Future Opportunities with Lepton-Hadron Collisions

Deep Inelastic lepton-hadron Scattering (DIS) is a cornerstone of particle physics discovery and the precision measurement of the structure of matter. This document surveys the international DIS landscape, exploring current and future opportunities to continue this rich heritage, leading to new understandings and enabling discoveries. Of immediate relevance to the future of the field in Europe, the Large Hadron electron Collider (LHeC) offers an impactful bridge between the end of the HL-LHC and the beginning of the next CERN flagship project, both in terms of technology development and new scientific exploration from Higgs physics to the structure of the proton. More generally, the facilities described here cover energies from a few GeV to multiple TeV and address a wide range of topics, with unique sensitivity to Quantum Chromodynamics and hadron structure at their core. Additionally, they enhance the science programmes at hadron-hadron colliders. The fixed-target CEBAF programme at JLab probes nucleon and light ion structure at large x in novel ways, while high energy neutrino DIS is enabled at the FASER and SND@LHC experiments by the intense LHC beams. The Electron Ion Collider (EIC) is on course for deployment at Brookhaven in the early 2030s. Its science includes a 3-dimensional mapping of hadrons, leading to a thorough understanding of the mechanisms behind proton mass and spin. Adding the LHeC provides a Europe-based lepton-hadron frontier, including a complementary Higgs, top and electroweak programme to the HL-LHC, together with precise determinations of proton and nuclear structure in a kinematic range that improves HL-LHC sensitivities. In the longer term, plasma wakefield acceleration and the FCC offer possible major steps forward in centre-of-mass energy, extending into a low parton momentum-fraction domain where new strong interaction discoveries are guaranteed.