Q-balls from thermal balls during a first-order phase transition: a numerical study

We numerically study the Q-ball formation triggered by a cosmological first-order phase transition within the Friedberg-Lee-Sirlin model. By performing lattice simulations, we track the nonequilibrium dynamics throughout the transition, providing a precise description of the Q-ball formation mechanism and the resulting mass spectrum. Collapsing false-vacuum regions first form thermal balls, which subsequently cool via dissipative interactions and stabilize into long-lived Q-balls with nonzero spin. We observe a large population of low-mass Q-balls, as well as rare, massive Q-balls that are several times larger than the analytical prediction. The final Q-ball population exhibits a broad mass spectrum spanning over two orders of magnitude, characterized by an exponential tail of number density at large masses. The simulations suggest that the Q-ball abundance is approximately $50\%$ higher than predicted by analytical estimates, adjusting the result in the context of Q-balls as dark matter candidates.