We point out that relevant constraints on the anomalous magnetic (a_\tauaτ) and electric (d_\taudτ) moment of the tau lepton can be derived from tau-pair production measurements performed at the LHC. Our conclusion is based on the observation that the leading relative deviations from the Standard Model prediction for pp \to \tau^+ \tau^-pp→τ+τ− due to a_\tauaτ and d_\taudτ are enhanced at high energies. Less precise measurements at hadron colliders can therefore offer the same or better sensitivity to new physics with respect to high-precision low-energy measurements performed at lepton machines. We derive bounds on a_\tauaτ and d_\taudτ using the full LHC Run II data set on tau-pair production and compare our findings with the current best limits on the tau anomalous moments.
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