  The Standard Model (SM) is characterized by a well-defined pattern of
couplings of the gauge bosons to the fermions. Any deviation from this
description would correspond to a definitive hint for beyond SM physics. These
deviations would manifest in terms of different yields for the final states in
a direct search. In this letter, we develop a universal framework to extract
the extent to which a direct search can probe these differences. Our strategy
is effectively demonstrated for a heavy neutral $Z'$ decaying into a pair of
electrons and muons with different branching fractions. We note the
implications of the drastically different reconstructions (especially in the
HL-LHC) on the computation of discovery significance as well as the extraction
of non-universality. The potential of the current and future $pp$ colliders,
quantifying the extent of the asymmetry (in yields) to which they are
sensitive, is explored. While the HL-LHC phase offers an optimistic but a
restricted picture, it naturally paves the way for the FCC-hh machine. The
latter being sensitive not only to heavier masses but also to minor departures
from universality in the couplings for the lighter masses.
