Pattern of fermion masses from high-scale evolution

Abstract

Dynamical equations for fermion masses are derived using high scale universal mass generation and consequent mass evolution due to $SU(3), SU(2)$, and U(1$ gauge interaction. Assuming mass generation at the GUT scale $M=10^{14}$ GeV, one obtains hierarchy and a large spread in fermion masses with roughly correct values of $m_\nu, m_\tau, m_t, m_b$ in the third generation. The smallness of neutrino mass, $\nu_3\sim 10^{-12} m_{t}$, naturally arises in the solution.