Natural soft leptogenesis

Successful soft leptogenesis requires small B-terms for the right-handed sneutrinos and a large CP violating phase between the A- and B-terms. We show that this situation is realized naturally within the framework of gauge mediated supersymmetry breaking. The A-term is dominated by contribution from gauge mediation, while supergravity effects are more important for the B-term. The different origins naturally explain simultaneously the smallness of the B-term and the large CP violating phase. The most stringent bounds on the model come from the cosmological gravitino problem. We find a viable parameter region with very light gravitino $m_{3/2} \lesssim 16 eV$, providing a consistent framework for supersymmetry phenomenology, soft leptogenesis and cosmology.