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We explore the possibilities for extending the sensitivity of currentsearches for the charged lepton flavor violating decays $\mu\ -> e \gamma$ and$\mu\ -> eee$. A future facility such as Project X at Fermilab could provide amuch more intense stopping $\mu^+$ beam, facilitating more sensitive searches,but improved detectors will be required as well. Current searches are limitedby accidental and physics backgrounds, as well as by the total number ofstopped muons. One of the limiting factors in current detectors for $\mu\ -> e\gamma$ searches is the photon energy resolution of the calorimeter. We presenta new fast Monte Carlo simulation of a conceptual design of a new experimentalconcept that detects converted $e^+e^-$ pairs from signal photons, takingadvantage of the improved energy resolution of a pair spectrometer based on asilicon charged particle tracker. We also study a related detector design for anext generation $\mu\to eee$ search experiment.

The next generation of $\mu\ -> e \gamma$ and $\mu\ -> 3e$ CLFV search experiments