A muon collider represents the ideal machine to reach very high center-of-mass energies and luminosities by colliding elementary particles. This is the result of the low level of beamstrahlung and synchrotron radiation compared to linear or circular electron-positron colliders. In contrast with other lepton machines, the design of a detector for a multi-TeV muon collider requires the knowledge of the interaction region due to the presence of a large amount of background induced by muon beam decays. The physics reaches can be properly evaluated only when the detector performance is determined. In this work, the background generated by muon beams of $750$ GeV is characterized and the performance of the tracking system and the calorimeter detector are illustrated. Solutions to minimize the effect of the beam-induced background are discussed and applied to obtain track and jet reconstruction performance. The $mu^+mu^-to H ubar{ u}to bbar b ubar{ u}$ process is fully simulated and reconstructed to demonstrate that physics measurements are possible in this harsh environment. The precision on Higgs boson coupling to $bbar b$ is evaluated for $sqrt{s}=1.5$, 3, and 10 TeV and compared to other proposed machines.
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