| Summary: | Abstract In a scalar theory which we use as a simplified model for the Higgs sector, we adopt the semiclassical formalism of Son for computations of n-particle production cross-sections in the high-multiplicity n → ∞ weak-coupling λ → 0 regime with the value of λn held fixed and large. The approach relies on the use of singular classical solutions to a certain boundary value problem. In the past this formalism has been successfully used and verified in computations of perturbative multi-particle processes at tree-level, and also at the next-to-leading order level in the small λn expansion near the multi-particle mass threshold. We apply this singular solutions formalism in the regime of ultra-high multiplicities where λn ≫ 1, and compute the leading positive ∼ n λ n $$ \sqrt{\lambda n} $$ contribution to the exponent of the multi-particle rate in this large λn limit. The computation is carried out near the multi-particle mass threshold where the multiplicity n approaches its maximal value allowed by kinematics. This calculation relies on the idea of Gorsky and Voloshin to use a thin wall approximation for the singular solutions that resemble critical bubbles. This approximation is justified in precisely the high-multiplicity λ n → ∞ $$ \sqrt{\lambda n}\to\ \infty $$ regime of interest. Based on our results we show that the scalar theory with a spontaneous symmetry breaking used here as a simplified model for the Higgs sector, is very likely to realise the high-energy Higgsplosion phenomenon.
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