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

Abstract

The minimal SO(5)/SO(4) linear σ model is extended including an additional complex scalar field, singlet under the global SO(5) and the Standard Model gauge symmetries. The presence of this scalar field creates the conditions to generate an axion à la KSVZ, providing a solution to the strong CP problem, or an axion-like-particle. Different choices for the PQ charges are possible and lead to physically distinct Lagrangians. The internal consistency of each model necessarily requires the study of the scalar potential describing the SO(5) → SO(4), electroweak and PQ symmetry breaking. A single minimal scenario is identified and the associated scalar potential is minimised including counterterms needed to ensure one-loop renormalizability. In the allowed parameter space, phenomenological features of the scalar degrees of freedom, of the exotic fermions and of the axion are illustrated. Two distinct possibilities for the axion arise: either it is a QCD axion with an associated scale larger than ∼ 10 5 TeV and therefore falling in the category of the invisible axions; or it is a more massive axion-like-particle, such as a 1 GeV axion with an associated scale of ∼ 200 TeV, that may show up in collider searches.

Exotic vectorlike quark phenomenology in the minimal linear σ model

“…The last two terms are just a subset of all the soft breaking terms, but are the ones necessary to absorbe divergencies once the one-loop Coleman-Weinberg contributions are considered (see Ref. [51] for a different treatment). For values λ 1, the non-linear model would be recovered, corresponding to a decoupling of the σ field.…”

“…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

“…By extending the MLσM spectrum with an additional complex scalar field s, singlet under SM and SO(5) symmetries, and by supplementing it with an additional global Abelian symmetryà la Peccei-Quinn (PQ) [38], U (1) PQ , an axion or an axion-like particle (ALP) can also be introduced. Such a framework has been dubbed Axion-MLσM (AMLσM) [39,40].…”

“…The tree-level renormalisable scalar potential associated to the AMLσM, describing the spontaneous SO(5)/SO(4) and PQ symmetry breaking, reads [40]…”

Same-sign WW scattering in the HEFT: discoverability vs. EFT validity

“…The physical Higgs field may be either a singlet of the diagonal, the so-called custodial, symmetry SU (2) C (if in an UV completion the SU (2) L × SU (2) R symmetry is realised linearly at a certain level) or an additional field never forming the Higgs doublet with the three Goldstone bosons (GBs). This Lagrangian is the most general description of the EW and Higgs couplings, satisfying the gauge symmetry of the SM: in specific limits, it may reduce to the SM Lagrangian, or may coincide with the SMEFT one, or may match the description of CH models [21][22][23][24][25][26][27][28][29][30][31] or even dilaton models [32][33][34].…”