The linear–non-linear frontier for the Goldstone Higgs

Abstract

The minimal SO(5)/SO(4) σ -model is used as a template for the ultraviolet completion of scenarios in which the Higgs particle is a low-energy remnant of some highenergy dynamics, enjoying a (pseudo) Nambu-Goldstoneboson ancestry. Varying the σ mass allows one 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.

The minimal axion minimal linear $$\sigma $$σ model

“…For λ s in the strongly interacting regime, the radial component r can be expanded in inverse powers of λ s (see Ref. [10] for a similar analysis): at the NLO, one has…”

“…Refs. [7][8][9][10] attempted to improve in this respect, providing a renormalisable description of the scalar sector. Following for definiteness the treatment done in Ref.…”

Exotic vectorlike quark phenomenology in the minimal linear σ model

“…Several studies have been conducted on this model to analyse its features at low-energies [35], projecting to the so-called Higgs effective field theory Lagrangian [36][37][38][39][40][41][42][43][44][45][46][47][48][49], to access its ability to solve the strong CP problem [50][51][52]. The focus of this paper, instead, is to study the phenomenology associated to the exotic vector-like quarks (VLQs).…”

Testable axion-like particles in the minimal linear σ model

“…The Minimal Linear σ-Model (MLσM) [8][9][10][11] is, instead, a renormalisable model that represents a convenient and well-defined framework that, at need, by integrating out the extra scalar degree of freedom (dof) σ, matches the usual effective non-linear MCHM [5,[12][13][14] Lagrangian, or the more general Higgs Effective Field Theory Lagrangian . Following the treatment of Ref.…”