Split Supersymmetry Breaking from Stuckelberg Mixing of Multiple U(1)'s

Abstract

We show that multiple Abelian sectors with Stuckelberg mass-mixing simply break supersymmetry via Fayet-Iliopoulos D-terms and straightforwardly mediate it to the other sectors. This mechanism naturally realizes a split supersymmetry spectrum for soft parameters. Scalar squared-masses (holomorphic and non-holomorphic) are induced through sizable portals and are not suppressed. Gaugino masses, a-terms and a mu-like term are generated by higher-dimensional operators and are suppressed. The hypercharge is mixed with extra U(1)'s, it's D-term in non-vanishing and supersymmetry is broken in the visible sector too. Scalar tachyonic directions are removed by unsuppressed interactions and hypercharge is preserved as supersymmetry is broken. Moreover, if a singlet chiral field is charged under additional $U(1)$'s proportional to its hypercharge, new interaction terms in the Kahler potential and the superpotential are added through Stuckelberg compensation. In this case supersymmetry is broken via F-terms or mixed F and D-terms.