The Higgs boson lineshape and perturbative unitarity

We discuss the lineshape of a heavy Higgs boson, and the behaviour well above resonance. Previous studies concluded that the energy-dependent Higgs width should be used in the resonance region, but must not be used well away from it. We derive the full result and show that it smoothly extrapolates these limits. It is extremely simple, and would be straightforward to implement in existing calculations.