$μ$LHC: Antimuon Ring and HL-LHC based μ⁺p Collider

Conceptual design and performance evaluation of HL-LHC based antimuon-proton collider ($μ$LHC) are presented. Leveraging the $μ$TRISTAN concept based on established J-PARC ultra-cold μ⁺ beam technology, $μ$LHC will give the opportunity to achieve a 5.3 TeV center-of-mass energy, significantly surpassing EIC and LHeC. Two booster ring options for μ⁺ acceleration, namely, a $μ$TRISTAN-based and a repurposed LHeC ERL-based systems, are explored. Achievable luminosities are predicted to exceed 10³³ cm⁻²s⁻¹. The $μ$LHC offers substantially wider kinematic plane coverage, particularly in small-x and high-Q² regions, significantly contributing to QCD basics and Higgs boson properties. Its unique potential for BSM 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 μ⁺ beam technology, $μ$LHC is highly feasible for earlier realization than the muon collider, positioning it as a critical tool for the future of high energy physics.