Planck Scale Origin of Non-zero $\theta_{13}$ and Super-WIMP Dark Matter
  We study a discrete flavour symmetric scenario for neutrino mass and dark
matter under the circumstances where such global discrete symmetries can be
explicitly broken at Planck scale, possibly by gravitational effects. Such
explicit breaking of discrete symmetries mimic as Planck suppressed operators
in the model which can have non-trivial consequences for neutrino and dark
matter sectors. In particular, we study a flavour symmetric model which, at
renormalisable level, gives rise to tri-bimaximal type neutrino mixing with
vanishing reactor mixing angle $\theta_{13}=0$, a stable inert scalar doublet
behaving like a weakly interacting massive particle (WIMP) and a stable singlet
inert fermion which does not interact with any other particles. The
introduction of Planck suppressed operators which explicitly break the discrete
symmetries, can give rise to the generation of non-zero $\theta_{13}$ in
agreement with neutrino data and also open up decay channels of inert scalar
doublet into singlet neutral inert fermion leading to the realisation of the
super-WIMP dark matter scenario. We show that the correct neutrino
phenomenology can be obtained in this model while discussing three distinct
realisation of the super-WIMP dark matter scenario.
