NMSSM with Lopsided Gauge Mediation
  We study a gauge mediated supersymmetry breaking version of the NMSSM in which the soft m_{H_u}^2 and m_{H_d}^2 masses receive extra contributions due to the presence of direct couplings between the Higgs and the messenger sector. We are motivated by the well-known result that minimal gauge mediation is phenomenologically incompatible with the NMSSM due to the small value of the induced effective mu term. The model considered in the present paper solves the aforementioned problem through a modified RG running of the singlet soft mass m_N^2. This effect, which is induced by the dominant m_{H_d}^2 term in the one-loop beta-function of m_N^2, shifts the singlet soft mass towards large negative values at the electroweak scale. That is sufficient to ensure a large VEV for the scalar component of the singlet which in turn translates into a sizeable effective mu term. We also describe a mechanism for generating large soft trilinear terms at the messenger scale. This allows us to make the mass of the lightest Higgs boson compatible with the current LHC bound without relying on exceedingly heavy stops. 
Ivan Donkin, Alexander K. Knochel
hep-ph