Induced tunneling in QFT: soliton creation in collisions of highly energetic particles

TL;DR

This paper investigates how highly energetic particle collisions induce soliton creation via tunneling in a quantum field theory, revealing different mechanisms below and above a critical energy, with tunneling remaining exponentially suppressed.

Contribution

It provides a first-principles semiclassical analysis of collision-induced tunneling across all energies, identifying the transition mechanisms and the role of real-time instantons.

Findings

Tunneling occurs below a critical energy E_c, with probability increasing with energy.

Above E_c, tunneling involves sphaleron-like states and energy release mechanisms.

Tunneling remains exponentially suppressed at all energies.

Abstract

We consider tunneling transitions between states separated by an energy barrier in a simple field theoretical model. We analyse the case of soliton creation induced by collisions of a few highly energetic particles. We present semiclassical, but otherwise first principle, study of this process at all energies of colliding particles. We find that direct tunneling to the final state occurs at energies below the critical value E_c, which is slightly higher than the barrier height. Tunneling probability grows with energy in this regime. Above the critical energy, the tunneling mechanism is different. The transition proceeds through creation of a state close to the top of the potential barrier (sphaleron) and its subsequent decay. At certain limiting energy E_l tunneling probability ceases to grow. At higher energies the dominant mechanism of transition becomes the release of energy excess E-E_l by the emission of a few particles and then tunneling at effectively lower energy E=E_l via the limiting semiclassical configuration. The latter belongs to a class of ``real--time instantons'', semiclassical solutions saturating the inclusive probability of tunneling from initial states with given number of particles. We conclude that the process of collision--induced tunneling is exponentially suppressed at all energies.