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

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• Exotic Vector-Like Quark Phenomenology in the Minimal Linear $\sigma$ Model
• Modelling vector-like quarks in partial compositeness framework
• Distinguishing A Higgs-Like Dilaton Scenario With A Complete Bosonic Effective Field Theory Basis
• Constraining Composite Higgs Models using LHC data
• Same-sign WW Scattering in the HEFT: Discoverability vs. EFT Validity
• Heavy vector-like quarks decaying to exotic scalars: a case study with triplets
• Probing the Higgs boson through Yukawa force
• The Axion and the Goldstone Higgs
• The Art of Counting: a reappraisal of the HEFT expansion
• Probing the Top-Higgs Sector with Composite Higgs Models at Present and Future Hadron Colliders
• Probing Effective Field Theory Approach in the CP Violating Minimal Linear $\sigma$ Model
• One Formula To Match Them All: The Bispinor Universal One-Loop Effective Action