Probing the Higgs potential at a Photon Collider

TL;DR

This work investigates probing the Higgs potential through Higgs-pair production at a γγ collider, comparing optical-laser and XFEL-based (XCC) implementations and their compatibility with an $e^+e^-$ collider. It derives and analyzes the partonic cross-sections for γγ→hh, incorporating the trilinear Higgs self-coupling modifier $κ_λ$ and the gauge-structure modifier $κ_{2V}$, and combines these with CAIN-based luminosity spectra to produce collider-level projections. The results show pronounced sensitivity to $κ_λ$ near $√s_{γγ} ≈ 280$ GeV, with XFCC options yielding order-of-magnitude higher event rates than optical setups, enabling κ_λ determinations at about 5% across most allowed ranges (assuming $κ_{2V}=1$). The γγ approach provides complementary information to HL-LHC and future $e^+e^-$ programs and may offer cost or feasibility advantages, underscoring the value of pursuing γγ-collider options alongside conventional collider facilities.

Abstract

A $γγ$ collider, either in conjunction with an $e^+e^-$ linear collider or as a stand-alone facility, offers a very attractive Higgs physics programme at relatively low centre-of-mass (c.m.) energies. While the Higgs boson that has been discovered at the LHC can be studied in detail in resonant production at 125~GeV, a c.m.\ energy as low as 280~GeV can probe the Higgs potential via the Higgs pair production process providing access to the trilinear Higgs-boson self-coupling. High polarisation of the photon beams (produced via Compton back-scattering) can be achieved and adjusted by flipping the polarisation of the incident laser. The prospects for exploring the Higgs pair production process at a $γγ$ collider are assessed by comparing different running scenarios utilising different types of the incident laser. The possibility to use photon polarisations for disentangling different kinds of contributions to the Higgs pair production process is emphasised.

Figures (4)

• Figure 1: Representative Feynman diagrams for the process $\gamma\gamma\to hh$. The upper row shows diagrams involving top-quark loops, while the diagrams in the lower row correspond to gauge-sector contributions.
• Figure 2: Higgs pair production cross section (at the partonic level) as a function of the photon-photon c.m. energy $\sqrt{s_{\gamma\gamma}}$. The orange lines indicate results for $\hat{\sigma}_{++}$ (i.e. $J_z=0$) for different values of $\kappa_\lambda$, while the green line shows the result for $\hat{\sigma}_{+-}$ (i.e. $J_z=2$). Right: Predictions for the unpolarised partonic cross-section for $\gamma\gamma\to hh$, defined as $(\hat{\sigma}_{++}+\hat{\sigma}_{+-})/2$, normalised to its value in the SM, shown as contours in the plane of $\kappa_\lambda$ and $\kappa_{2V}$, for $\sqrt{s_{\gamma\gamma}}=280\text{ GeV}$. The blue line indicates the current ATLAS limits at the 95% C.L. ATLAS:2024ish.
• Figure 3: The luminosity spectrum for the photon collider using an optical laser at a 380 GeV $e^-e^-$-collider (left), for the XCC at a 280 GeV $e^-e^-$-collider (centre) and for an optical photon collider at a 380 GeV $e^+e^-$-collider (right), showing the total (blue), $J_z=0$ (orange) and $J_z=2$ (green) luminosity spectra. Calculated with CAIN using a beam setup adapted from the ILC design Bechtel:2006mr, with the new parameters given in tables 23 and 24 of Ref. LinearColliderVision:2025hlt.
• Figure 4: Number of Higgs pair production events at different options of $\gamma\gamma$ colliders as a fuction of $\kappa_\lambda$. The blue and orange lines indicate the results for XCC options with $E_{e^-e^-}=280$ GeV and 380 GeV, respectively. The green and red lines correspond to optical laser based colliders with $E_{e^-e^-}=$ 380 GeV and 550 GeV, respectively.