  Employing the framework of the Standard Model Effective Field Theory, we
perform a detailed reinterpretation of measurements of the Weinberg angle in
dilepton production as a search for new-physics effects. We truncate our signal
prediction at order $1/\Lambda^2$, where $\Lambda$ denotes the new-physics mass
scale, and introduce a theory error to account for unknown contributions of
order $1/\Lambda^4$. Two linear combinations of four-fermion operators with
distinct angular behavior contribute to dilepton production with growing impact
at high energies. We define suitable angular observables and derive bounds on
those two linear combinations using data from the Tevatron and the LHC. We find
that the current data is able to constrain interesting regions of parameter
space, with important contributions at lower cutoff scales from the Tevatron,
and that the future LHC data will eventually be able to simultaneously
constrain both independent linear combinations which contribute to dilepton
production.
