<i>μ</i> LHC: Antimuon Ring and High Luminosity-LHC-Based <i>μ</i>  + <i>p</i> Collider

Abstract A conceptual design and a performance evaluation of the High Luminosity-Large Hadron Collider (HL-LHC)-based antimuon–proton collider $\mu$LHC are presented. Leveraging the $\mu$TRISTAN concept based on established Japan Proton Accelerator Research Complex (J-PARC) ultra-cold $\mu ^+$ beam technology, $\mu$LHC will give the opportunity to achieve a 5.3-TeV center-of-mass energy, significantly surpassing the Electron Ion Collider (EIC) and Large Hadron-electron Collider (LHeC). Two booster ring options for $\mu ^+$ acceleration, namely, a $\mu$TRISTAN-based and a repurposed LHeC Energy Recovery Linac (ERL)-based system, are explored. Achievable luminosities are predicted to exceed $10^{33} \text{cm}^{-2} \text{s}^{-1}$. The $\mu$LHC offers substantially wider kinematic plane coverage, particularly in small-x and high-$Q^2$ regions, significantly contributing to QCD basics and Higgs boson properties. Its unique potential for Beyond the Standard Model physics extends to muon-related phenomena like excited muons, color-octet muons, leptoquarks, and contact interactions. A possible detector concept is also outlined. Given the maturity of ultra-cold $\mu ^+$ beam technology, $\mu$LHC is highly feasible for earlier realization than the muon collider, positioning it as a critical tool for the future of high-energy physics.