Towards the correspondence between Q-clouds and sphalerons

TL;DR

This paper explores the relationship between Q-clouds and sphalerons in non-linear classical field theories, proposing that Q-clouds act as sphalerons mediating transitions between stable Q-balls and condensates, with a focus on analytic solutions and quantum production rates.

Contribution

It establishes a theoretical connection between Q-clouds and sphalerons, providing analytic formulas for quantum Q-ball production at high temperatures.

Findings

Q-clouds correspond to sphalerons between Q-balls and condensates

Derived Arrhenius formula for quantum Q-ball production

Analytic solutions illustrating the transition mechanism

Abstract

Non-linear classical equations of motion may admit degenerate solutions at fixed charges. While the solutions with lower energies are classically stable, the ones with larger energies are unstable and refereed as Q-clouds. We consider a theory in which the homogeneous charged condensate is classically stable and argue that Q-clouds correspond to sphalerons between the stable Q-balls and the condensate. For the model with analytic solution, we present Arrhenius formula for the quantum production of Q-balls from the condensate at large temperatures.