| Summary: | Abstract In this paper we explore the possibility of observable gravitational waves as a manifestation of the QCD axion dynamics. In particular, we focus on dynamical axion models which solve the strong CP problem, and include the confinement of a QCD-like gauge group at the TeV scale. We study the resulting chiral symmetry breaking phase transition for models with N F = 3 and N F = 4 light flavors using the linear sigma model. This model describes the scalar meson spectrum and its interactions, with the diagonal field φ as the order parameter. We find that the amplitude of the gravitational wave spectrum depends on the mass of the dynamical axion η′ via the ratio m η ′ / m φ $$ {m}_{\eta^{\prime }}/{m}_{\varphi } $$ . The resulting spectra may be observed at future mid-range gravitational wave experiments such as AION/MAGIS, DECIGO, and BBO. Moreover, the TeV states can be searched for at colliders and their quantum numbers characterized, providing a unique connection between axion physics, gravitational waves and collider searches.
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