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Affleck-Dine (AD) baryogenesis along a d=6 flat direction in gauge-mediatedsupersymmetry-breaking (GMSB) models can produce unstable Q-balls whichnaturally have field strength similar to the messenger scale. In this case anew kind of Q-ball is formed, intermediate between gravity-mediated andgauge-mediated type. We study in detail these new Q-ball solutions, showing howtheir properties interpolate between standard gravity-mediated andgauge-mediated Q-balls as the AD field becomes larger than the messenger scale.It is shown that E/Q for the Q-balls can be greater than the nucleon mass butless than the MSSM-LSP mass, leading to Q-ball decay directly to Standard Modelfermions with no MSSM-LSP production. More significantly, if E/Q is greaterthan the MSSM-LSP mass, decaying Q-balls can provide a natural source ofnon-thermal MSSM-LSPs, which can subsequently decay to gravitino dark matterwithout violating nucleosynthesis constraints. The model therefore provides aminimal scenario for baryogenesis and gravitino dark matter in thegauge-mediated MSSM, requiring no new fields.

New Q-ball Solutions in Gauge-Mediation, Affleck-Dine Baryogenesis and Gravitino Dark Matter