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Search for muon-to-electron conversion with the COMET experiment

Charged Lepton Flavor Violation is expected to be one of the most powerful tools to reveal physics beyond the Standard Model. The COMET experiment aims to search for the neutrinoless coherent transition of a muon into an electron in the field of a nucleus. Muon-to-electron conversion has never been observed, and can be, and would be, clear evidence of new physics if discovered. The experimental sensitivity of this process, defined as the ratio of the muon-to-electron conversion rate to the total muon capture rate, is expected to be significantly improved by a factor of 100 to 10,000 in the coming decade. The COMET experiment will take place at J-PARC with single event sensitivities of the orders of $10^{-15}$ and $10^{-17}$ in Phase-I and Phase-II, respectively. The ambitious goal of the COMET experiment is achieved by realizing a high-quality pulsed beam and an unprecedentedly powerful muon source together with an excellent detector apparatus that can tolerate a severe radiation environment. The construction of a new beam line, superconducting magnets, detectors and electronics is in progress towards the forthcoming Phase-I experiment. We present the experimental methods, sensitivity and backgrounds along with recent status and prospects.