  We demonstrate how masses of new states, beyond direct experimental reach,
could nevertheless be extracted in the framework of effective field theory
(EFT), given broad assumptions on the underlying UV physics, however not
sticking to a particular setup nor fixing the coupling strength of the
scenario. The flat direction in the $g_\ast$ vs. $M$ plane is lifted by
studying correlations between observables that depend on operators with a
different $\hbar$ scaling. We discuss the remaining model dependence (which is
inherent even in the EFT approach to have control over the error due to the
truncation of the power series), as well as prospects to test paradigms of UV
physics. In particular, we provide an assessment of which correlations are best
suited regarding sensitivity, give an overview of possible/expected effects in
different observables, and demonstrate how perturbativity and direct search
limits corner possible patterns of deviations from the SM in a given UV
paradigm.
