The Geometric SMEFT description of curved Higgs Field Space(s)

In recent years, the effective field theory approach to the Standard Model, the SMEFT, has been used to study LHC data with ever increasing theoretical precision and sophistication. However, the complexity of this theory lead to several barriers  to substantial theoretical progress. In particular, the explosion in the number of parameters in the SMEFT as a function of operator mass dimension, and the technical challenge or reformulating SM predictions consistently into the SMEFT were very serious problems. This called into question the possible success and value of the SMEFT physics program over the long term. I will discuss how these challenges have been overcome. The key point leading to this advance, is the understanding that the projection of curved scalar field spaces generated by the Higgs onto a naive flat field space understanding-- implicitly embedded into the usual SMEFT  Lagrangian, and approach -- was the root cause of many problems, technical challenges and confusions. Many outstanding issues have now been addressed and immediately overcome by reformulating the SMEFT noting its curved scalar field space(s) - in the Geometric SMEFT. Some examples of the benefits of this approach will be presented, and explained.