On the Higgs boson pair production at the LHC

TL;DR

This work addresses the theoretical description of Higgs boson pair production in proton collisions, focusing on the impact of finite top-quark mass on NLO QCD corrections. The authors implement a heavy-top expansion to generate ${1/M_t}$-suppressed terms up to high orders for the dominant $gg\to HH$ channel and for quark-initiated channels, using forward-scattering amplitudes, integration-by-parts reduction, and threshold expansions of master integrals. A key finding is that naive expansions converge poorly near the top threshold, but normalizing the NLO corrections to the exact LO cross section stabilizes predictions up to $\sqrt{s_{\rm cut}} \lesssim 600$ GeV, yielding a hadronic cross section at 14 TeV of about 38 fb with modest scale uncertainty and a 7–14% shift from finite-$M_t$ terms. Overall, the results justify continuing use of the large-$M_t$ approximation for QCD corrections and provide a quantified framework for NNLO estimates and for probing the triple-Higgs coupling in future LHC analyses.

Abstract

We compute the production cross section of a pair of Standard Model Higgs bosons at the LHC at next-to-leading order in QCD, including corrections in inverse powers of the top quark mass. We calculate these power corrections through ${\cal O}(1/M_t^8)$ and study their relevance for phenomenology of the double Higgs production. We find that power corrections are significant, even for moderate values of partonic center-of-mass energies, and that convergence of the $1/M_t$ expansion can be dramatically improved by factorizing the leading order cross section with full $M_t$-dependence.

Figures (10)

• Figure 1: Box and triangle diagrams that contribute to double Higgs boson production at leading order. Solid lines refer to top quarks and dashed lines refer to Higgs bosons.
• Figure 2:
• Figure 3: Examples of forward scattering amplitudes that we need to consider. Dashed vertical lines represent unitarity cuts. Solid lines are top and light quarks, dashed lines are Higgs bosons.
• Figure 4: The master integrals $I_1$, $I_2$, $I_3$, $I_4$ and $I_V$. Dashed lines cut through propagators that are replaced by the mass-shell conditions. Dashed lines are the Higgs boson propagators and solid lines correspond to massless scalar propagators. In the case of $I_4$ the cross indicates a propagator raised to power minus one. $I_V$ contributes to the virtual corrections at next-to-leading order.
• Figure 5: Leading order partonic $gg \to HH$ cross section (left pane) and next-to-leading order contribution to $gg \to HH$ cross section $\alpha_s/\pi \times \sigma_{gg}^{(1)}$ (right pane), in fb. Different lines correspond to 1) exact leading order cross section -- black solid; 2) cross sections expanded to ${\cal O}(\rho^0)$ -- short-dashed red; to ${\cal O}(\rho^1)$ -- short-dashed green; to ${\cal O}(\rho^2)$ -- dashed orange; to ${\cal O}(\rho^3)$ -- dashed blue; to ${\cal O}(\rho^4)$ -- dashed violet; to ${\cal O}(\rho^5)$ -- long-dashed light gray; to ${\cal O}(\rho^6)$ -- long-dashed dark gray; See text for the description of input parameters.