Explaining muon magnetic moment and AMS-02 positron excess in a gauged horizontal symmetric model

We extended the standard model with a fourth generation of fermions to explain the discrepancy in the muon magnetic moment and to describe the positron excess observed by AMS-02 experiment. We introduce a gauged $SU(2)_{HV}$ horizontal symmetry between the muon and the 4th generation lepton families and identified the 4th generation right-handed neutrino as the dark matter with mass $\sim 700$ GeV. The dark matter annihilates through $SU(2)_{HV}$ gauge boson into final states $(\mu^+ \mu^-)$ and $(\nu^c_\mu ~\nu_\mu)$. The $SU(2)_{HV}$ gauge boson with mass $\sim 1.4$ TeV gives the required contribution to the muon $(g-2)$ and satisfy the experimental constraint from BNL measurement.