Phenomenology of the trilinear Higgs coupling at proton-proton colliders

TL;DR

This work investigates Higgs pair production via gluon fusion at proton colliders with a focus on the HL-LHC, examining how the Higgs trilinear coupling $λ_{3H}$ shapes both rate and kinematics. By contrasting exact top-quark loop calculations with the EFT in the LO amplitude, the authors show sizable discrepancies in kinematics, especially outside the near-threshold region, and identify $\hat{s}\lesssim400$ GeV as where self-coupling effects can be most visible albeit still subdominant. They examine differential distributions and the $pp\to HH\to b\bar{b}\gamma\gamma$ channel, highlighting substantial background challenges and the need for precise matrix-element treatment. The study also explores non-SM values of $λ_{3H}$, noting how triangle, box, and interference contributions respond and how this affects prospects at 14 TeV and 100 TeV. Overall, extracting $λ_{3H}$ demands exact calculations and optimized selection strategies, as EFT approximations can mislead both rate and shape predictions and backgrounds remain a major hurdle even at future colliders.

Abstract

We investigate Higgs pair production at proton-proton colliders, with emphasis on the gluon fusion channel at the HL-LHC. We study the behaviour of the leading order matrix element using exact computation of quark loops and infinite quark mass approximation. We analyse di-Higgs kinematics in search for phase space regions where the contribution of Higgs self-coupling to SM Higgs pair production is enhanced. We discuss how non-SM values of the Higgs trilinear coupling may affect the kinematics of the Higgs pair.

Figures (10)

• Figure 1: Leading order Feynman diagrams for SM Higgs pair production in gluon-gluon fusion.
• Figure 2: Comparison between: $\triangle^{EFT}\equiv|C_{\triangle}F_{\triangle}^{EFT}|^2$ (red-dashed), $\square^{EFT}\equiv|C_{\square}F_{\square}^{EFT}|^2$ (green-dotted), $(\triangle + \square)^{EFT}\equiv|C_{\triangle}F_{\triangle}^{EFT} + C_{\square}F_{\square}^{EFT}|^2$ (blue-solid), $\triangle^{\text{exact}}\equiv |C_{\triangle}F_{\triangle}|^2$ (thick red-dot-dashed).
• Figure 3: The $gg\to H^0H^0 \to b\bar{b}\gamma\gamma$ cross-section as a function of $\sqrt{\hat{s}}$. The results are obtained using Madgraph5 (EFT) Alwall:2014hca. Red-dashed line -- 'triangle' only contribution, green-dotted line -- only 'box' contribution, Blue-solid line -- full result.
• Figure 4: The differential Higgs pair production cross-section at leading order for the triangle, box, and both diagrams (including their interference). All contributions are obtained using both EFT and exact calculations (see legend).
• Figure 5: Left plot: comparison between the distributions of the opening angle between the two Higgs momenta in EFT (thin lines) and exact calculation (thick lines) for the triangle (red lines) and box (green lines). Right plot: Comparison between the inclusive Higgs pseudorapidity distributions for EFT (thin light line) and exact (thick dark line) calculation.