Gauged R-symmetry, fermion and Higgs mass problem

We consider the simplest model of SU(3) x SU(2) x U(1)(Y) x 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) = 5/3g(1)(2) of the gauge coupling constants is assumed, the Higgs mass parameter mu similar to m(3/2) can arise taking into account the uncertainty in the ultraviolet relation m(e)m(mu)m(tau)/m(d)m(s)m(b) similar or equal to lambda(q) with q not equal 0. When q = 0 is taken only a suppressed value of mu similar to lambda m(3/2) can be obtained.