Measuring the muon EDM at Fermilab g-2 and confirming the hadronic contribution to the muon MDM using MuonE.

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The g-2 experiment monitors the orientation of a muon's spin as it precesses in a magnetic field by injecting positive muons into a storage ring and measuring the decay positrons as they orbit in the ring. The speed of the muons' precession is used to calculate the muon magnetic dipole moment (MDM) as well as the muon electric dipole moment (EDM).The g-factor is a proportionality constant that relates the muon MDM to its spin, charge, and mass. Originally Dirac calculated it as 2 for muons but because of interactions with virtual particles, the g-factor is altered, and the difference is quantified as the anomalous magnetic dipole moment (AMM). Many processes with virtual particles contribute to this slight alteration - these include processes containing new particles and thus the MDM measurement acts as a probe for New Physics. If there is a significant difference between the theoretical and experimental values for the g-factor (or for the EDM), this will expose new discrepancies within the Standard Model (SM). The size of the AMM and EDM can be used to restrict the properties of new particles and models. MUonE is also extremely important as it will help to ensure the validity of the g-2 discovery and the theoretical MDM value.Though hadronic contributions to the MDM are smaller than other contributions, they produce the largest uncertainties, and so to validate the g-2 theoretical prediction, the uncertainty from this sector must be reduced. This is done in the MUonE experiment by investigating muon-electron scattering, where a muon beam will scatter off a stationary electron target. MUonE will measure and determine the shape of the differential cross section of the process and use this to calculate the hadronic contribution to the MDM.I will be analysing the final g-2 data run taken at Fermilab and completing the EDM measurement, which will be the most sensitive measurement of the muon EDM. I will also be optimising the detector design and orientation and working on the tests and first runs of MUonE