Probing the symmetric Higgs portal with di-Higgs boson production

A coupling of a scalar, charged under an unbroken global $U(1)$ symmetry, to the Standard Model via the Higgs portal is one of the simplest gateways to a dark sector. Yet, for masses $m_S\ge m_H/2$ there are few probes of such an interaction. In this note, we evaluate the sensitivity to the Higgs portal coupling of di-Higgs boson production at the LHC as well as at a future high-energy hadron collider, FCC-hh, taking into account the full momentum dependence of the process. This significantly impacts the sensitivity compared to estimates of changes in the Higgs coupling based on the effective potential. We also compare our findings to precision single Higgs-boson probes such as the cross section for vector-boson-associated Higgs production at a future lepton collider, e.g., FCC-ee, as well as searches for missing energy-based signatures.

Figure 1

Representative leading-order Feynman topologies contributing to $gg\to HH$ production.

Figure 2

One-loop contribution to $s$-channel $gg\to HH$ production. The shaded area represents the remainder (one-loop top insertion part) of the amplitude.

Figure 3

Counterterm contribution to $s$-channel $gg\to HH$ production. The shaded area represents the remainder of the amplitude as in Fig. 2.

Figure 4

Counterterm contribution to the box graphs of $gg\to HH$ production. The shaded area represents the remainder (one-loop top insertion part) of the box amplitude.

Figure 5

(a) Comparison of the imaginary and the real parts of the three-point function $\mathrm{\Gamma }$ for ($\lambda =1$) relative to SM ($\lambda =0$) as a function of the invariant di-Higgs mass $\sqrt{s}=m_{HH}$. The turn-on of absorptive parts is visible for $m_S=400\mathrm{GeV}$ at $\sqrt{s}=m_{HH}=2m_S=800\mathrm{GeV}$. (b) The modulus of the three-point function relative to the SM as a function of $m_S$ (again for $\lambda =1$) for fixed $\sqrt{s}=400\mathrm{GeV}$, which only allows us to resolve thresholds for up to $\sqrt{s}/2$.

Figure 6

Comparison of the cross section as a function of $\lambda$ for different approximations, $m_S=95\mathrm{GeV}$ and $\sqrt{s}=100\mathrm{TeV}$; for details, see text.

Figure 7

Invariant di-Higgs mass spectra relative to the SM and 6% self-coupling extraction as described in Ref. [24].

Figure 8

Sensitivity projections for the di-Higgs boson production as well as other approaches. LHC di-Higgs results are shown as the red dashed line. For FCC-hh (100 TeV, 30/ab), we show as the solid (dashed) line the sensitivities obtainable from di-Higgs boson production based on a calculation without (with) terms $\sim |{\mathcal{M}}_{\mathrm{virt}}{|}^2$. The blue region shows the intersection of these two calculations and is in this sense conservative. The green dashed line shows the sensitivity expected from a simple effective potential approximation for the self-coupling [7, 21]. The red, orange, and yellow regions correspond to the 1.7%, 1.06%, and 0.5% measurements [50] of the cross section of vector-boson-associated Higgs boson production at the future ILC-250 (International Linear Collider at 250 GeV), CLIC-380 (Compact Linear Collider at 380 GeV) and FCC-ee (electron-positron option of the FCC at 240 GeV), respectively. Finally, the light-green region indicates the best sensitivity curve from missing energy searches according to Ref. [8]. Regions where the electroweak vacuum is potentially endangered, obtained in Ref. [7], are shown in gray.