Luminosity and physics considerations on HL-LHC–and HE-LHC–based $\mu$p colliders

Construction of the future muon collider tangential to the Large Hadron Collider will give opportunity to realize μp collisions at multi-TeV center-of-mass energies. Using the nominal parameters of high-luminosity and high-energy upgrades of the LHC, as well as the design parameters of muon colliders, it is shown that L $_{μp}$ of the order of 10$^{33}$ cm$^{−2}$s$^{−1}$ is achievable for different options with from 4.58 TeV to 12.7 TeV. Certainly, the proposed μp colliders have a huge potential for clarifying QCD basics and searches for new physics.