Analytical and numerical properties of Affleck-Dine condensate formation

TL;DR

This paper investigates the analytical and numerical characteristics of the Affleck-Dine condensate, focusing on pressure behavior, orbit ellipticity effects, and the conditions for Q-ball formation and equilibration.

Contribution

It provides new insights into how orbit ellipticity influences pressure and the conditions under which Q-balls equilibrate after condensate fragmentation.

Findings

Pressure is zero for circular orbits and most negative for oscillating fields.

Ellipticity affects the pressure and stability of the condensate.

Equilibration of Q-balls depends on the energy-to-charge ratio, with a specific range identified.

Abstract

We present analytical and numerical properties of the coherently rotating Affleck-Dine condensate formed along MSSM flat directions with the radiative corrections to the mass terms included. We analyse the pressure $p$ of the condensate, which is known to be negative if the potential grows slower than the field squared. We show that ellipticity of the orbit of the rotating field also affects the pressure. For circularly orbiting field the $p=0$ while the smallest negative value, corresponding to the most unstable configuration, is obtained for a coherently oscillating field. The AD condensate is known to fragment into non-topological solitons called Q-balls. We also study equilibration of Q-ball distribution resulting from the fragmentation of the condensate analytically. We find that equilibration is dependent on the energy-to-charge ratio $x$ of the condensate. We find the allowed range of $x$ numerically and deduce that equilibration is likely to happen.