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 FN(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=Fmin(N) at a certain threshold energy E=Ert(N), and stays constant at higher energies. We show that the minimal suppression Fmin(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 Ert(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 Ert; the energy excess E-Ert remains in the colliding particles till the end of the process.