  The measurement of Higgs couplings constitute an important part of present
Standard Model precision tests at colliders. In this article, we show that
modifications of Higgs couplings induce energy-growing effects in specific
amplitudes involving longitudinally polarized vector bosons, and we initiate a
novel program to study these very modifications of Higgs couplings off-shell
and at high-energy, rather than on the Higgs resonance. Our analysis suggests
that these channels are complementary and, at times, competitive with familiar
on-shell measurements; moreover these high-energy probes offer endless
opportunities for refinements and improvements.
