Abstract
The minimal SO(5) / SO(4) linear sigma 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)rightarrow 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 sim 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 sim 200 TeV, that may show up in collider searches.
Highlights
In order to completely fix the Peccei– Quinn (PQ) charge assignment the following requirements are imposed: the SM fermion masses are generated at tree-level through the fermion partial compositeness mechanism [40,41,42,43], which is the only explicit S O(5) breaking sector; the PQ scalar field s couples to the exotic fermions providing a portal between the axion and the colour interactions
When f 2 > 0 and fs2 > 0, the minimum of the potential allows for the S O(5), U (1)PQ and EW spontaneous symmetry breaking with non-vanishing vacuum expectation value (VEV), vh2
The Axion Minimal Linear σ Model (AMLσ M) [39] represents a class of models that extend the MLσ M [9] by the introduction of a complex scalar singlet, that allows to supplement the S O(5) and EW symmetries with an extra U (1)PQ
Summary
The MLσ M based on the linear S O(5)/S O(4) symmetry breaking realisation has been analysed in Ref. [9]. 2. A real scalar field φ in the fundamental representation of S O(5), which includes the three would-be-longitudinal components of the SM gauge bosons πi , i = 1, 2, 3, the Higgs field h and the additional complex scalar field σ , singlet under the SM gauge group:. 3. Exotic vector fermions, which couple directly to the S O(5) scalar sector through S O(5) invariant protoYukawa interactions. Exotic vector fermions, which couple directly to the S O(5) scalar sector through S O(5) invariant protoYukawa interactions These fermions transform either in the fundamental of S O(5), and they will be labelled as ψ, or in the singlet representation of S O(5), dubbed χ. The explicit expression for each piece will be detailed in the following subsections
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