Abstract
We calculate the double pole contribution to two to four fermion scattering through $W^{\pm}$ currents at tree level in the Standard Model Effective Field Theory (SMEFT). We assume all fermions to be massless, $\rm U(3)^5$ flavour and $\rm CP$ symmetry. Using this result, we update the global constraint picture on SMEFT parameters including LEPII data on these charged current processes, and also include modifications to our fit procedure motivated by a companion paper focused on $W^{\pm}$ mass extractions. The fit reported is now to 177 observables and emphasises the need for a consistent inclusion of theoretical errors, and a consistent treatment of observables. Including charged current data lifts the two-fold degeneracy previously encountered in LEP (and lower energy) data, and allows us to set simultaneous constraints on 20 of 53 Wilson coefficients in the SMEFT, consistent with our assumptions. This allows the model independent inclusion of LEP data in SMEFT studies at LHC, which are projected into the SMEFT in a consistent fashion. We show how stronger constraints can be obtained by using some combinations of Wilson coefficients, when making assumptions on the UV completion of the Standard Model, or in an inconsistent analysis. We explain why strong bounds at the per-mille or sub-per-mille level on some combinations of Wilson coefficients in the Effective Lagrangian can be artificially enhanced in fits of this form in detail. This explains some of the different claims present in the literature.
Highlights
Where the Ci(k) are the Wilson coefficients1 associated to the operators Oi(k)
We update the global constraint picture on Standard Model Effective Field Theory (SMEFT) parameters including LEPII data on these charged current processes, and modifications to our fit procedure motivated by a companion paper focused on W ± mass extractions
We demonstrate how UV assumptions strongly enhance the strength of bounds on the Wilson coefficients of the individual operators in the SMEFT, and how fits to some combinations of Wilson coefficients in the Effective Lagrangian5 can be subject to significant theoretical errors
Summary
This paper further develops the results reported in refs. Our notation and conventions are consistent with these works. We use bar superscripts for parameters in the canonically normalized SMEFT, and hat superscripts for measured input parameters, or parameters directly related to input parameters at tree level using SM relations. We use the input parameter set {GF , m Z, α}
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