Formation of theQball in the thermal logarithmic potential and its properties

Abstract

We investigate the $Q$-ball formation in the thermal logarithmic potential by means of the lattice simulation, and reconfirm qualitatively the relation between $Q$-ball charge and the amplitude of the Affleck-Dine field at the onset of its oscillation. We find time dependence of some properties of the $Q$ ball, such as its size and the field value at its center. Since the thermal logarithmic potential decreases as the temperature falls down, the gravity-mediation potential will affect the properties of the $Q$ ball. Even in the case when the gravity-mediation potential alone does not allow $Q$-ball solution, we find the transformation from the thick-wall type of the $Q$ ball to the thin-wall type, contrary to the naive expectation that the $Q$ balls will be destroyed immediately when the gravity-mediation potential becomes dominant at the center of the $Q$ ball.