Problems with Higgsplosion

A recent calculation of the multi-Higgs boson production in scalar theories with spontaneous symmetry breaking has demonstrated the fast growth of the cross section with the Higgs multiplicity at sufficiently large energies, called “Higgsplosion.” It was argued that Higgsplosion solves the Higgs hierarchy and fine-tuning problems. In our paper we argue that: (a) the formula for Higgsplosion has a limited applicability and inconsistent with unitarity of the Standard Model; (b) that the contribution from Higgsplosion to the imaginary part of the Higgs boson propagator cannot be re-summed in order to furnish a solution of the Higgs hierarchy and fine-tuning problems.