  With the upgrade of the LHC, the couplings of the observed Higgs particle to
fermions and gauge bosons will be measured with a much higher experimental
accuracy than current measurements, but will still be limited by an order 10%
theoretical uncertainty. In this paper, we re-emphasize the fact that the ratio
of Higgs signal rates into two photons and four leptons, $D_{\gamma \gamma}=
\sigma(pp\to H \to \gamma \gamma)/\sigma(pp\to H \to ZZ^* \to 4\ell^\pm)$ can
be made free of these ambiguities. Its measurement would be limited only by the
statistical and systematic errors, which can in principle be reduced to the
percent level at a high-luminosity LHC. This decay ratio would then provide a
powerful probe of new physics effects in addition to high precision electroweak
observables or the muon g-2. As an example, we show that the Higgs couplings to
top quarks and vector bosons can be constrained at the percent level and that
new Higgs or supersymmetric particles that contribute to the H$\gamma\gamma$
loop can be probed up to masses in the multi-TeV range and possibly larger than
those accessible directly.
