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The future opportunities for high-density QCD studies with ion and protonbeams at the LHC are presented. Four major scientific goals are identified: thecharacterisation of the macroscopic long wavelength Quark-Gluon Plasma (QGP)properties with unprecedented precision, the investigation of the microscopicparton dynamics underlying QGP properties, the development of a unified pictureof particle production and QCD dynamics from small (pp) to large(nucleus--nucleus) systems, the exploration of parton densities in nuclei in abroad ($x$, $Q^2$) kinematic range and the search for the possible onset ofparton saturation. In order to address these scientific goals, high-luminosityPb-Pb and p-Pb programmes are considered as priorities for Runs 3 and 4,complemented by high-multiplicity studies in pp collisions and a short run withoxygen ions. High-luminosity runs with intermediate-mass nuclei, for example Aror Kr, are considered as an appealing case for extending the heavy-ionprogramme at the LHC beyond Run 4. The potential of the High-Energy LHC toprobe QCD matter with newly-available observables, at twice largercenter-of-mass energies than the LHC, is investigated.

Future physics opportunities for high-density QCD at the LHC with heavy-ion and proton beams