Title: SMEFT spectroscopy: how to probe dimension-8 operators in the Higgs and EW sectors?

The SMEFT is not just a parametrisation but is, in fact, also a predictive framework. This is because up to a given order in the expansion the number of free parameters, which equals the number of operators, is smaller than the number of possible deviations from the SM. As a result correlations exist between different measurements probing these deviations. These can then be used to predict/constrain some measurements in terms of others. These predictions are valid only up to the given order and as we go to the next order new operators increase the number of free parameters thus breaking these correlations. In this work we will show in detail how the breaking of SMEFT predictions at dimension-6 (D6) level can be used to probe dimension-8 (D8) operators. To this end, we list all the D8 operators that contribute to Higgs and EW physics and map the breaking of D6 predictions to the D8 Wilson coefficients. We also discuss several phenomenological examples.

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