High-energy limit of collision-induced false vacuum decay

Abstract

We develop a consistent semiclassical description of field-theoretic collision-induced tunneling at arbitrary high collision energies. As a playground we consider a (1+1)-dimensional false vacuum decay initiated by a collision of N particles at energy E, paying special attention to the realistic case of N=2 particles. We demonstrate that the cross section of this process is exponentially suppressed at all energies. Moreover, the respective suppressesion exponent F_N(E) exhibits a specific behavior which is significant for our semiclassical method and assumed to be general: it decreases with energy, reaches absolute minimum F=F_min(N) at a certain threshold energy E=E_rt(N), and stays constant at higher energies. We show that the minimal suppression F_min(N) and threshold energy can be evaluated using a special class of semiclassical solutions which describe exponentially suppressed transitions but nevertheless evolve in real time. Importantly, we argue that the cross section at energies above E_rt(N) is computed perturbatively in the background of the latter solutions, and the terms of this perturbative expansion stay bounded in the infinite-energy limit. Transitions in the high-energy regime proceed via emission of many soft quanta with total energy E_rt; the energy excess E-E_rt remains in the colliding particles till the end of the process.