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In MSSM scenarios where the gravitino is the lightest supersymmetric particle(LSP), and therefore a viable dark matter candidate, the stop $\tilde{t}_1$could be the next-to-lightest superpartner (NLSP). For a mass spectrumsatisfying: $m_{\widetilde{G}}+m_t>m_{\tilde{t}_1}>m_{\widetilde{G}}+m_b+m_W$,the stop decay is dominated by the 3-body mode $\tilde{t}_1\rightarrowb\,W\,\tilde{G}$. We calculate the stop life-time, including the fullcontributions from top, sbottom and chargino as intermediate states. We alsoevaluate the stop lifetime for the case when the gravitino can be approximatedby the goldstino state. Our analytical results are conveniently expressed usingan expansion in terms of the intermediate state mass, which helps to identifythe massless limit.  In the region of low gravitino mass ($m_{\widetilde{G}}\ll m_{\tilde{t}_1}$)the results obtained using the gravitino and goldstino cases turns out to besimilar, as expected. However for higher gravitino masses $m_{\widetilde{G}}\lesssim m_{\tilde{t}_1}$ the results for the lifetime could show a differenceof O(100)\%.

Stop Decay with LSP Gravitino in the final state: $\tilde{t}_1\to\widetilde{G}\,W\,b$