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The running of the SM couplings is a theoretical prediction, which can be tested at several different energy scales. I will present a sensitivity study, demonstrating that the LHC experiments, in the Run III and with the High-Luminosity phase of operation, will have sensitivity to test the running of the weak mixing angle, defined in the MSbar renormalization scheme. The actual determination of this coupling requires an intense theoretical effort, to avoid that missing higher-order corrections can are reabsorbed in the fit, faking a BSM contribution.