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      Problems with Higgsplosion

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          Abstract

          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.

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          Non-Perturbative Production of Multi-Boson States and Quantum Bubbles

          M. B. Voloshin, A. Gorsky (1993)
          The amplitude of production of \(n\) on-mass-shell scalar bosons by a highly virtual field \(\phi\) is considered in a \(\lambda \phi^4\) theory with weak coupling \(\lambda\) and spontaneously broken symmetry. The amplitude of this process is known to have an \(n!\) growth when the produced bosons are exactly at rest. Here it is shown that for \(n \gg 1/\lambda\) the process goes through `quantum bubbles', i.e. quantized droplets of a different vacuum phase, which are non-perturbative resonant states of the field \(\phi\). The bubbles provide a form factor for the production amplitude, which rapidly decreases above the threshold. As a result the probability of the process may be heavily suppressed and may decrease with energy \(E\) as \(\exp (-const \cdot E^a)\), where the power \(a\) depends on the number of space dimensions. Also discussed are the quantized states of bubbles and the amplitudes of their formation and decay.
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            Breakdown of perturbation theory at tree level in theories with scalars

            Haim Goldberg (1990)
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              Semiclassical approach for multiparticle production in scalar theories

              D. Son (1995)
              We propose a semiclassical approach to calculate multiparticle cross sections in scalar theories, which have been strongly argued to have the exponential form \(\exp(\lambda^{-1}F(\lambda n,\epsilon))\) in the regime \(\lambda\to0\), \(\lambda n\), \(\epsilon=\) fixed, where \(\lambda\) is the scalar coupling, \(n\) is the number of produced particles, and \(\epsilon\) is the kinetic energy per final particle. The formalism is based on singular solutions to the field equation, which satisfy certain boundary and extremizing conditions. At low multiplicities and small kinetic energies per final particle we reproduce in the framework of this formalism the main perturbative results. We also obtain a lower bound on the tree--level cross section in the ultra--relativistic regime.
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                Author and article information

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                Publication date Created: 16 August 2018
                Article
                ArXiV ID: 1808.05641
                SO-VID: f6184449-5ddf-4418-adb5-d28f0d8bd9d1
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                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Categories hep-ph hep-th

                ScienceOpen disciplines: High energy & Particle physics
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                ScienceOpen disciplines: High energy & Particle physics

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