Abstract
Abstract It has been recently proposed by Dvali et al. [1] that high energy scattering in non-renormalizable theories, like the higgsless Standard Model, can be unitarized by the formation of classical configurations called classicalons. In this work we argue that clas- sicalons should have analogs of thermodynamic properties like temperature and entropy and perform a model-independent statistical mechanical analysis of classicalon decays. We find that, in the case of massless quanta, the decay products have a Planck distribution with an effective temperature $$ {\text{T}}\sim {1}/{{\text{r}}_{*}} $$ , where r ∗ is the classicalon radius. These results, in particular a computation of the decay multiplicity, N ∗, allow us to make the first collider analysis of classicalization. In the model for unitarization of WW scattering by classical- ization of longitudinal Ws and Zs we get spectacular multi-W/Z final states that decay into leptons, missing energy and a very high multiplicity (at least 10) of jets. We find that for the classicalization scale, $$ {M_{ * }} = \upsilon = {246}\, {\text{GeV}}({{\text{M}}_{ * }} = {\text{1TeV}}) $$ discovery should be possible in the present 7 TeV (14 TeV) run of the LHC with about 10 fb−1 (100 fb−1) data. We also consider a model to solve the hierarchy problem, where the classicalons are configurations of the Higgs field which decay into to multi-Higgs boson final states. We find that, in this case, for M ∗ = 500 GeV (M ∗ = 1 TeV), discovery should be possible in the top fusion process with about 10 fb−1 (100 fb−1) data at 14 TeV LHC.
Highlights
Particles and decays to two particles are suppressed leading to a suppression of the 2→2 scattering amplitudes
What about the transverse length of the wave-packets? In the transverse direction the wave-packets can have a length much bigger than r∗. This leads to the existence of a field outside the classicalon radius r∗ when the wave-packets superpose at the origin at t = 0, as is clear from figure 2(right), but, as we show in appendix A, the field outside the classicalon radius drops off as φ ∼ 1/r so that most of the energy is still inside the classicalon radius r∗
We have argued that classicalons must have analogs of thermodynamic properties and we have carried out a model-independent statistical mechanical analysis of classicalons
Summary
We will describe a more precise formulation of the intuitive picture in figure 1 and obtain quantitative results. In theories that exhibit classicalization, in addition to the free l√agrangian there are non-linear self-sourcing terms which are important only if the energy sgets localized in a radius√r∗ given by eq (1.3). This leads to the formation of a classical configuration of mass M = swhich decays into many particles. The combinatoric exercise of counting the number of ways of choosing these four vectors such that the energy adds up to the classicalon mass would be very similar to the statistical mechanical analysis of ideal Bose gasses or blackbody radiation. The wave-packets must have a size and shape such that the second condition is satisfied and this leads to a density of states function different from the blackbody radiation case. We will see what the condition for localization of the energy inside the radius r∗ tells us about the geometry of the incoming wave-packets
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