Non-Perturbative Production of Multi-Boson States and Quantum Bubbles

Abstract

The amplitude of production of $n$ on-mass-shell scalar bosons by a highly virtual field $ϕ$ is considered in a $λϕ^4$ theory with weak coupling $λ$ and spontaneously broken symmetry. The amplitude of this process is known to have an $n!$ growth when the produced bosons are exactly at rest. Here it is shown that for $n \gg 1/λ$ the process goes through `quantum bubbles', i.e. quantized droplets of a different vacuum phase, which are non-perturbative resonant states of the field $ϕ$. The bubbles provide a form factor for the production amplitude, which rapidly decreases above the threshold. As a result the probability of the process may be heavily suppressed and may decrease with energy $E$ as $\exp (-const \cdot E^a)$, where the power $a$ depends on the number of space dimensions. Also discussed are the quantized states of bubbles and the amplitudes of their formation and decay.