Probing the weak mixing angle at high energies at the LHC and HL-LHC

Measurements of neutral current Drell-Yan production at large invariant dilepton masses can be used to test the energy scale dependence (running) of the electroweak mixing angle. In this work, we make use of a novel implementation of the full next-to-leading order electroweak radiative corrections to the Drell-Yan process using the $\overline{\mathrm{M}\mathrm{S}}$ renormalization scheme for the electroweak mixing angle. The potential of future analyses using proton-proton collisions at $\sqrt{s}=13.6\mathrm{T}\mathrm{e}\mathrm{V}$ in the Run 3 and High-Luminosity phases of the LHC is explored. In this way, the Standard Model predictions for the $\overline{\mathrm{M}\mathrm{S}}$ running at $\mathrm{T}\mathrm{e}\mathrm{V}$ scales can be probed.