  The conventional oblique parameters analyses of precision electroweak data
can be consistently cast in the modern framework of the Standard Model
effective field theory (SMEFT) when restrictions are imposed on the SMEFT
parameter space so that it describes universal theories. However, the
usefulness of such analyses is challenged by the fact that universal theories
at the scale of new physics, where they are matched onto the SMEFT, can flow to
nonuniversal theories with renormalization group (RG) evolution down to the
electroweak scale, where precision observables are measured. The departure from
universal theories at the electroweak scale is not arbitrary, but dictated by
the universal parameters at the matching scale. But to define oblique
parameters, and more generally universal parameters at the electroweak scale
that directly map onto observables, additional prescriptions are needed for the
treatment of RG-induced nonuniversal effects. We perform a RG analysis of the
SMEFT description of universal theories, and discuss the impact of RG on
simplified, universal-theories-motivated approaches to fitting precision
electroweak and Higgs data.
