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Muon anomalous magnetic moment and positron excess at AMS-02 in a gauged horizontal symmetric model

We studied an extension of the standard model with a fourth generation of fermions to explain the discrepancy in the muon $(g-2)$ and explain the positron excess seen in the AMS-02 experiment. We introduce a gauged $SU(2)_{HV}$ horizontal symmetry between the muon and the 4th generation lepton families. The 4th generation right-handed neutrino is identified as the dark matter with mass $\sim 700$ GeV. The dark matter annihilates only to $(μ^+ μ^-)$ and $(ν^c_μ~ν_μ)$ states via $SU(2)_{HV}$ gauge boson. The $SU(2)_{HV}$ gauge boson with mass $\sim 1.4$ TeV gives an adequate contribution to the $(g-2)$ of muon and fulfill the experimental constraint from BNL measurement. The higgs production constraints from 4th generation fermions is evaded by extending the higgs sector.