The Fermi effective theory of the weak interaction helped identify the structure of the electroweak sector of the Standard Model, and the chiral effective Lagrangian pointed towards QCD as the theory of the strong interactions. The Standard Model Effective Field Theory (SMEFT) is a systematic and model-independent framework for characterizing experimental deviations from the predictions of the Standard Model and pointing towards the structures of its possible extensions that is complementary to direct searches for new physics beyond the Standard Model. This talk summarizes results from the first global fit to data from LHC Run 2 and earlier experiments including dimension-6 SMEFT operators, and gives examples how it can be used to constrain scenarios for new physics beyond the Standard Model. In addition, some windows for probing dimension-8 SMEFT operators are also mentioned.
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