Statistical approach to Higgs couplings in the standard model effective field theory

We perform a parameter fit in the Standard Model Effective Field Theory (SMEFT) with an emphasis on using regularized linear regression to tackle the issue of the large number of parameters in the SMEFT. In regularized linear regression a positive definite function of the parameters of interest is added to the usual cost function. A cross-validation is performed to try to determine the optimal value of the regularization parameter to use, but it selects the Standard Model (SM) as the best model to explain the measurements. Nevertheless as proof of principle of this technique we apply it to fitting Higgs boson signal strengths in SMEFT, including the latest Run-2 results. Results are presented in terms of the eigensystem of the covariance matrix of the least squares estimators as it has a degree model-independent to it. We find several results in this initial work: the SMEFT predicts the total width of the Higgs boson to be consistent with the SM prediction; the ATLAS and CMS experiments at the LHC are currently sensitive to non-resonant double Higgs boson production. Constraints are derived on the viable parameter space for electroweak baryogenesis in the SMEFT, reinforcing the notion that a first order phase transition requires fairly low scale Beyond the SM physics. Finally, we study which future experimental measurements would give the most improvement on the global constraints on the Higgs sector of the SMEFT.