Remarks on analyticity and unitarity in the presence of a Strongly Interacting Light Higgs

Abstract

Applying the three axiomatic criteria of Lorentz invariance, analyticity and unitarity to scattering amplitudes involving the Goldstone bosons and the Higgs boson, we derive a general sum rule for the Strongly Interacting Light Higgs Lagrangian. This sum rule connects the IR coefficient $c_H$ to the UV properties of the theory, and can be used, for instance, to capture the role of resonances in processes like $V_{\mathrm{L}}{V}_{\mathrm{L}}\to hh$ and $V_{\mathrm{L}}{V}_{\mathrm{L}}\to V_{\mathrm{L}}{V}_{\mathrm{L}}$, with $V=W^{\pm },Z$.

Comments: 14 pages, two column format. v2: references added, one figure added, typos fixed. v3: references added. v4: minor changes