuring the calculation into virtual, single-real, and double-real contributions and performing mass factorization, the authors obtain explicit soft-limit partonic cross sections and verify consistency with universal infrared structures and threshold resummation. They compare the soft results to existing full NNLO estimates, arguing that hard scattering contributions remain essential and that NNLO PDFs will be crucial for accurate predictions. The work also explores an approximate hard contribution by combining soft NNLO results with subleading logarithmic terms from resummation, finding that these subleading terms can dominate the total NNLO effect. The findings underscore the need for a complete NNLO calculation of the hard scattering piece and NNLO parton distributions to fully quantify Higgs production rates at hadron colliders.

Abstract

The contributions of virtual corrections and soft gluon emission to the inclusive Higgs production cross section pp -> H + X are computed at next-to-next-to-leading order in the heavy top quark limit. We show that this part of the total cross section is well behaved in the sense of perturbative convergence, with the NNLO corrections amounting to an enhancement of the NLO cross section by \sim 5% for LHC and 10-20% for the Tevatron. We compare our results with an existing estimate of the full NNLO effects and argue that an analytic evaluation of the hard scattering contributions is needed.

Figures (7)

• Figure 1: Leading order diagram to the process $gg\to H$: (a) in full QCD; (b) in the effective theory [Eq. (\ref{['eqn::leff']})]. The straight solid lines represent the top quark, the symbol $\otimes$ denotes the effective vertex.
• Figure 2: Sample two-loop diagrams contributing to the virtual corrections at NNLO.
• Figure 3: Typical diagrams contributing to (a) single and (b) double real radiation of gluons and (c) double real radiation of quark-antiquark pairs at NNLO. The dashed line is the Higgs boson and "$\otimes$" denotes the effective Higgs-gluon vertex.
• Figure 4: $K$ factor as defined in Eq. (\ref{['eq::kfactor']}), using the purely soft approximation of Eq. (\ref{['eq::sigmahat']}). Dashed and solid lines correspond to NLO and NNLO, respectively. The dotted line represents the approximate result $\bar{\sigma}_{gg}^{\rm soft}$ of gghresum. (a): $\sqrt{S} = 14$ TeV, (b): $\sqrt{S} = 2$ TeV, where $\sqrt{S}$ is the c.m.s. energy of the proton-proton system.
• Figure 5: Cross section $\sigma(pp\to H+X)$ in the purely soft approximation ( cf. caption of Fig. \ref{['fig::khksoft']}). Dash-dotted, dashed, and solid line correspond to LO, NLO, and NNLO results obtained from Eq. (\ref{['eq::sigmahat']}). The dotted line is the soft part of the NNLO approximation of ref. gghresum. (a): $\sqrt{S} = 14$ TeV, (b): $\sqrt{S} = 2$ TeV.