${\mu}$LHC: Antimuon Ring and HL-LHC based ${\mu}^+p$ Collider

Conceptual design and performance evaluation of HL-LHC based antimuon-proton collider (${\mu}$LHC) are presented. Leveraging the ${\mu}$TRISTAN concept based on established 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 EIC and LHeC. Two booster ring options for ${\mu}^{+}$ acceleration, namely, a ${\mu}$TRISTAN-based and a repurposed LHeC ERL-based systems, are explored. Achievable luminosities are predicted to exceed $10^{33} cm^{-2}s^{-1}$. 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 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 ${\mu}^{+}$ 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.