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We present the calculation of the stop ($\tilde{t}$) lifetime that resultsfrom its decay into gravitinos ($\tilde{\Psi}^{\mu}$) in the final state,namely $\tilde{t}\to \tilde{\Psi}^{\mu} + X$, where $X=t, bW, b l\nu_l$ for thetwo-, three- and four-body decay modes. The full calculation is obtained usingthe Feynman rules for massive gravitino, which is compared with the resultsobtained employing the equivalence theorem, where the longitudinal component ofthe gravitino is replaced by the goldstino. The stop turns out to be verylong-lived in these scenarios, with lifetimes of $\mathcal{O}$($10^8$s,$10^{14}$s, $10^{20}$s) for the corresponding 2-,3- and 4-body modes underconsideration, and therefore all of them are safe from the big bangnucleosynthesis problem. However, the lifetime for the four body decay modeoccurs during the epoch of galaxy formation. When the stop is produce atcolliders, in these scenarios, it will hadronize and decay outside of thedetector, even for the lowest values of stop lifetime.

Very long-lived Stop NLSP in MSSM scenarios with Gravitino LSP