Bound-state effects on light-element abundances in gravitino dark matter scenarios

If the gravitino is the lightest supersymmetric particle and the long-lived next-to-lightest sparticle (NSP) is the stau, the charged partner of the tau lepton, it may be metastable and form bound states with several nuclei. These bound states may affect the cosmological abundances of ⁶Li and ⁷Li by enhancing nuclear rates that would otherwise be strongly suppressed. We consider the effects of these enhanced rates on the final abundances produced in Big-Bang nucleosynthesis (BBN), including injections of both electromagnetic and hadronic energy during and after BBN. We calculate the dominant two- and three-body decays of both neutralino and stau NSPs, and model the electromagnetic and hadronic decay products using the PYTHIA event generator and a cascade equation. Generically, the introduction of bound states drives light element abundances further from their observed values; however, for small regions of parameter space bound-state effects can bring lithium abundances in particular into better accord with observations. We show that in regions where the stau is the NSP with a lifetime longer than 10³-10⁴ s, the abundances of ⁶Li and ⁷Li are far in excess of those allowed by observations. For shorter lifetimes of order 1000 s, we comment on the possibility in minimal supersymmetric and supergravity models that stau decays could reduce the ⁷Li abundance from standard BBN values while at the same time enhancing the ⁶Li abundance.