Multiparticle production in $\lambda\phi^4$ theory: the method of singular solutions and numerical results

The report is devoted to the probabilities of the production of $n\gg1$ particles from several ones colliding in the (3+1)-dimensional $\lambda\phi^4$ theory without spontaneous symmetry breaking. In the weak coupling mode $\lambda\ll 1$, they can be calculated using the quasi-classical method of singular solutions. We numerically implemented this method and for the first time obtained reliable results for probabilities in the region of an exceptionally large number of particles in the final state $\lambda n\gg 1$, where the probability decreases exponentially with increasing $n$. The exponent depends linearly on $n$, and its slope depends on the average kinetic energy $\epsilon$ of the produced particles. In the opposite limit $\lambda n\ll 1$, our numerical data coincide with the known tree results, and the transition region $\lambda n\sim 1$ interpolates between them. Thus, the results obtained prove exponential suppression of the probability of multiparticle production in the theory under consideration for an arbitrary $\epsilon$. The report will cover both the singular solutions method itself and its numerical implementation, as well as the results obtained.