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

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 $\treh\lsim {\rm a few}\times 10^7\gev$ from over-production of $^6{\rm Li}$ from bound state effects. We also find an upper limit on the stau lifetime of $3\times10^4 \sec$, 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 $\treh$ is relaxed to $\lsim {\rm a few}\times 10^8\gev$ when we use a more conservative bound on ${^6}{\rm Li}/{^7}{\rm Li}$, in which case a new region at small stau mass at $\sim 100\gev$ and much longer lifetimes opens up. Such a low stau mass region can be easily tested at the LHC.

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