XEFT, the challenging path up the hill: dim = 6 and dim = 8

There is increasing need to assess the impact and the interpretation of dim = 6 and dim = 8 operators within the context of the Standard Model Effective Field Theory (SMEFT). The observational and mathematical consistency of a construct based on dim = 6 and dim = 8 operators is critically examined in the light of known theoretical results. The discussion is based on a general dim = 4 theory X and its effective extension, XEFT; it includes elimination of redundant operators and their higher order compensation, SMEFT in comparison with ultraviolet completions incorporating a proliferation of scalar and mixings, canonical normalization of effective field theories, gauge invariance and gauge fixing, role of tadpoles when constructing XEFT at NLO, heavy-light contributions to the low energy limit of theories containing bosons and fermions, one-loop matching, EFT fits and their interpretation and effective field theory interpretation of derivative-coupled field theories.