Electroweak physics in inclusive deep inelastic scattering at the LHeC

At the proposed electron-proton collider LHeC electroweak interactions can be uniquely studied in a largely unexplored kinematic region of spacelike momentum transfer. We simulate inclusive neutral- and charged-current deep-inelastic lepton proton scattering cross section data at center-of-mass energies of 1.2 and 1.3 TeV, and estimate the uncertainties of Standard Model parameters as well as of parameters describing physics beyond the Standard Model. A precision at sub-percent level is expected for the measurement of the weak neutral-current couplings of the light-quarks to the Z boson, $$g_{A/V}^{u/d}$$ g A / V u / d , improving their present precision by more than an order of magnitude. The weak mixing angle can be determined with a precision of about $$\Delta \sin ^2\theta _\text {W}=\pm \,0.00015$$ Δ sin 2 θ W = ± 0.00015 , and its scale dependence can be studied in the range between about 25 and 700 GeV. An indirect determination of the W-boson mass in the on-shell scheme is possible with an experimental uncertainty down to $$\Delta m_{W}=\pm \,6\,\text {MeV}$$ Δ m W = ± 6 MeV . We discuss how measurements in deep-inelastic scattering compare with those in the timelike domain, and which aspects are unique, for instance electroweak parameters in charged-current interactions. We conclude that the LHeC will determine electroweak physics parameters, in the spacelike region, with unprecedented precision leading to thorough tests of the Standard Model and possibly beyond.