The linear-non-linear frontier for the Goldstone Higgs

Abstract

The minimal $SO(5)/SO(4)$ sigma model is used as a template for the ultraviolet completion of scenarios in which the Higgs particle is a low-energy remnant of some high-energy dynamics, enjoying a (pseudo) Nambu-Goldstone boson ancestry. Varying the $\sigma$ mass allows to sweep from the perturbative regime to the customary non-linear implementations. The low-energy benchmark effective non-linear Lagrangian for bosons and fermions is obtained, determining as well the operator coefficients including linear corrections. At first order in the latter, three effective bosonic operators emerge which are independent of the explicit soft breaking assumed. The Higgs couplings to vector bosons and fermions turn out to be quite universal: the linear corrections are proportional to the explicit symmetry breaking parameters. Furthermore, we define an effective Yukawa operator which allows a simple parametrization and comparison of different heavy fermion ultraviolet completions. In addition, one particular fermionic completion is explored in detail, obtaining the corresponding leading low-energy fermionic operators.

23 pages, 1 figure and 3 tables

References in corpus (13)

• Big-Bang Nucleosynthesis
• Light custodians in natural composite Higgs models
• The Higgs boson from an extended symmetry
• Evidence for Electroweak Production of $W^{\pm }{W}^{\pm }jj$ in $pp$ Collisions at $\sqrt{s}=8$ TeV with the ATLAS Detector
• Implications of a Light Higgs in Composite Models
• Minimal Composite Higgs Models at the LHC
• Low Scale Flavor Gauge Symmetries
• A naturally light Higgs without light Top Partners
• Sigma Decomposition
• The Excitation of the Global Symmetry-Breaking Vacuum in Composite Higgs Models
• The Global Higgs as a Signal for Compositeness at the LHC
• Vacuum alignment with(out) elementary scalars
• The Dynamical Composite Higgs

Cited by in corpus (2)

• Exotic Vector-Like Quark Phenomenology in the Minimal Linear $\sigma$ Model
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