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$\mu^{+} \to e^{+} \gamma$ and $\mu^{+} \to e^{+}e^{+}e^{-}$ processes areanalyzed in detail with polarized muons in supersymmetric grand unifiedtheories. We first present Dalitz plot distribution for $\mu^{+} \toe^{+}e^{+}e^{-}$ decay based on effective Lagrangian with generallepton-flavor-violating couplings and define various P- and T-odd asymmetries.We calculate branching ratios and asymmetries in supersymmetric SU(5) andSO(10) models taking into account complex soft supersymmetry breaking terms.Imposing constraints from experimental bounds on the electron, neutron andatomic electric dipole moments, we find that the T-odd asymmetry for $\mu^{+}\to e^{+}e^{+}e^{-}$ can be 15% in the SU(5) case. P-odd asymmetry with respectto muon polarization for $\mu^{+} \to e^{+} \gamma$ varies from -20% to -100%for the SO(10) model while it is $+100%$ in the SU(5) case. We also show thatthe P-odd asymmetries in $\mu^{+} \to e^{+}e^{+}e^{-}$ and the ratio of$\mu^{+} \to e^{+}e^{+}e^{-}$ and $\mu^{+} \to e^{+} \gamma$ branchingfractions are useful to distinguish different models.Comment: 52 pages, 15 figure

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

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μ→eγandμ→3