Differentiating solutions to the gauge hierarchy problem through rare muon decays

We demonstrate the potential of forthcoming mu -> e gamma and mu-e conversion experiments to implicate or disfavor solutions to the gauge hierarchy problem before the advent of the CERN Large Hadron Collider. Solutions of dynamical electroweak symmetry breaking, little Higgs, supersymmetry, and extra dimensions are considered. Correlations of mu -> e gamma and mu-e conversion branching ratios are analyzed for discriminating patterns. Measurements of these exotic muon decays may have compelling implications for supersymmetric solutions.