Gluon-fusion contributions to Higgs plus two-jet production

TL;DR

This paper presents a complete calculation of Higgs plus two jets produced via gluon fusion at order $\alpha_s^4$, incorporating full top-quark mass dependence through triangle, box, and pentagon loop topologies. The authors derive analytic expressions for the $qq$, $qQ$, and $qg$ subprocesses and provide a largely numeric treatment for $gg\to ggH$, with extensive checks for gauge invariance and consistency with the heavy-top limit. Applying the results to LHC phenomenology, they compare gluon-fusion to weak-boson fusion, analyze scale uncertainties, and study kinematic distributions that distinguish the two production mechanisms, highlighting how cuts and jet observables can separate backgrounds from signals. The work enables more precise background modeling for Higgs coupling measurements and opens pathways to NLO studies by validating the heavy-top approximation in relevant regions. Overall, the study provides compact analytic forms where possible and a robust computational framework for Higgs plus two-jet production via gluon fusion, with clear implications for LHC analyses and future higher-order refinements.

Abstract

Real emission corrections to Higgs production via gluon fusion, at order alpha_s^4, lead to a Higgs plus two-jet final state. We present the calculation of these scattering amplitudes, as induced by top-quark triangle-, box- and pentagon-loop diagrams. These diagrams are evaluated analytically for arbitrary top mass m_t. We study the renormalization and factorization scale-dependence of the resulting H + 2 jet cross section, and discuss phenomenologically important distributions at the LHC. The gluon fusion results are compared to expectations for weak-boson fusion cross sections.

Figures (13)

• Figure 1: Examples of Feynman graphs contributing to $H+2$ jet production via gluon fusion.
• Figure 2: Feynman graphs contributing to the process $qg\hbox{$\rightarrow$} qgH$. Graphs (3) and (4) are the same as (1) and (2), but with gluon labels interchanged. No distinction is made between the two orientations of the fermion arrow on the top-quark loop, because they are related by Furry's theorem.
• Figure 3: $H+2$ jet cross sections in pp collisions at $\sqrt{s}=14$ TeV as a function of the Higgs boson mass. Results are shown for gluon-fusion processes induced by a top-quark loop with $m_t=175$ GeV and in the $m_t\,\hbox{$\rightarrow$}\,\infty$ limit, computed using the heavy-top effective Lagrangian, and for weak-boson fusion. The two panels correspond to two sets of jet cuts: (a) inclusive selection (see Eq. (\ref{['eq:cuts_min']})) and (b) WBF selection (Eqs. (\ref{['eq:cuts_min']}) and (\ref{['eq:cut_gap']})).
• Figure 4: $H+2$ jet contributions to the cross section in pp collisions at $\sqrt{s}=14$ TeV as a function of the Higgs boson mass. Results are shown for the different contributions to the gluon-fusion process ($gg, qg$ and $qq$ amplitudes) using (a) the inclusive cuts of Eq. (\ref{['eq:cuts_min']}) and (b) the WBF cuts of Eqs. (\ref{['eq:cuts_min']}) and (\ref{['eq:cut_gap']}).
• Figure 5: Renormalization-scale dependence of the total cross section for $H$ plus two jet production with the inclusive cuts of Eq. (\ref{['eq:cuts_min']}). The renormalization scale $\mu_r=\xi \mu_0$ is varied in the range $1/5 < \xi < 5$. The five curves correspond, from top to bottom, to the following choice of $\mu_0$: the geometric mean of the transverse momenta of the two jets, the $Z$ mass, the invariant mass of the two jets, the geometric mean of the two invariant masses of the Higgs and the jets, and the partonic center-of-mass energy.