Entropy production by Q-ball decay for diluting long-lived charged particles

The cosmic abundance of a long-lived charged particle such as a stau is tightly constrained by the catalyzed big bang nucleosynthesis. One of the ways to evade the constraints is to dilute those particles by a huge entropy production. We evaluate the dilution factor in a case that non-relativistic matter dominates the energy density of the universe and decays with large entropy production. We find that large Q balls can do the job, which is naturally produced in the gauge-mediated supersymmetry breaking scenario.