Numerical study of multiparticle production in $\lambda\phi^4$ theory

TL;DR

This paper investigates multiparticle production in a four-dimensional $mbda\u03c6^4$ theory, revealing exponential suppression of probabilities at large multiplicities and the dominance of loop effects beyond a certain threshold.

Contribution

It introduces a semiclassical approach to analyze multiparticle production, demonstrating the exponential suppression and the transition to loop-dominated regimes at high multiplicities.

Findings

Probabilities are exponentially suppressed for large multiplicities at small coupling.

At multiplicities much larger than the inverse coupling, loop effects dominate.

First demonstration of exponential decrease of probabilities with multiplicity in this regime.

Abstract

We study multiparticle production in the unbroken $(3+1)$-dimensional $\lambda\phi^4$ theory using the semiclassical method of singular solutions. We show that the probabilities of these processes are exponentially suppressed in terms of a small coupling constant $\lambda \ll 1$ if the multiplicity of the final state is large: $n \gg 1$. At $ n \ll \lambda^{-1}$ the probabilities agree with well-known perturbative results. At $ n \gg \lambda^{-1}$ they are dominated by loop effects and decrease exponentially with $n$, as we show for the first time.