Constraints on Supersymmetric Theories from $\mu\to e,\gamma$

In the absence of any additional assumption it is natural to conjecture that sizeable flavour-mixing mass entries, $\Delta m^2$, may appear in the mass matrices of the scalars of the MSSM, i.e. $\Delta m^2\sim O(m^2)$. This flavour violation can still be reconciled with the experiment if the gaugino mass, $M_{1/2}$, is large enough, leading to a {\em gaugino dominance} framework (i.e. $M_{1/2}^2\gg m^2$), which permits a remarkably model--independent analysis. We study this possibility focussing our attention on the $\mu\rightarrow e,\gamma$ decay. In this way we obtain very strong and general constraints, in particular $\frac{M_{1/2}^2}{\Delta m}\simgt 34\ {\rm TeV}$. On the other hand, we show that our analysis and results remain valid for values of $m^2$ much larger than $\Delta m^2$, namely for $\frac{\Delta m^2}{m^2}\simgt \frac{m^2} {10\ {\rm TeV^2}}$, thus extending enormously their scope of application. Finally, we discuss the implications for superstring scenarios.