An $SU(5)\times U(1)^\prime$ SUSY GUT with a "vector-like chiral" fourth family to fit all low energy data, including the muon $g-2$

Abstract: An additional generation of quarks and leptons and their SUSY counterparts, which are vector-like under the Standard Model gauge group but are chiral with respect to the new U(1)${3-4}$ gauge symmetry, are added to the Minimal Supersymmetric Standard Model (MSSM). We show that this model is a GUT and unifies the three SM gauge couplings and also the additional U(1)${3-4}$ coupling at a GUT scale of $\approx 5 \times 10^{16}$ GeV and explains the experimentally observed deviation of the muon $g-2$. We also fit the quark flavor changing processes consistent with the latest experimental data and look at the effect of the new particles on the $W$ boson mass without obviously conflicting with the observed masses of particles, CKM matrix elements, neutrino mixing angles, their mass differences, and the lepton-flavor violating bounds. This model predicts sparticle masses less than 25 TeV, with a gluino mass $\approx 2.3 - 3$ TeV consistent with constraints, and one of the neutralinos as the LSP with a mass of $\approx 480 - 580$ GeV, which is a potential dark matter candidate. The model is string theory motivated and predicts the VL quarks, leptons, a massive $Z'$ and two Dirac neutrinos at the TeV scale and the branching ratios of $\mu \longrightarrow e \gamma$, $\tau \longrightarrow \mu \gamma$ and $\tau \longrightarrow 3\mu$ with BR($\mu \longrightarrow e \gamma$) within reach of future experiments.