Abstract
We review a class of models which generalize the traditional Peccei-Quinn (PQ) axion solution by a St\uckelberg psedudoscalar. Such axion models represent a significant variant respect to those scenarios where axion fields are associated with global anomalies, being a St\uckelberg field, essential for the cancellation of gauge anomalies in the presence of extra $U(1)$ symmetries. The extra neutral currents associated with these models have been investigated in the past in orientifold models with intersecting branes, under the assumption that the St\uckelberg scale was in the multi-TeV region. Such constructions, at the field theory level, are quite general and can be interpreted as the four-dimensional field theory realization of the Green-Schwarz mechanism of anomaly cancellation of string theory. We present an overview of models of this type in the TeV/multi TeV range in their original formulation and their recent embeddings into an ordinary GUT theory, presenting an $E_6\times U(1)_X$ model as an example. In this case the model contains two axions, the first corresponding to a Peccei-Quinn axion, whose misalignment takes place at the QCD phase transition, with a mass in the milli-eV region and which solves the strong CP problem. The second axion is ultralight, in the $10^{-18}-10^{-22}$ eV region, due to a misalignment and a decoupling taking place at the GUT scale. The two scales introduced by the PQ solution, the PQ breaking scale and the misalignment scale at the QCD hadron transition, become the Planck and the GUT scales respectively, with a global anomaly replaced by a gauge anomaly. The periodic potential and the corresponding oscillations are related to a particle whose De Broglie wavelength can reach 10 kpc. Such a sub-galactic scale has been deemed necessary in order to resolve several dark matter issues at the astrophysical level.
Highlights
It is well established that astrophysical and cosmological data coming either from measurements of the velocities of stars orbiting galaxies, in their rotation curves, or from the cosmic microwave background, indicate that about ∼ 80% of matter in the universe is in an unknown form, and the expectations for providing an answer to such a pressing question run high
Cold dark matter with small density fluctuations, growing gravitationally and a spectral index of the perturbations nS ∼ 1 is compatible with an early inflationary stage and accounts for structure formation in most of the early universe eras
While the agreement between CDM and the observations is significant at most scales, at a small sub-galactic scale, corresponding to astrophysical distances relevant for the description of the stellar distributions (∼10 kpc), cold dark matter models predict an abundance of low-mass halos in excess of observations [5]
Summary
It is well established that astrophysical and cosmological data coming either from measurements of the velocities of stars orbiting galaxies, in their rotation curves, or from the cosmic microwave background, indicate that about ∼ 80% of matter in the universe is in an unknown form, and the expectations for providing an answer to such a pressing question run high. The possibility that more than one axion is part of the spectrum of a certain gauge theory is not excluded, with the mass of each axion controlled by independent mechanism(s) of vacuum misalignment induced at several scales, if distinct gauge couplings for each of such particles with different gauge sectors are present [12, 13] We will illustrate this point in the extended E6 theory, where the inclusion of an extra anomalous U(1) gauge symmetry realizes such a scenario. Different mechanisms of vacuum misalignment may be responsible for the generation of axions of different masses, whose sizes may vary considerably
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