Eluding the BBN constraints on the stable gravitino

We investigate how late-time entropy production weakens the Big-Bang Nucleosynthesis (BBN) constraints on the gravitino as lightest superparticle with a charged slepton as next-to-lightest superparticle. We find that with a moderate amount of entropy production, the BBN constraints can be eluded for most of the parameter space relevant for the discovery of the gravitino. This is encouraging for experimental tests of supergravity at LHC and ILC. Introduction The gravitino G̃ is a unique and inevitable prediction of supergravity (SUGRA) [1], and hence the discovery of the gravitino would provide unequivocal evidence for SUGRA. It has been pointed out that this test of SUGRA may be possible at LHC or ILC, if the gravitino is the lightest superparticle (LSP) and the long-lived next-to-lightest superparticle (NLSP) is a charged slepton [2]. From an experimental point of view, a relatively large gravitino mass m G̃ comparable to the slepton mass ml̃, mG̃ > ∼O(0.1)ml̃, is particularly interesting [2, 3]. This is because in such a gravitino mass region the kinematical reconstruction of the gravitino mass becomes possible, which leads to a determination of the “Planck scale”, and even the gravitino spin might become measurable. However, such a parameter region is strongly constrained by cosmology. In particular, the BBN constraints on a late decaying particle [4, 5] lead to an upper bound on the gravitino mass for a given slepton mass [6, 7], which makes the SUGRA test at collider experiments very challenging. It is, however, easy to evade the BBN constraints if late-time entropy production occurs after the slepton decoupling (and before BBN). In this letter we explicitly show how much late-time entropy production weakens the BBN constraints on the NLSP decay into the gravitino. We find most of the relevant parameter space to survive for a moderate amount of entropy production. This is very encouraging with respect to experimental tests of SUGRA at LHC and ILC. It has also interesting implications for leptogenesis, which will be discussed elsewhere [8]. BBN constraint with late-time entropy production For concreteness, we assume that the NLSP is the superpartner of the tau lepton, stau (τ̃). In the early universe, the stau NLSP is in thermal equilibrium until its decoupling at Td ∼ mτ̃/20. If the stau particle decays during or after BBN, TBBN ∼ 1 MeV, it may spoil the successful BBN predictions [4, 5]. In the model with stau NLSP and gravitino LSP, this leads to severe constraints on the parameter space (mτ̃ , mG̃), in particular to upper bounds on the gravitino mass for a given stau mass [6, 7]. If there is no entropy production after the stau decoupling, the thermal relic abundance