Physics potential of a muon-proton collider

We propose a muon-proton collider with asymmetrical multi-TeV beam energies and integrated luminosities of $0.1-1$ ab$^{-1}$. With its large center-of-mass energies and yet small Standard Model background, such a machine can not only improve electroweak precision measurements but also probe new physics beyond the Standard Model to an unprecedented level. We study its potential in measuring the Higgs properties, probing the R-parity-violating Supersymmetry, as well as testing heavy new physics in the muon $g-2$ anomaly. We find that for these physics cases the muon-proton collider can perform better than both the ongoing and future high-energy collider experiments.