On-shell SMEFT for Electro-Weak precision observables

We present an on-shell interpretation of Electro-Weak precision observables. We first identify the minimal set of measurements required to determine the three-point amplitudes responsible for Z- and W- decay. Matching the amplitudes to the Standard Model Effective Field Theory (SMEFT) leads to linear relations among the couplings. Violations of these relations would indicate effects beyond the SMEFT.  We then derive the three-point amplitudes from the amplitudes of the unbroken SMEFT up to dimension 8, using "on-shell Higgsing". This circumvents the need for field redefinitions and the rescaling of couplings. Our on-shell formulation provides a convenient framework for a spurion analysis, capturing the pattern of Electro-Weak symmetry breaking to all orders in the Higgs vacuum-expectation-value.