Probing the Weak Mixing Angle at high energies at the LHC

The electroweak mixing angle is a fundamental parameter of the theory of electroweak interactions. Its value has been measured precisely at the $\mathrm{Z}$-pole at colliders. 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 energy scale dependence (running) of the electroweak mixing angle in the $\bar{\text{MS}}$ renormalisation scheme, $\sin^2\theta_{W,\ell}^{\bar{\text{MS}}}(\mu)$. Such a measurement can be used to confirm the Standard Model predictions for the $\bar{\text{MS}}$ running at $\text{TeV}$ scales, and to set model-independent constraints on new states with electroweak quantum numbers. To this end, we make use of a dedicated implementation of $\sin^2\theta_{W,\ell}^{\bar{\text{MS}}}(\mu)$ in the POWHEG-BOX-V2 Monte Carlo event generator, which we use to explore the potential of future analyses using the data of the LHC Run 3 and High-Luminosity.