Semiclassical calculation of multiparticle scattering cross sections in classicalizing theories

It has been suggested that certain derivatively coupled nonrenormalizable 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 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 2→N ceases to be exponentially suppressed for the particle number in the final state N smaller than a critical particle number N _crit∼(EL _*)4 ^/3. It coincides with the typical particle number produced in two-particle collisions at high energies predicted by classicalization arguments.