Supersymmetric three-body decays of the Top Quark in the MSSM

We survey all possible supersymmetric three-body decays of the top quark in the framework of the MSSM and present detailed numerical analyses of the most relevant cases. Although the two-body channels are generally dominant, it is not inconceivable that some or all of our most favourite two-body SUSY candidates, such as e.g. $t\rightarrow\tilde{t}_1 \chi^0_{\alpha}$, could be phase-space blocked up. In this event there is still the possibility that some of the available three-body SUSY modes might exhibit a substantial branching fraction and/or carry exotic signatures that would facilitate their identification. Furthermore, in view of the projected inclusive measurement of the top-quark width $\Gamma_t$ in future colliders, one should have at one's disposal the full second order (electroweak and strong) value of that parameter. Our analysis confirms that some supersymmetric three-body decays could be relevant and thus contribute to $\Gamma_t$ at a level comparable to the largest one loop supersymmetric effects on two-body modes recently computed in the literature.