Restrictions on the scale of horizontal symmetry breaking in grand unification theory

A restriction on the scale of horizontal symmetry breaking (M/sub H/) is found which is characteristic of grand unification theory. In the limit M/sub H//M/sub G/→0, where M/sub G/ is the scale at which the grand unification group is broken, either certain quark masses go to zero or the mixing angles vanish, which leads to a restriction on M/sub H//M/sub G/. The result M/sub H/>10-6M/sub G/ depends weakly on the specific features of the group structure and is independent of whether the horizontal symmetry is local or global in nature