  We study the potential for precision electroweak (EW) measurements and
beyond-the-Standard Model (BSM) searches using cross-section asymmetries in
neutral-current (NC) deep inelastic scattering at the electron-ion collider
(EIC). Our analysis uses a complete and realistic accounting of systematic
errors from both theory and experiment and considers the potential of both
proton and deuteron beams for a wide range of energies and luminosities. We
also consider what can be learned from a possible future positron beam and a
potential ten-fold luminosity upgrade of the EIC beyond its initial decade of
running. We use the SM effective field theory (SMEFT) framework to parameterize
BSM effects and focus on semi-leptonic four-fermion operators, whereas for our
precision EW study, we determine how well the EIC can measure the weak mixing
angle. New features of our study include the use of an up-to-date detector
design of EIC Comprehensive Chromodynamics Experiment (ECCE) and accurate
running conditions of the EIC, the simultaneous fitting of beam polarization
uncertainties and Wilson coefficients to improve the sensitivity to SMEFT
operators, and the inclusion of the weak mixing angle running in our fit
template. We find that the EIC can probe BSM operators at scales competitive
with and in many cases exceeding LHC Drell-Yan bounds while simultaneously not
suffering from degeneracies between Wilson coefficients.
