  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.
