Light "Higgs", yet strong interactions

TL;DR

This paper examines the implications of a light Higgs boson on electroweak symmetry breaking, constructing an effective theory for W, Z, and scalar interactions, and finds that high-energy W scattering is generally strongly interacting.

Contribution

It develops a comprehensive effective Lagrangian for electroweak Goldstone bosons and a light scalar, analyzing unitarization and scattering amplitudes in the absence of new physics.

Findings

High-energy W_L W_L scattering is strongly interacting in most parameter space.

A second sigma-like scalar pole in the W_L W_L amplitude is identified.

The minimal Standard Model remains a notable exception with weaker interactions.

Abstract

The claimed finding of a light Higgs boson makes the minimal Standard Model unitary. Yet we recall that the general low-energy dynamics for the minimal electroweak symmetry breaking sector with three Goldstone bosons and one light scalar is not so. We construct the effective Lagrangian for these four particles and their scattering amplitudes, that can be extracted from LHC experiments when longitudinal W, Z modes be properly isolated for E>>M_W (Equivalence Theorem). We then observe the known increase in interaction strength with energy and explore various unitarization methods in the literature in the absence of other new physics (as LHC experiments fail to report anything up to 600 GeV). Our generic conclusion is that for most of parameter space the high energy scattering of the longitudinal W's is strongly interacting (with the Minimal Standard Model a remarkable exception). We find and study a second sigma-like scalar pole of the W_L W_L amplitude.