Upper bound on Hot Dark Matter Density from $SO(10)$ Yukawa Unification

Details Upper bound on Hot Dark Matter Density from $SO(10)$ Yukawa Unification Upper bound on Hot Dark Matter Density from $SO(10)$ Yukawa Unification

1994-06-26

arxiv.org/abs/hep-ph/9406397v1

Phys.Lett.B335:345-354,1994

Physics

High Energy Physics

High Energy Physics - Phenomenology

LBL-35774, RU-94-51, 18 pages, plain LaTeX, two PostScript figures appended in uuencoded format

Scientific paper

10.1016/0370-2693(94)90362-X

We study low-energy consequences of supersymmetric $SO(10)$ models with Yukawa unification $h_t = h_N$ and $h_b = h_\tau$. We find that it is difficult to reproduce the observed $m_b/m_\tau$ ratio when the third-generation right-handed neutrino is at an intermediate scale, especially for small $\tan \beta$. We obtain a conservative lower bound on the mass of the right-handed neutrino $M_N > 6 \times 10^{13}$~GeV for $\tan \beta < 10$. This bound translates into an upper bound on the $\tau$-neutrino mass, and therefore on its contribution to the hot dark matter density of the present universe, $\Omega_\nu h^2 < 0.004$. Our analysis is based on the full two-loop renormalization group equations with one-loop threshold effects. However, we also point out that physics above the GUT-scale could modify the Yukawa unification condition $h_b = h_\tau$ for $\tan \beta \lsim 10$. This might affect the prediction of $m_b/m_\tau$ and the constraint on $M_N$.

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