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 $V=W^{\pm },Z$.

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

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Cited by in corpus (15)

• The Composite Nambu-Goldstone Higgs
• Composite Higgses
• Beyond Amplitudes' Positivity and the Fate of Massive Gravity
• Softness and Amplitudes' Positivity for Spinning Particles
• Geometry of the Scalar Sector
• Symmetries, Sum Rules and Constraints on Effective Field Theories
• ZZ and Zgamma still haven't found what they are looking for
• The $\hat{H}$-Parameter: An Oblique Higgs View
• To Positivity and Beyond, where Higgs-Dilaton Inflation has never gone before
• Strongly Interacting Light Dark Matter
• Theoretical Constraints on Additional Higgs Bosons in Light of the 126 GeV Higgs
• Four-fermion operators at dimension 6: dispersion relations and UV completions
• Interpreting a 2 TeV resonance in WW scattering
• Introducing tools to test Higgs interactions via $WW$ scattering II: the coupled channel formalism and scalar resonances
• Softness, Polynomial Boundedness and Amplitudes' Positivity