Q-balls without a potential

We study nontopological Q-ball solutions of the (3 + 1)-dimensional Friedberg-Lee-Sirlin two-component model. The limiting case of the vanishing potential term yields an example of hairy Q-balls, which possess a long-range massless real field. We discuss the properties of these stationary field configurations and determine their domain of existence. Considering the Friedberg-Lee-Sirlin model, we present numerical evidence for the existence of spinning axially symmetric Q-balls with different parity. A solution of this type exists also in the limiting case of vanishing scalar potential. We find that the hairy Q-balls are classically stable for all range of values of angular frequency.