Explosive production of Higgs particles and implications for heavy dark matter

It is widely believed that the parameter space for Higgs-portal dark matter that achieves the relic abundance through thermal freeze-out has already been tightly constrained, typically at masses on the order of ${\cal O}(10-100)$ GeV. We point out the possibility that the multiple Higgs production due to its self-interaction dramatically changes this picture. We show that the multiplicity can be as large as ${\cal O}(200)$ for the parameters of the Standard Model Higgs, independently of the kinematics of the particle production process. Consequently, heavy Higgs-portal dark matter of $m_\chi\gtrsim{\cal O}(1)$ TeV can achieve the required relic abundance in the same mechanism with that for canonical weakly interacting massive particle models.