Fermion masses in SO(10): The case of the tree-level relationmb≠mτ

By considering the renormalization-group flow of the top-quark generation Yukawa couplings in SO(10), we can constrain the tree-level value for the ratio $\frac{m_b}{m_{\tau }}$. Analytic bounds on the flow show that the tree-level ratio must satisfy $0.6\lesssim \frac{m_b}{m_{\tau }}\lesssim 1.1$ for the model with one Higgs particle at low energies, and $0.95\lesssim \frac{m_b}{m_{\tau }}\lesssim 1.5$ for the two-Higgs-particle case.