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. We propose that the trilinear Higgs self-coupling be measured in the process {gamma}{gamma}{yields}HH just above the kinematic threshold of 2M{sub H}, where M{sub H} is the Higgs mass. Our calculation shows that the statistical sensitivity of the cross section {sigma}{sub {gamma}}{sub {gamma}}{sub {yields}}{sub HH} to the Higgs self-coupling is maximal near the 2M{sub H} threshold for M{sub H} between 115 and 150 GeV, and is larger than the statistical sensitivities of {sigma}{sub e{sup +}}{sub e{sup (->)}}{sub ZHH} and {sigma}{sub e{sup +}}{sub e{sup (->)}{sub {nu}}{sub {nu}}{sub HH} to this coupling for 2E{sub e}{<=}700 GeV.