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We consider leptogenesis induced by soft supersymmetry breaking terms ("softleptogenesis"), in the context of the inverse seesaw mechanism. In this modelthere are lepton number (L) conserving and L-violating softsupersymmetry-breaking B-terms involving the singlet sneutrinos which, togetherwith the -- generically small-- L-violating parameter responsible of theneutrino mass, give a small mass splitting between the four singlet sneutrinostates of a single generation. In combination with the trilinear softsupersymmetry breaking terms they also provide new CP violating phases neededto generate a lepton asymmetry in the singlet sneutrino decays. We obtain thatin this scenario the lepton asymmetry is proportional to the L-conserving softsupersymmetry-breaking B-term, and it is not suppressed by the L-violatingparameters. Consequently we find that, as in the standard see-saw case, thismechanism can lead to sucessful leptogenesis only for relatively small value ofthe relevant soft bilinear coupling. The right-handed neutrino masses can besufficiently low to elude the gravitino problem. Also the corresponding Yukawacouplings involving the lightest of the right-handed neutrinos are constrainedto be \sum |Y_{1k}|^2\lesssim 10^{-7} which generically implies that theneutrino mass spectrum has to be strongly hierarchical.Comment: 28 pages, 1 figure; some references added; final version to appear in  JHE

Soft leptogenesis in the inverse seesaw model