Dark matter, mu problem and neutrino mass with gauged R-symmetry

We show that the mu problem and the strong CP problem can be resolved in the context of the gauged U(1)_R symmetry, realizing an automatic Peccei-Quinn symmetry. In this scheme, right-handed neutrinos can be introduced to explain small Majorana or Dirac neutrino mass. The U(1)_R D-term mediated SUSY breaking, called the U(1)_R mediation, gives rise to a specific form of the flavor-conserving superpartner masses. For the given solution to the mu problem, electroweak symmetry breaking condition requires the superpartners of the Standard Model at low energy to be much heavier than the gravitino. Thus dark matter candidate can be either gravitino or right-handed sneutrino. In the Majorana neutrino case, only gravitino is a natural dark matter candidate. On the other hand, in the Dirac neutrino case, the right-handed sneutrino can be also a dark matter candidate as it gets mass only from SUSY breaking. We discuss the non-thermal production of our dark matter candidates from the late decay of stau and find that the constraints from the Big Bang Nucleosynthesis can be evaded for a TeV-scale stau mass.