The US Mu2e experiment is hoping to be the first experiment to observe a lepton-flavour violating, neutrinoless transition of a muon into an electron. Such an observation would be certain to signal new physics beyond our present understanding of fundamental particles since in the Standard Model the rate of this decay is approximately 10-50 that of the usual muon decay producing two neutrinos.
The US g-2 experiment will make the world's most precise measurement of the muon's magnetic moment. The current most precise measurement differs from that predicted by the Standard Model by 3.5 standard deviations and this new measurement will establish unambigiously whether this is a sign of new physics or not.
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