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

TL;DR

This paper re-evaluates gravitino dark matter in the constrained MSSM, incorporating recent improvements in production, decay spectra, and BBN effects, resulting in updated bounds on reheating temperature and stau lifetime.

Contribution

It introduces refined calculations for gravitino production, decay spectra, and bound-state effects, updating constraints on reheating temperature and stau lifetime in the MSSM framework.

Findings

Upper bound on reheating temperature $ reh\, ext{~a few} imes 10^7 ext{ GeV}$ from $^6$Li overproduction.

Upper limit on stau lifetime of $3 imes 10^4$ seconds, larger than previous estimates.

A more conservative bound on lithium isotopes allows higher $ reh$ and a low stau mass region testable at the LHC.

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 $\treh\lsim {\rm a few}\times 10^7\gev$ 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.