  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 $\mu \to e + \gamma$.
