A Family--Universal Anomalous U(1) in String Models as the Origin of Supersymmetry Breaking and Squark Degeneracy

Abstract

Recently a promising mechanism for supersymmetry breaking that utilizes both an anomalous U(1) gauge symmetry and an effective mass term m ~ 1TeV of certain relevant fields has been proposed. In this paper we examine whether such a mechanism can emerge in superstring derived free fermionic models. We observe that certain three generation string solutions, though not all, lead to an anomalous U(1) which couples universally to all three families. The advantages of this three-family universality of $U(1)_A$, compared to the two-family case, proposed in earlier works, in yielding squark degeneracy, while avoiding radiative breaking of color and charge, are noted. The root cause of the flavor universality of $U(1)_A$ is the cyclic permutation symmetry that characterizes the $Z_2\times Z_2$ orbifold compactification with standard embedding, realized in the free fermionic models by the NAHE set. It is shown that non--renormalizable terms which contain hidden--sector condensates, generate the required suppression of the relevant mass term $m$, compared to the Planck scale. While the D-term of the family universal $U(1)_A$ leads to squark degeneracy, those of the family dependent U(1)'s, remarkably enough, are found to vanish for the solutions considered, owing to minimization of the potential.