A Muon-Ion Collider at BNL: the future QCD frontier and path to a new energy frontier of $\mu^+\mu^-$ colliders

We propose the development and construction of a novel muon-ion collider (MuIC) at Brookhaven National Laboratory (BNL) in the USA as an upgrade to succeed the electron-ion collider (EIC) that is scheduled to commence in the early 2030s, by a joint effort of the nuclear and particle physics communities. The BNL facility could accommodate a muon storage beam with an energy up to about 1~TeV with existing magnet technology. When collided with a 275~GeV hadron beam, the MuIC center-of-mass energy of about 1~TeV will extend the kinematic coverage of deep inelastic scattering physics at the EIC (with polarized beams) by more than an order of magnitude in $Q^2$ and $x$, opening a new QCD frontier to address many fundamental scientific questions in nuclear and particle physics. This coverage is comparable to that of the proposed Large Hadron-Electron Collider (LHeC) at CERN, but with complementary lepton and hadron kinematics and beam polarization. Additionally, the developmentof a MuIC at BNL will focus the worldwide R\&D efforts on muon collider technology and serve as a demonstrator toward a future muon-antimuon collider at {$\mathcal O$}(10)~TeV energies, which is an attractive option to reach the next high energy frontier in particle physics at an affordable cost and a smaller footprint than a future circular hadron collider. We discuss here the possible design parameters of the MuIC, kinematic coverage, science cases, and detector design considerations including estimates of resolutions on DIS kinematic variables. A possible road map toward the future MuIC and muon-antimuon colliders is also presented.