  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.
