Neutrino mass matrix in triplet Higgs models with $A_4$ symmetry

We consider triplet Higgs model with $A_4$ symmetry to generate the neutrino mass matrix. The tribimaximal form of the neutrino mixing matrix can be naturally obtained. Imposing the neutrino oscillation data, we show that 1) both normal and inverted mass hierarchy are allowed, 2) there is a lower bound on the lightest neutrino mass and the effective mass for neutrinoless double beta decay, 3) the non-vanishing $\th_{13}$ can be accommodated by considering small perturbation, 4) $\th_{\rm atm}$ should be very close to $\pi/4$ even after perturbation. }