Flavored gauge mediation in the Peccei-Quinn NMSSM

We investigate a particular version of the Peccei-Quinn (PQ) NMSSM characterized by an economical and rigidly hierarchical flavor structure and based on flavored gauge mediation and on some considerations inspired by string theory GUTs. In this way we can express the Lagrangian of the PQ NMSSM through very few parameters. The obtained model is studied numerically and confronted with the most relevant phenomenological constraints. We show that typical spectra are for the most part too heavy to be significantly probed at the LHC, but regions of the parameter space exist yielding signatures that might possibly be observed during Run II. We also calculate the fine tuning of the model. We show that, in spite of the appearance of large scales in the superpotential and soft terms, it does not exceed the tuning present in the MSSM for equivalent spectra, which is of the order of 10^4.