Q ball Decay Rates into Gravitinos and Quarks

The Affleck-Dine mechanism, which is one of the most attractive candidates for the baryogenesis in supersymmetric theories, often predicts the existence of baryonic Q balls in the early universe. In this scenario, there is a possibility to explain the observed baryon-to-dark matter ratio because Q balls decay into supersymmetric particles as well as into quarks. If the gravitino mass is small compared to the typical interaction energy, the longitudinal component of the gravitino behaves like the massless goldstino. We numerically calculate the goldstino production rates from Q balls in the leading semi-classical approximation without using large radius limit or effective coupling. We also calculate the quark production rates from Q balls in the Yukawa theory with a massive fermion. In deriving the decay rate we also take into account the scalar field configuration of the Q ball. These results are applied to a realistic model in the gauge-mediated supersymmetry breaking and yield the branching ratio of the Q ball decay into the gravitino. We obtain the branching ratio much smaller than the one estimated in the previous analysis.