Q-ball decay through A-term in the gauge-mediated SUSY breaking scenario

Q-balls are non-topological solitons whose classical stability is ensured by a global $U(1)$ charge. In particular, Q-balls are produced in the framework of the Affleck-Dine baryogenesis where $U(1)$ charge is the baryon number. Since some type of Q-balls is stable against quantum decay into nucleons, it can work as the dark matter. When the dark matter Q-balls are captured into the neutron star, they absorb the surrounding neutrons and grow to consume all the neutrons, which leads to a stringent constraint on the Q-ball dark matter. However, the Q-ball growth stops due to the $U(1)$ breaking A-term. We revisit the constraint by the neutron star for the gauge-mediation type and the new type Q-ball, and find the allowed parameter space, in which Q-balls work as the dark matter.