Higgs couplings and electroweak observables: a comparison of precision tests

Is the weak scale natural? This ever pending question makes the search for new particle production a highly motivated primary goal of the next LHC phase. These searches may or may not be successful. While waiting for a needed higher energy collider to extend the direct exploration, the search for signs of new physics might be confined to indirect tests for quite some time. In a few fully calculable models, weakly or semi-strongly interacting, we compare the significance to measure the Higgs couplings versus the electroweak observables.
Comment: 14 pages, 3 figures. v2) one reference added, typos corrected