IEM–FT–118/95 NATURAL FLAVOUR MIXING IN THE MSSM AND µ → e, γ

In the absence of any additional assumption it is natural to conjecture that sizeable flavour-mixing mass entries, ∆m 2 , may appear in the mass matrices of the scalars of the MSSM, i.e. ∆m 2 ∼ O(m 2). This flavour violation can still be reconciled with the experiment if the gaugino mass, M 1/2 , is large enough to yield (through the renormalization group running) a sufficiently small ∆m 2 /m 2 at low energy. This leads to a gaugino dominance framework (i.e. M 2 1/2 ≫ m 2), which permits a remarkably model–independent analysis. We study this possibility focussing our attention on the µ → e, γ decay. In this way we obtain very strong and general constraints, in particular M 2 1/2 ∆m > ∼ 34 TeV. It is well-known that FCNC processes are very sensitive tests to physics beyond the standard model (SM) and, in particular, to supersymmetric extensions of the SM (SSM) 1. Furthermore supersymmetry provides new direct sources of flavour violation, namely the possible (and even natural as we will see) presence of off-diagonal terms (say generically ∆m 2) in the squark and slepton mass matrices 2,3,4,5,6,7. In the present talk we will focus all our attention on the constraints on ∆m 2 from the µ → e, γ process because they are very strong and, as we will see, their evaluation is remarkably model–independent. The minimal supersymmetric standard model (MSSM) is defined by the superpotential, W (from which the supersymmetric part of the Lagrangian is readily obtained), and the soft supersymmetry breaking terms coming from the (unknown) supersymmetry breaking mechanism