Neutrino Masses and $b-\tau$ unification in the Supersymmetric Standard Model

Abstract

There are several indications that the Majorana masses of the right-handed neutrino components, $M_R,$ are at the intermediate scale: $M_R\sim (10^{10}-10^{12})$ GeV or even lighter. The renormalization effects due to large Yukawa couplings of neutrinos from region of momenta $M_R \ltap q \ltap M_G$ are studied in the supersymmetric standard model. It is shown that neutrino renormalization effect can increase the $m_b/m_\tau$ ratio up to $(10\div 15)\%.$ This strongly disfavours $m_b-m_\tau$ unification for low values of $\tan\beta < 10$ especially at large values of $\alpha_s.$ Lower bounds on $M_R$ and $\tan\beta$ from the $b-\tau$ unification condition were found. The implications of the results to the see-saw mechanism of the neutrino mass generation are discussed.