Probing the Higgs potential at a Photon Collider

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.