On the Determination of the Higgs Self-Coupling from Photon–Photon Collisions

We propose a laser--plasma $\gamma\gamma$ collider concept to probe the Higgs trilinear self-coupling through double-Higgs production in polarized photon--photon collisions. Two staged wakefield linacs accelerate electron bunches to energy $E_e$ and collide them with conversion lasers at upstream conversion points (CPs), generating collimated high-energy photon beams by Compton backscattering without positrons. The physics reach is controlled by the effective high-energy, $J_z=0$ polarized luminosity, take the high-energy part of the photon-collision beam, and count only the portion whose photon helicities are aligned in the way that gives the strongest sensitivity to $\kappa_\lambda$. We connect $\Delta\kappa_\lambda$ to $L_{0,\mathrm{HE}}$, beam quality, conversion efficiency, and detector performance, and outline a feasibility-driven R\&D path with collider-tier CP tests and a separate extreme-intensity ultrafast-laser validation line for strong-field and background benchmarking.