Semiclassical computation of quantum effects in multiparticle production at large lambda n

Abstract

We use the semiclassical formalism based on singular solutions in complex time to compute scattering rates for multiparticle production at high energies. In a weakly coupled $\lambda \phi^4$ scalar field theory in four dimensions, we consider scattering processes where the number of particles $n$ in the final state approaches its maximal value $n \to E/m \gg 1$, where $m$ is the particle mass. Quantum corrections to the known tree-level amplitudes in this regime are characterised by the parameter $\lambda n$ and we show that they become large at sufficiently high multiplicities. We compute full amplitudes in the large $\lambda n$ limit on multiparticle mass thresholds using the thin-wall realisation of the singular solutions in the WKB approach. We show that the scalar theory with spontaneous symmetry breaking, used here as a simplified model for the Higgs sector, leads to exponentially growing multi-particle rates within our regime which is likely to realise the high-energy Higgsplosion phenomenon. We also comment on realisation of Higgsplosion in dimensions lower than four.