The Supersymmetric Flavor Problem and Mu to E Plus Gamma

Abstract

The supersymmetric $SU(3)\times SU(2)\times U(1)$ theory with minimal particle content and general soft supersymmetry breaking terms has 110 physical parameters in its flavor sector: 30 masses, 39 mixing angles, and 41 phases. These parameters contain many new measurable sources of flavor violations unless either the sparticle mass splittings and mixing angles are small or the sparticle masses are large. In chapter 1 of this report, we discuss the origins of sparticle mass splittings and mixing angles in a theory explaining flavor, and we review the upper limits of sparticle masses that arise from naturalness among the electroweak breaking parameters. By examining the flavor changing processes $\mu \to e + \gamma$ and $K^0 - \bar{K}^0$ mixing, we show it is not possible to simultaneously satisfy the requirements of flavor differentiation among sparticles and naturalness in electroweak breaking. This indicates that a crucial ingredient is missing from our understanding of the theory. We discuss one possible solution in which the messengers that transmit supersymmetry breaking to ordinary particles are much lighter than $M_{Planck}$. In our analysis, we found the most important constraint was the process $\mu \to e + \gamma$. Furthermore, this process is currently being experimentally investigated. In spite of its importance, the complete branching ratio calculation has not yet been done. In chapter 2 we present the full one-loop calculation for $\mu \to e + \gamma$.