The Higgs Boson Lineshape and Perturbative Unitarity

Abstract

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.

Figures (8)

• Figure 1: Lowest order Feynman diagrams for $W^+W^-\to ZZ$ in the electroweak theory (a), and the high-energy effective theory (b), in which the vector bosons are represented by the corresponding Goldstone bosons.
• Figure 2: All orders resummation leading to the Higgs boson self-energy.
• Figure 3: All orders resummation leading to the vector boson pair self-energy. Note that both resonant and non-resonant diagrams are included.
• Figure 4: The $I\!=\!0,\;J\!=\!0$ partial wave for elastic vector boson scattering with various treatments of the Higgs boson width: zero width (dotted), fixed width (dashed), using the Higgs boson self-energy (dot-dashed), and the full result using the vector boson pair self-energy (solid).
• Figure 5: As in Fig. \ref{['f4']}, using the full result (solid), the naı ve $s$-channel approximation (dotted) and the improved $s$-channel approximation (dashed).