The Supersymmetric Flavor Problem

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The supersymmetric SU(3)× SU(2)× U(1) theory with minimal particle content and general soft supersymmetry breaking terms has 110 physical parameters in its flavor sector: 30 masses, 39 real mixing angles and 41 phases. The absence of an experimental indication for the plethora of new parameters places severe constraints on theories posessing Planck or GUT-mass particles and suggests that theories of flavor conflict with naturalness. We illustrate the problem by studying the processes μ→ e + γ and K⁰ - K⁰ mixing which are very sensitive probes of Planckian physics: a single Planck mass particle coupled to the electron or the muon with a Yukawa coupling comparable to the gauge coupling typically leads to a rate for μ→ e + γ exceeding the present experimental limits. A possible solution is that the messengers which transmit supersymmetry breaking to the ordinary particles are much lighter than M Planck.