RG-invariant Sum Rule in a Generalization of Anomaly Mediated SUSY Breaking Models

We study a generalization of anomaly-mediated supersymmetry breaking (AMSB) scenarios, under the assumption that the effects of the high-scale theory do not completely decouple and D-term type contributions can be therefore present. We investigate the effect of such possible D-term additional contributions to soft scalar masses by requiring that, for non-vanishing, renormalizable Yukawa couplings $Y^{ijk} $, the sum of squared soft supersymmetry breaking mass parameters, $M^2_{ijk} \equiv m_i^2+m_j^2+m_k^2$, is RG-invariant, in the sense that it becomes independent of the specific ultraviolet boundary conditions as it occurs in the AMSB models. These type of models can avoid the problem of tachyonic solutions for the slepton mass spectrum present in AMSB scenarios. We implement the electroweak symmetry breaking condition and explore the sparticle spectrum associated with this framework. To show the possible diversity of the sparticle spectrum, we consider two examples, one in which the D-terms induce a common soft supersymmetry breaking mass term for all sfermion masses, and another one in which a light stop can be present in the spectrum.