Soft Scalar Masses in String Models with Anomalous $U(1)$ symmetry

TL;DR

The paper investigates soft scalar masses in 4D string models with an anomalous U(1) symmetry, deriving the low-energy effective theory below U(1)_A breaking. A dominant D-term contribution and moduli-dependent F-terms yield a compact scalar-mass formula $m^2_{\kappa} = m_{3/2}^2[1 + n_{\kappa} \cos^2\theta + (q_{\kappa}/q_X)(7 - n_X \cos^2\theta - 6 \cos^2\theta)]$, revealing strong non-universality. It analyzes degeneracy and positivity constraints, showing FCNC suppression and mass positivity compete with fermion mass hierarchies, and demonstrates these tensions in a Z3 orbifold example with extensive negative masses. The study highlights significant phenomenological implications for model-building with anomalous U(1) symmetries and motivates exploring alternative SUSY-breaking and symmetry-breaking schemes in string-inspired frameworks.

Abstract

We obtain the low-energy effective theory from string models with anomalous $U(1)$ symmetry. The feature of soft supersymmetry breaking scalar masses and some phenomenological implications are discussed. We show that it is, in general, difficult to keep the degeneracy and the positivity of squared soft scalar masses at the Planck scale.