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 $M_R\text{ltap}q\text{ltap}{M}_G$ are studied in the supersymmetric standard model. It is shown that neutrino renormalization effect can increase the $m_b/m_{\tau }$ ratio up to $(10÷15)\%.$ 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.

Comments: LATeX, 10 pages of text + 4 PostScript figures appended at the end, SISSA 63/94/EP and IC/94/102