  We analyze the potential of future high-energy deep-inelastic scattering
(DIS) experiments to probe new physics within the framework of the Standard
Model Effective Field Theory (SMEFT). We perform a detailed study of SMEFT
probes at a future Large Hadron-electron Collider (LHeC) and a Future Circular
lepton-hadron Collider (FCC-eh) machine, and extend previous simulations of the
potential of a Electron-Ion Collider (EIC) to include Z-boson vertex
corrections. Precision Z-pole constraints on vertex corrections suffer from
numerous degeneracies in the Wilson-coefficient parameter space. We find that
both the LHeC and the FCC-eh can help remove these degeneracies present in the
existing global fits of precision Z-pole observables and LHC data. The FCC-eh
and LHeC will in many cases improve upon the existing precision electroweak
bounds on the SMEFT parameter space. This highlights the important role of
precision DIS measurements for new physics studies.
