Non-holomorphic Contributions in GMSB with Adjoint Messengers

We consider models of gauge mediated supersymmetry breaking, in which the breaking is transmitted to the visible sector by the messenger fields from the adjoint representation of MSSM's gauge group. We include the non-holomorphic terms induced by the supersymmetry breaking and involve them in the renormalization group evolution. The main impact from the non-holomorphic terms arises in the right-handed stau mass, which requires large hypercharge interactions with the messengers to accommodate non-tachyonic staus. With the non-holomorphic terms, the stau mass-square can remain positive in the renormalization group evolution, even if the hypercharge interactions are small. Although the radiative non-holomorphic contributions enhance the mass spectrum, their effects in the sparticle mixing rather reduce their overall contributions such that we realize about 25 GeV difference in the right-handed stau mass, while the difference is lowered by about 5 TeV in the lightest mass-eigenstate of staus. We realize 6-7 TeV difference in the sbottom mass, and about 15 TeV in the stop mass. These contributions in the sparticle masses also affect the SM-like Higgs boson mass, and we find that the SM-like Higgs boson can be enhanced as much as about 80 GeV. In a small region of the parameter space we also observe negative non-holomorphic contributions which do not exceed about 1 TeV for the sparticles, and 20 GeV for the SM-like Higgs boson. An interesting impact from the non-holomorphic terms happens in the muon g-2 results. We find that the non-holomorphic contributions can provide a significant decreasing in supersymmetric contributions to muon g-2. We realize that the muon g-2 results can be decreased as much as about -50 x 10^-10 by the non-holomorphic contributions, and consequently one can still accommodate light sleptons and gauginos in the spectrum.