A Re-analysis of Gravitino Dark Matter in the Constrained MSSM

Abstract

We re-consider the gravitino as dark matter in the framework of the Constrained MSSM. We include several recently suggested improvements on: (i) the thermal production of gravitinos, (ii) the calculation of the hadronic spectrum from NLSP decay and (iii) the BBN calculation including stau bound-state effects. In most cases we find an upper bound on the reheating temperature $\text{treh}\text{lsim}\mathrm{afew}\times 10^7\text{gev}$ from over-production of ${}^6\mathrm{Li}$ from bound state effects. We also find an upper limit on the stau lifetime of $3\times 10^4\sec$, which is nearly an order of magnitude larger than the simple limit $5\times 10^3\sec$ often used to avoid the effect of bound-state catalysis. The bound on $\text{treh}$ is relaxed to $\text{lsim}\mathrm{afew}\times 10^8\text{gev}$ when we use a more conservative bound on ${}^6\mathrm{Li}/{}^7\mathrm{Li}$, in which case a new region at small stau mass at $\sim 100\text{gev}$ and much longer lifetimes opens up. Such a low stau mass region can be easily tested at the LHC.

Comments: 18 pages, matches JHEP version