Double Higgs Production at the Linear Colliders and the Probing of the Higgs Self-Coupling

TL;DR

This paper analyzes double Higgs production at TeV-scale linear colliders to probe the Higgs self-coupling $h_3$ and the scalar potential. It combines a detailed tree-level study of $\gamma\gamma\to W^+W^-HH$ with a structure-function (effective $W$) approach to $WW$ fusion, and introduces a generalized non-linear gauge fixing that simplifies multiparticle electroweak amplitudes and connects to background-field methods. The results show small cross sections overall, with $e^+e^-$ colliders typically offering better sensitivity for a light Higgs, while the $\gamma\gamma$ mode becomes competitive for heavier Higgs; sensitivity to $h_3$ can reach about 10% for $M_H\sim100$ GeV, with complementary channels across Higgs masses. The work demonstrates the feasibility of probing the scalar potential at future linear colliders, provides practical guidance on polarization, spectra, and gauge choices, and delivers full Feynman rules in the Appendix for the generalized nonlinear gauge.

Abstract

We study double Higgs production in the $e^+ e^-$ and $γγ$ modes of the linear collider. It is also shown how one can probe the scalar potential in these reactions. We discuss the effective longitudinal $W$ approximation in $γγ$ processes and the $W_L W_L$ luminosities in the two modes of a high-energy linear collider. A generalised non-linear gauge-fixing condition, which is particularly useful for tree-level calculations of electroweak processes for the laser induced collider, is presented. Its connection with the background-field approach to gauge fixing is given.

Figures (26)

• Figure 1: Representative diagrams that contribute to $e^{+} e^{-}\; \rightarrow ZHH$ and $e^{+} e^{-} \rightarrow \nu_e \bar{\nu}_e HH\;$.
• Figure 2: Different topologies of Feynman diagrams contributing to $\gamma \gamma \rightarrow W^+ W^- H H\;$ in the unitary gauge. Figures (1a), (2) and (3) are the fusion type diagrams. All others can be considered bremstrahlung. (1a-c) contain the triple Higgs vertex.
• Figure 3: Some extra topologies of Feynman diagrams that have to be added in a renormalisable gauge even when the $W^\pm \varphi^\mp \gamma$ is absent. The last 4 topologies are cancelled with the gauge-fixing that we take.
• Figure 4: Contribution of the different polarisation states of the $W$'s.
• Figure 5: Contribution of the $J_Z=0$ and $J_Z=2$ to the total cross section.