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We investigate baryogenesis via leptogenesis and generation of neutrinomasses and mixings through the Type I plus Type III seesaw plus an one-loopmechanism in the context of Renormalizable Adjoint SU(5) theory. One lightneutrino remains massless, because the contributions of three heavy Majoranafermions \rho_0, \rho_3 and \rho_8 to the neutrino mass matrix are not linearlyindependent. However none of these heavy fermions is decoupled from thegeneration of neutrino masses. This opens a new range in parameter space forsuccessful leptogenesis, in particular, allows for inverted hierarchy of theneutrino masses.

New Solution for Neutrino Masses and Leptogenesis in Adjoint SU(5)