Condensates of ultralight axions and a link of leptonic scales to dark matter

Abstract

The mass of ultralight axions is determined in order to get the explicit U(1)$_A$ symmetry breaking scale $ \Lambda $ at a Peccei-Quinn scale of the magnitude of the Planck mass. It is assumed that the dominant contribution to the mass of a galaxy with low surface brightness is only determined by one axionic species in the sense of fuzzy dark matter (lumps). For rotation curve fits to galactic rotation curves, therefore the Soliton-Navarro-Frenk-White model is used, which assumes a condensate core plus correlated axions in the halo according to the solution of the Poisson-Schr\"odinger system. In addition, three commonly used mass density profiles are considered: Navarro-Frenk-White, pseudo-isothermal and the Burkert model. An axion mass $m_a$ of $0.675\times10^{-23}\,$eV is extracted, which reproduces previous results in the literature. This implies an effective Yang-Mills scale of $\Lambda \sim 287\,$ eV, which is only a factor of $15$ smaller than the Yang-Mills scale of an SU(2) theory that is used to describe the first lepton family. The cosmological model SU(2)$_{\rm CMB} $ suggests that three SU(2) Yang-Mills theories, each for the formation of the lepton doublets (e,$\nu_e$), ($\mu$,$\nu_\mu$), and ($\tau$,$\nu_\tau$) are equally responsible for contributing to the current density of dark matter. Parameters of an isolated lump, such as the gravitational Bohr radius or the virial mass, are determined solely by the Planck mass and the corresponding lepton mass. If the dominant constituent of the dark mass contained in a galaxy is represented by e-lumps, a mixture of $ \tau- $ and $ \mu$-lumps could possibly explain the presence of massive compact objects in galactic centers, and $ \tau$-lumps could be related to globular clusters and the halo mass. This might provide a theoretical explanation for the mass gap between stellar and super massive black holes.