The transverse-momentum spectrum of Higgs bosons near threshold at NNLO

TL;DR

Problem: accurate prediction of the Higgs transverse-momentum spectrum at large p_T in hadronic collisions is challenging due to large perturbative corrections. Approach: the authors compute the NNLO threshold cross section using a factorization into hard, jet, and soft functions, with RG evolution and matching to NLO, and implement results in the PeTeR code. Key findings: the NNLO corrections are sizeable, dominated by large two-loop virtual corrections in the hard function, while real-emission pieces are moderate; RG-improvement offers only modest gains, and there is no strong hierarchy between the jet, soft, and hard scales. Significance: the results provide a robust threshold prediction, serve as a cross-check for future full NNLO Higgs+jet calculations, and inform estimates of beyond-NNLO effects and finite top-mass corrections at high p_T.

Abstract

We give next-to-next-to-leading order (NNLO) predictions for the Higgs production cross section at large transverse momentum in the threshold limit. Near the partonic threshold, all radiation is either soft or collinear to the final state jet which recoils against the Higgs boson. We find that the real emission corrections are of moderate size, but that the virtual corrections are large. We discuss the origin of these corrections and give numerical predictions for the transverse-momentum spectrum. The threshold result is matched to the known NLO result and implemented in the public code PeTeR.

Figures (8)

• Figure 1: Size of the corrections to the hard, jet, and soft function for $Z$-production.
• Figure 3: Size of the corrections to the hard function for real and complex $\mu_h$. The results are for $p_T=0.2\,{\rm TeV}$ and $\hat{s}=(0.5\,{\rm TeV})^2$. The solid lines show the hard function $H_{ gg} (\hat{u},\hat{t},\mu_h)$, while the dashed lines show the result for the reduced hard function $\widetilde{H}_{ gg}(\hat{u},\hat{t})$.
• Figure 4: Relative contribution of different partonic channels to the NNLO correction for the default scale choice $\mu= p_T$. The $qg$ contribution includes all partonic channels with a single (anti-)quark in the initial state.
• Figure 5: Scale dependence of the cross section at LO (gray), NLO (purple) and NNLO$_{\rm sing} +$NLO (black). The dashed lines show the result with RG improvement according to the prescription \ref{['eq:impr']}.
• Figure 6: LO result at finite $m_t$ versus the result in the $m_t\to \infty$ limit. For the plot we have varied the scale in the range $p_T/2< \mu<2 p_T$ and have computed results for both $\sqrt{s}=8\,{\rm TeV}$ (purple) and $\sqrt{s}=13\,{\rm TeV}$ (gray). The resulting bands are very narrow and the ratio is also to very good accuracy independent of $\sqrt{s}$.