Constraining the Higgs potential using multi-Higgs production

Abstract

The Higgs self-couplings remain only weakly constrained by current Large Hadron Collider (LHC) measurements, leaving ample room for physics beyond the Standard Model that could modify the structure of the Higgs potential. Multi-Higgs production processes provide a particularly sensitive probe of deviations in both the Higgs trilinear and quartic self-couplings. In this note, we summarize the current status of next-to-leading-order electroweak (EW) corrections to double-Higgs production computed within the Standard Model Effective Field Theory and Higgs Effective Field Theory frameworks, emphasizing how these calculations introduce sensitivity to the Higgs self-couplings beyond what is accessible at leading order. We discuss the key conceptual and technical differences between the two effective field theory approaches, including their treatment of higher-dimensional operators, renormalization procedures, and the structure of EW two-loop amplitudes. Despite these differences, both approaches yield broadly consistent constraints, illustrating the complementarity of double- and triple-Higgs measurements. With the high-luminosity LHC and future high-energy colliders on the horizon, these developments and further advances provide an essential foundation for extracting increasingly precise information on the dynamics of EW symmetry breaking.

Figures (5)

• Figure 1: Constraints in the $\kappa_3\space$--$\space\kappa_4$ plane at the LHC Run 2 (left) and the HL-LHC (right). The red and green contours correspond to the preferred $68\%$ CL regions that arise from inclusive double- and triple-Higgs production, respectively. The SM is indicated by the black points, and the black dashed lines correspond to $\kappa_4 - 1 = 6 \, ( \kappa_3 - 1 )$, i.e., the relation between $\kappa_3$ and $\kappa_4$ that holds in the SMEFT at the level of dimension-six operators. The yellow regions, outlined with black dotted lines, indicate the constraint from perturbative unitarity derived from tree-level $HH \to HH$ scattering.
• Figure 2: Feynman diagrams contributing to $gg \to HH$ that contain a single Higgs trilinear self-coupling (black dot) and three top-quark Yukawa couplings. The diagrams with reversed fermion flow are omitted.
• Figure 3: Feynman diagrams contributing to $gg \to HH$ that contain at least two Higgs trilinear self-couplings or a single Higgs quartic self-coupling. The modified Higgs self-interactions are indicated by black dots. The diagrams with reversed fermion flow are omitted.
• Figure 4: Left: Cross sections for double-Higgs production in the combined ggF and VBF channels at the LHC with $\sqrt{s} = 14 \, {\rm TeV}$ as a function of $\kappa_\lambda = \kappa_3 = \kappa_4$. The black line shows the LO prediction, the green line includes QCD corrections, and the red line incorporates NLO QCD and NLO EW in ggF and N$^3$LO QCD and NLO EW in VBF, collectively referred to as QCD+EW. Right: Constraints in the $\kappa_3\space-\space\kappa_4$ plane from LHC Run 2. The red contour corresponds to the preferred $68\%$ CL region derived from the HEFT calculation of the QCD+EW corrections to double-Higgs production presented here. For comparison, the $68\%$ CL region from triple-Higgs production, as obtained by the ATLAS collaboration ATLAS:2024xcs, is shown as a black contour.
• Figure 5: Kinematic distributions for double-Higgs production in the combined ggF and VBF channels at the LHC with $\sqrt{s} = 14 \, {\rm TeV}$ for three different $\kappa_\lambda$ values, assuming $\kappa_\lambda = \kappa_3 = \kappa_4$. The black lines show the LO predictions, the green dash-dotted lines include QCD corrections, and the red dashed lines incorporate both QCD and EW corrections. The upper panels display $m_{HH}$ spectra, while the lower panels show $p_{T}^{H}$ distributions.