Symmetry Principles toward Solutions of $μ$ Problem

Abstract

We stress that a natural solution of the $μ$ problem requires two ingredients: a symmetry that would enforce $μ= 0$ as well as the occurence of a small breaking parameter that generates a nonzero $μ$. It is suggested that both the Peccei-Quinn symmetry and the spontaneously broken $R$ symmetry may be the sources of the needed $μ$ term in the minimal supersymmetric standard model provided that they are spontaneously broken at a scale $10^{10}-10^{12}$ GeV. To solve the strong CP problem with a hidden sector confining group, both of these symmetries are needed in superstring models with an anomalous $U(1)_A$.