Burgeoning the Higgs mass to 125 GeV through messenger-matter interactions in GMSB models

A 125 GeV Higgs renders the simpler GMSB models unnatural, essentially pushing the soft spectrum beyond the LHC reach. A direct coupling of the matter and messenger fields, that facilitates an enhanced mixing in the squark sector, is a way to ameliorate this deficiency. We construct all possible messenger-matter interaction terms considering the messenger multiplets in 1, 5 and 10 dimensional representations of the SU(5). A Froggatt-Nielsen like flavor framework connected with the origin of fermion mass hierarchy is utilized to control the interaction terms and suppress FCNC. We perform a detailed comparative study of the efficiency of such interaction terms to boost the Higgs mass keeping the soft spectrum light. We identify the more promising models and comment on their status in present and future collider studies.