Gauged R-symmetry, Fermion and Higgs Mass Problem

Abstract

We consider the simplest model of $SU(3)\times SU(2)\times U(1{)}_Y\times U(1{)}_R$ gauge symmetry with one extra singlet field whose vacuum expectation value breaks the horizontal $R$-symmetry $U(1{)}_R$ and gives rise to Yukawa textures. The $U(1{)}_R$ symmetry is able to provide both acceptable fermion mass hierarchies and a natural solution to the $\mu$ problem only if its mixed anomalies are cancelled by the Green-Schwarz mechanism. When the canonical normalization $g_3^2=g_2^2=\frac{5}{3}{g}_1^2$ of the gauge coupling constants is assumed, the Higgs mass parameter $\mu \sim m_{3/2}$ can arise taking into acount the uncertainty in the ultraviolet relation $m_e{m}_{\mu }{m}_{\tau }/m_d{m}_s{m}_b\simeq {\lambda }^q$ with $q\ne 0$. When $q=0$ is taken only a suppressed value of $\mu \sim \lambda m_{3/2}$ can be obtained.

Comments: 6 pages, Latex, no figures