Revisiting the gravitino dark matter and baryon asymmetry from Q-ball decay in gauge mediation

We reconsider the Q-ball decay and reinvestigate the scenario that the amount of the baryons and the gravitino dark matter is naturally explained by the decay of the Q balls in the gauge-mediated SUSY breaking. We refine the decay rates into baryons, NLSPs, and gravitinos, and estimate their branching ratios based on the consideration of Pauli blocking. We obtain a smaller branching into gravitinos than the previous estimate, and the NLSPs are more produced by the Q-ball decay. However, the efficient annihilations of NLSPs occur afterward so that their abundance does not spoil the successful BBN and they only produce negligible amount of the gravitinos to the dark matter density by their decay. In this way, we find that the scenario with the direct production of the gravitino dark matter from the Q-ball decay works naturally.