Supersymmetric Leptogenesis and the Gravitino Bound

Supersymmetric thermal leptogenesis with a hierarchical right-handed neutrino mass spectrum requires the mass of the lightest right-handed neutrino to be heavier than about 109 GeV. This is in conflict with the upper bound on the reheating temperature which is found by imposing that the gravitinos generated during the reheating stage after inflation do not jeopardize successful nucleosynthesis. In this paper we show that a solution to this tension is actually already incorporated in the framework, because of the presence of flat directions in the supersymmetric scalar potential. Massive right-handed neutrinos are efficiently produced non-thermally and the observed baryon asymmetry can be explained even for a reheating temperature respecting the gravitino bound if two conditions are satisfied: the initial value of the flat direction must be close to Planckian values and the phase-dependent terms in the flat direction potential are either vanishing or sufficiently small. The observed baryon number asymmetry (normalized with respect to the entropy density) of the Universe YB = (0.87± 0.03)× 10 −10 [1] can be explained by the mechanism of thermal leptogenesis [2, 3], the simplest implementation of this mechanism being realised by adding to the Standard Model (SM) three heavy right-handed (RH) neutrinos. In thermal leptogenesis the heavy RH neutrinos are produced by thermal scatterings after inflation and subsequently decay out-of-equilibrium in a lepton number and CP-violating way. The dynamically generated lepton asymmetry is then converted into a baryon asymmetry due to (B + L)-violating sphaleron interactions [4]. If RH neutrinos are hierarchical in mass, successful leptogenesis requires that the massM1 of the lightest RH neutrino N1 is larger than 2×10 9 GeV, for vanishing initial N1 density [5]. This lower limit on M1 is reduced to 5×10 8 GeV when N1 is initially in thermal equilibrium and to 2 × 10 GeV when N1 initially dominates the energy density of the Universe [6]. These results do not substantially change when flavour effects are accounted for [7]. Hence, in the standard framework of thermal leptogenesis, the required reheating temperature after inflation TRH cannot be lower than about 2 × 10 9 GeV [6]. In supersymmetric scenarios this is in conflict with the upper bound on the reheating temperature necessary to avoid the overproduction of gravitinos during reheating [8]. Being only gravitationally coupled to SM particles (and their supersymmetric partners), gravitinos decay very late jeopardizing the successful predictions of Big Bang nucleosynthesis. This does not happen, however, if gravitinos are not efficiently produced during reheating, that is if the reheating temperature TRH is small enough. For gravitino masses in the natural range from 100 GeV to 1 TeV, within the minimal supergravity framework, the reheating tempeature should be smaller than about 10–10 GeV [8], depending on the chosen values of the supersymmetric parameters and of the primordial element abundances. The severe bound on the reheating temperature makes the thermal generation of the RH neutrinos impossible, thus rendering the supersymmetric thermal leptogenesis scenario not viable if RH neutrinos are hierarchical. Of course, there are several ways out to this drawback. First of all, one can modify the usual assumptions on gravitinos. If the gravitino is stable, the nucleosynthesis limit depends on the nature of the next-to-lightest supersymmetric particle, but values of TRH even larger than 10 9 GeV can be obtained [9]. Assuming the existence of small R-parity violation, the next-to-lightest supersymmetric particle can decay before the onset of supersymmetry, evading the bound on TRH [10]. Also, gravitinos lighter than 1 KeV (as possible in gauge mediation) or heavier than about 50 TeV (as possible in anomaly mediation) avoid the stringent limits on TRH. Alternatively, one can modify the standard mechanism of leptogenesis, and rely on supersymmetric resonant leptogenesis [11] or soft