Dark matter and sub-GeV hidden U(1) in GMSB models

Motivated by the recent PAMELA and ATIC data, one is led to a scenario with heavy vector-like dark matter in association with a hidden $U(1)_X$ sector below GeV scale. Realizing this idea in the context of gauge mediated supersymmetry breaking (GMSB), a heavy scalar component charged under $U(1)_X$ is found to be a good dark matter candidate which can be searched for direct scattering mediated by the Higgs boson and/or by the hidden gauge boson. The latter turns out to put a stringent bound on the kinetic mixing parameter between $U(1)_X$ and $U(1)_Y$: $θ\lesssim 10^{-6}$. For the typical range of model parameters, we find that the decay rates of the ordinary lightest neutralino into hidden gauge boson/gaugino and photon/gravitino are comparable, and the former decay mode leaves displaced vertices of lepton pairs and missing energy with distinctive length scale larger than 20 cm for invariant lepton pair mass below 0.5 GeV. An unsatisfactory aspect of our model is that the Sommerfeld effect cannot raise the galactic dark matter annihilation by more than 60 times for the dark matter mass below TeV.