  High-energy neutral and charged Drell--Yan differential cross-section
measurements are powerful probes of quark-lepton contact interactions that
produce growing-with-energy effects. This paper provides theoretical
predictions of the new physics effects at the Next-to-Leading order in QCD and
including one-loop EW corrections at the single-logarithm accuracy. The
predictions are obtained from SM Monte Carlo simulations through analytic
reweighting. This eliminates the need of performing a scan on the new physics
parameter space, enabling the global exploration of all the relevant
interactions. Furthermore, our strategy produces consistently showered events
to be employed for a direct comparison of the new physics predictions with the
data, or to validate the unfolding procedure than underlies the cross-section
measurements. Two particularly relevant interactions, associated with the W and
Y parameters of EW precision tests, are selected for illustration. Projections
are presented for the sensitivity of the LHC and of the HL-LHC measurements.
The impact on the sensitivity of several sources of uncertainties is
quantified.
