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 λφ 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 → E/m 1, where m is the particle mass. Quantum corrections to the known tree-level amplitudes in this regime are characterised by the parameter λn and we show that they become large at sufficiently high multiplicities. We compute full amplitudes in the large λn 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 multiparticle 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.

The Breakdown of Resummed Perturbation Theory at High Energies

“…In addition, we remark that it matches the expectations from its quantum mechanical analogue, which corresponds to transition amplitudes in the sextic anharmonic oscillator [58]. Similar to earlier works on the high-energy behavior of ϕ 4 theory (see, e.g., [1][2][3][4][5][6][7][8][9][10]), we observe that the tree-level 1 → n amplitude for ϕ 6 theory given in (2.10) grows factorially with the number of final-state particles. 5 Therefore, at least naively, the amplitude clearly violates unitarity in the regime n → ∞, independent of the coupling λ.…”

“…Calculations of high-energy processes involving the production of a large number of particles in weakly-coupled scalar quantum field theories indicate the need for novel non-perturbative behavior or even new physical phenomena. In particular, the factorial growth of high multiplicity 1 → n amplitudes at tree level, as suggested by both perturbative [1][2][3][4][5][6][7] as well as semiclassical [8][9][10] methods, has sparked new ideas towards this pursuit. A prominent example of the latter is the "Higgsplosion" mechanism [21].…”

“…The role of perturbation theory in weakly-coupled scalar quantum field theories has previously been challenged by computations of high-energy processes involving the production of a large number of particles. High multiplicity threshold amplitudes of the form 1 → n exhibit a factorial growth for large n at tree level, as suggested by perturbative [1][2][3][4][5][6][7] as well as semiclassical [8][9][10] calculations (see also [11] for a comprehensive review of the latter). This is in strong contradiction to the requirement of unitarity for a consistent quantum theory, independent of its coupling.…”

“…While this seems to strongly contradict one of the fundamental principles of quantum physics, one should note that highenergy processes of the form 1 → n may intrinsically be non-perturbative for large n, even in a weakly-coupled theory. That is, here, a naive perturbative approach at tree level may be problematic for n 1/λ, as, for large-order perturbation theory, the effective expansion parameter λn is strongly coupled in this regime (see, e.g., [9,10]). Nevertheless, in principle, we still expect a suitable resummation of large-order perturbation theory to yield a physically meaningful answer.…”

“…2 Recently, semiclassical expansions in parameters of the form λn have also proven useful in quantum theories for the investigation of physical quantities at large quantum numbers, see, e.g., [27][28][29][30][31][32][33][34][35][36][37][38][39][40]. 3 For theories featuring a spontaneously broken symmetry the situation is more complicated, as the first quantum correction to the exponent is positive [7,9,10].…”