Split supersymmetry from anomalous $U(1)$

Abstract

We present a scenario wherein the anomalous $U(1)$ D-term of string origin triggers supersymmetry breaking and generates naturally a split supersymmetry spectrum. When the gaugino and the higgsino masses (which are of the same order of magnitude) are set at the TeV scale, we find the scalar masses to be in the range $({10}^6\text{–}{10}^8)\text{GeV}$. The $U(1)$ D-term provides a small expansion parameter which we use to explain the mass and mixing hierarchies of quarks and leptons. Explicit models utilizing exact results of $N=1$ supersymmetric gauge theories consistent with anomaly constraints, fermion mass hierarchy, and supersymmetry breaking are presented.