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Higgs Pair Production at the LHC and ILC from general potential

Higgs cubic coupling plays a crucial role to probe an origin of electroweak symmetry breaking. It is expected that the cubic coupling is measured by Higgs pair production at the LHC and ILC, and the deviations from the standard model can be extracted from the Higgs pair production process, and those can give us a hint of new physics beyond the standard model. We consider a general potential that achieves the suitable electroweak symmetry breaking. As one of the interesting models, we suggest a non-perturbative Higgs model in which a run-away type of potential is used. In the model, the cross sections of pair production at the LHC is enlarged compared to the standard model. We also study the Higgs pair production induced by a non-canonical kinetic term of Higgs fields which will be important to search the pair-production at the ILC.