A Higgs mass of 125 GeV can be accommodated in the MSSM + Minimal Gauge Mediation only with a heavy SUSY spectrum. In the NMSSM there are additional tree-level contributions to the Higgs mass, but in the NMSSM + Minimal Gauge Mediation it is difficult to achieve correct electroweak symmetry breaking. This motivates to consider modifications of Minimal Gauge Mediation that can provide large stop mixing in the MSSM or generate large singlet masses in the NMSSM. I will discuss several examples of such modifications that lead to a rich collider and/or flavor phenomenology.

LPTHE-Jussieu