Abstract
We studied an extension of the standard model with a vector lepton doublet to
explain the discrepancy in the muon \$g-2\$ and explain the positron excess seen
in the AMS-02 experiment. We introduced a gauge \$SU(2)\_H\$ horizontal
symmetry between the muon family and the 4th generation leptons. The neutral
components of the 4th generation lepton doublet act as inelastic pseudo-Dirac
dark matter. In this leptophilic model no antiproton excess predicted and the
direct detection constraints are evaded. We get a boost factor of order 100
needed to explain the AMS-02 positron flux by dark matter annihilation into
muons, by a Sommerfeld enhancement from \$Z\$ exchange.
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