Classifying extended Higgs models through the trilinear Higgs boson coupling measurement at future colliders

TL;DR

This work addresses how to distinguish extended Higgs sector scenarios by measuring the trilinear Higgs coupling $\lambda_{hhh}$ (via $\kappa_{\lambda}$) at future colliders. It classifies Higgs potentials by their functional forms in the broken phase and derives one-loop expressions for $\lambda_{hhh}$ in several frameworks, including naHEFT with dimension-six operators, CSI models, pNGB/MCHM scenarios, and tadpole-induced models, while incorporating top-quark and new-particle loop effects. The study finds that CSI and tadpole-induced models can produce sizable, potentially observable deviations in $\kappa_{\lambda}$ at planned facilities (HL-LHC, ILC, muon collider, 100 TeV pp), whereas some pNGB and SMEFT scenarios remain challenging to probe directly, with gravitational-wave signals offering a complementary probe of the underlying Higgs potential and EW phase transition. The results underscore a multi-pronged approach—collider measurements of $\kappa_{\lambda}$ together with gravitational-wave observations—to discriminate the dynamics of electroweak symmetry breaking and the global structure of the Higgs potential.

Abstract

We investigate the trilinear Higgs boson coupling derived from the functional forms of various extended Higgs potentials. In light of experimental constraints on Higgs boson couplings, we focus on extended Higgs models in which the trilinear Higgs boson coupling is predominantly determined by the Standard Model (SM) Higgs field. Such models include the nearly aligned Higgs effective field theory, classically scale-invariant models, pseudo-Nambu-Goldstone boson scenarios, tadpole-induced models, and others. We also consider higher-order corrections, including top quark and new particle contributions that are often neglected, and discuss their impact on the trilinear Higgs boson coupling. Finally, we show to what extent the functional forms of the Higgs potentials can be probed at future colliders.

Figures (5)

• Figure 1: Contours of $A / f_{}^{4}$ obtained from the vacuum and mass conditions in Eq. \ref{['eq:MCHM4higher_VEV&Mass']}. In the perturbative regime for $A$, the range $-0.12 < C / f_{}^{4} < 0.19$ is allowed.
• Figure 2: Contours of $B$ from the mass condition in Eq. (\ref{['eq:MCHM4higher_VEV&Mass']}). We consider the region where $\xi < 0.1$. At $\xi = 0.1$, the magnitude of $B / f_{}^{4}$ must be roughly three times larger than that of $C / f_{}^{4}$. For positive $B / f_{}^{4}$, one finds $C / f_{}^{4} \lesssim 0.04$.
• Figure 3: Allowed parameter region of MCHM4$_{(1)}$ including higher-order corrections, under the (expected) constraint on $\kappa_{\lambda}$ from the LHC and future collider experiments. The solid, dashed, and dotted contours represent the allowed regions in light of the results from the LHC Run 2, the HL-LHC, and the ILC with $\sqrt{s}=\qty{1}{\TeV}$. The gray-shaded area corresponds to the region where $\xi > 0.1$.
• Figure 4: The potential shapes of the tadpole-induced model at the one-loop level, assuming $\lambda=0$ (solid), $0.005$ (dashed), and $0.1$ (dotted).
• Figure 5: Benchmark study on the one-loop predictions for the trilinear Higgs boson coupling $\kappa_\lambda$ in various extended Higgs models. Each point corresponds to a different model: the SM, extended models with dimension-six operators, the O($N$) scalar singlet model, the CSI model, MCHM4 without $\sin_{}^{4} (\phi / f)$ term, MCHM4 with $\sin_{}^{4} (\phi / f)$ term, MCHM5, and the tadpole-induced model (Tadpole), from left to right. We show benchmark cases of $D = 0.1~\mathrm{TeV}_{}^{-2}$ for the dimension-six model, $N = 1$ and $m_{S}^{} = \qty{500}{\GeV}$ for the O($N$), $\xi = 0.1$ for MCHM4$_{(0)}$ and MCHM5, $(\xi, C / f_{}^{4}) = (0.1, \, 0.1)$ for MCHM4$_{(1)}$, $\lambda = 0$ for the tadpole-induced model. The shaded regions in yellow, cyan, magenta, and green indicate the $1 \sigma$ regions for $\kappa_{\lambda}^{\mathrm{exp}} = 1$ at HL-LHC (ATLAS), ILC 1, muon Collider, and 100$pp$ Collider, respectively.