  We present a non-thermal leptogenesis scenario following standard
supersymmetric hybrid inflation, in the case where light neutrinos acquire mass
via the usual seesaw mechanism and inflaton decay to heavy right-handed
neutrino superfields is kinematically disallowed, or the right-handed neutrinos
which can be decay products of the inflaton are unable to generate sufficient
baryon asymmetry via their subsequent decay. The primordial lepton asymmetry is
generated through the decay of the inflaton into light particles by the
interference of one-loop diagrams with exchange of different right-handed
neutrinos. The mechanism requires superpotential couplings explicitly violating
a U(1) R-symmetry and R-parity. We take into account the constraints from
neutrino masses and mixing and the preservation of the primordial asymmetry. We
consider two models, one without and one with SU(2)(R) gauge symmetry. We show
that the former is viable, whereas the latter is ruled out. Although the broken
R-parity need not have currently observable low-energy signatures, some
R-parity-violating slepton decays may be detectable in the future colliders.
