Numerical Study of Induced False Vacuum Decay at High Energies

Abstract

We calculate numerically the probability $\exp [\frac{1}{\lambda }F(E/E_{sph},N/N_{sph})]$ of the false vacuum decay in the massive four-dimensional $-\lambda {\varphi }^4$ model from multiparticle initial states with fixed number of particles $N$ and energy $E$ greater than the height of the barrier $E_{sph}$. We find that at $E\text{lsim}3E_{sph}$ and $N\text{lsim}0.4N_{sph}$ the decay is classically forbidden and thus is exponentially suppressed. We argue that the classically forbidden region extends at small $N$ at least up to $E\sim 10E_{sph}$ and, most likely, to all energies. Our data suggest that the false vacuum decay induced by two-particle collisions is exponentially suppressed at all energies.

Comments: 14 pages, latex, 4 PostScript figures, Factor of 2 normalization error propagating through some equations and few misprints corrected