Gauged R-symmetry, fermion and Higgs mass problem

We consider the simplest model of SU(3) × SU(2) × U(1)Y × 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 μ problem only if its mixed anomalies are cancelled by the Green-Schwarz mechanism. When the canonical normalization g32 = g22 = 5/3g12 of the gauge coupling constants is assumed, the Higgs mass parameter μ ∼ m32 can arise taking into acount the uncertainty in the ultraviolet relation memμmτmdmsmb ⋍ λq with q ≠ 0. When q = 0 is taken only a suppressed value of μ ∼ λm32 can be obtained.