  Higgs coupling deviations from Standard Model predictions contain information
about two scales of Nature: that of new physics responsible for the deviation,
and the scale where new bosons must appear. The two can coincide, but they do
not have to. The scale of new bosons can be calculated by going beyond an
effective field theory description of the coupling deviation. We compute
model-independent upper bounds on the scale of new bosons for deviations in
Higgs to $WW$ and $ZZ$ couplings, finding that any measured deviation at
present or future colliders requires the existence of new bosons within
experimental reach. This has potentially interesting implications for
naturalness.
