Affleck-Dine baryogenesis and the Q-ball dark matter in the gauge-mediated SUSY breaking

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We consider the Affleck-Dine baryogenesis comprehensively in the minimal supersymmetric standard model with gauge-mediated supersymmetry breaking. Considering the high temperature effects, we see that the Affleck-Dine field is naturally deformed into the form of the Q ball. In the natural scenario where the initial amplitude of the field and the A-terms are both determined by the nonrenormalizable superpotential, we obtain a narrow allowed region in the parameter space in order to explain the baryon number and the dark matter of the universe simultaneously. Therefore, the Affleck-Dine baryogenesis is successful, although difficult.