We study a simple extension of the Standard Model supplemented by an electroweak triplet scalar field to accommodate small neutrino masses by the type-II seesaw mechanism, while an additional singlet scalar field can play the role of cold dark matter (DM) in our Universe. This DM candidate is leptophilic for a wide range of model parameter space, and the lepton flux due to its annihilation carries information about the neutrino mass hierarchy. Using the recently released high precision data on positron fraction and flux from the AMS-02 experiment, we examine the DM interpretation of the observed positron excess in our model for two kinematically distinct scenarios with the DM and triplet scalar masses (a) non-degenerate ($m_{rm DM}gg m_{Delta}$), and (b) quasi-degenerate ($m_{rm DM} simeq m_Delta$). We find that a good fit to the AMS-02 data can be obtained in both cases (a) and (b) with a normal hierarchy of neutrino masses, while the inverted hierarchy case is somewhat disfavored. Although we require a larger boost factor for the normal hierarchy case, this is still consistent with the current upper limits derived from Fermi-LAT and IceCube data for case (a). Moreover, the absence of an excess anti-proton flux as suggested by PAMELA data sets an indirect upper limit on the DM-nucleon spin-independent elastic scattering cross section which is stronger than the existing DM direct detection bound from LUX in the AMS-02 preferred DM mass range.
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