  It is well-known but sometimes overlooked that constraints on the oblique
parameters (most notably $S$ and $T$ parameters) are generally speaking only
applicable to a special class of new physics scenarios known as universal
theories. In the effective field theory (EFT) framework, the oblique parameters
should not be associated with Wilson coefficients in a particular operator
basis, unless restrictions have been imposed on the EFT so that it describes
universal theories. We work out these restrictions, and present a detailed EFT
analysis of universal theories. We find that at the dimension-6 level,
universal theories are completely characterized by 16 parameters. They are
conveniently chosen to be: 5 oblique parameters that agree with the
commonly-adopted ones, 4 anomalous triple-gauge couplings, 3 rescaling factors
for the $h^3$, $hff$, $hVV$ vertices, 3 parameters for $hVV$ vertices absent in
the Standard Model, and 1 four-fermion coupling of order $y_f^2$. All these
parameters are defined in an unambiguous and basis-independent way, allowing
for consistent constraints on the universal theories parameter space from
precision electroweak and Higgs data.
