Abstract
Recently proposed Future Circular Collider based muon-proton colliders will allow investigating lepton-hadron interactions at the highest center-of-mass energy. In this study, we investigate the potential of these colliders for a four-fermion contact interactions search. Regarding the constructive and destructive interferences of contact interactions, we estimated discovery, observation, and exclusion limits on the compositeness scale for the left-left, right-right, left-right, and right-left helicity structures. Thus, it is shown that the FCC-based $\mu p$ colliders have great potential for investigating four-fermion contact interactions.
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