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A bstract We calculate the $$ \mathcal{O}\left({\left\langle {H}^{\dagger }H\right\rangle}^2/{\Lambda}^4\right) $$ O H † H 2 / Λ 4 corrections to LEP electroweak precision data using the geometric formulation of the Standard Model Effective Field Theory (SMEFT). We report our results in simple-to-use interpolation tables that allow the interpretation of this data set to dimension eight for the first time. We demonstrate the impact of these previously unknown terms in the case of a general analysis in the SMEFT, and also in the cases of two distinct models matched to dimension eight. Neglecting such dimension-eight corrections to LEP observables introduces a theoretical error in SMEFT studies. We report some preliminary studies defining such a theory error, explicitly demonstrating the effect of previously unknown dimension-eight SMEFT corrections on LEP observables. 

A bstract The Standard Model Effective Field Theory (SMEFT) theoretical framework is increasingly used to interpret particle physics measurements and constrain physics beyond the Standard Model. We investigate the truncation of the effective-operator expansion using the geometric formulation of the SMEFT, which allows exact solutions, up to mass-dimension eight. Using this construction, we compare the exact solution to the expansion at $$ \mathcal{O} $$ O ( v 2 / Λ 2 ), partial $$ \mathcal{O} $$ O ( v 4 / Λ 4 ) using a subset of terms with dimension-6 operators, and full $$ \mathcal{O} $$ O ( v 4 / Λ 4 ), where v is the vacuum expectation value and Λ is the scale of new physics. This comparison is performed for general values of the coefficients, and for the specific model of a heavy U(1) gauge field kinetically mixed with the Standard Model. We additionally determine the input-parameter scheme dependence at all orders in v/ Λ, and show that this dependence increases at higher orders in v/ Λ.