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Semiclassical Calculation of Multiparticle Scattering Cross Sections in Classicalizing Theories

It has been suggested in arXiv:1010.1415 that certain derivatively coupled non-renormalizable scalar field theories might restore the perturbative unitarity of high energy hard scatterings by classicalization, i.e. formation of multiparticle states of soft quanta. Here we apply the semiclassical method of calculating the multiparticle production rates to the scalar Dirac-Born-Infeld (DBI) theory which is suggested to classicalize. We find that the semiclassical method is applicable for the energies in the final state above the cutoff scale of the theory L_*^{-1}. We encounter that the cross section of the process two to N ceases to be exponentially suppressed for the particle number in the final state N smaller than a critical particle number N_{crit} ~ (E L_*)^{4/3}. It coincides with the typical particle number produced in two-particle collisions at high energies predicted by classicalization arguments.