Higgs Self-Coupling in gamma-gamma Collisions
  To establish the Higgs mechanism experimentally, one has to determine the Higgs self-interaction potential responsible for the electroweak symmetry breaking. This requires a measurement of the trilinear and quadrilinear self-couplings of the Higgs particle, as predicted by the Standard Model (SM). We propose to measure the trilinear Higgs self-coupling in gamma-gamma collisions just above the kinematic threshold E_thr = 2M_H, where M_H is the Higgs mass. Our calculation reveals that the sensitivity of the cross-section sigma(gamma gamma -> HH) to the Higgs self-coupling is maximal near the 2M_H threshold for M_H = 115-150 GeV, and is larger than the sensitivities of sigma(e+e- -> ZHH) and sigma(e+e- -> nu nu HH) to this coupling for 2E_e < 700 GeV. We envisage to (a) study gamma gamma -> H by constructing an X-band e-e- linac and a terawatt laser system in order to produce Compton-scattered gamma-ray beams for a 160-GeV photon collider (2E_e = 200 GeV); (b) add a positron source and repeat all measurements done at LEP and SLC with much better precision; and (c) subsequently install 70-MeV/m rf cavities in order to study e+e- -> H+Z, e+e- -> tt and gamma gamma -> H+H at 2E_e = 350 GeV. The total length of the linac would be about 7 km. 
R. Belusevic, G. Jikia