The weak mixing angle is a probe of the vector-axial coupling structure of electroweak interactions. It has been measured precisely at the Z-pole by experiments at the LEP and SLD colliders, but its energy dependence above $m_Z$ remains unconstrained.
In this contribution we propose to exploit measurements of Neutral-Current Drell-Yan production at the Large Hadron Collider at large invariant dilepton masses to determine the scale dependence of the weak mixing angle in the MSbar renormalisation scheme, $sin^2\theta_W(\mu)$.
Such a measurement can be used to confirm the Standard Model predictions for the MSbar running at TeV scales, and to set model-independent constraints on new states with electroweak quantum numbers.
To this end, we present an implementation of $sin^2\theta_W(\mu)$ in a Monte Carlo event generator in Powheg-Box, which we use to explore the potential of future dedicated analyses with the LHC Run3 and High-Luminosity datasets.
In particular, we study the impact of higher order electroweak corrections and of uncertainties due the knowledge of parton distribution functions.