Muon g-2 and lepton flavor violation in a two Higgs doublets model for the fourth generation

In the minimal Standard Model (SM) with four generations (the so called SM4) and in "standard" two Higgs doublets model (2HDM) setups, e.g., the type II 2HDM with four fermion generations, the contribution of the 4th family heavy leptons to the muon magnetic moment is suppressed and cannot accommodate the measured $ \sim 3 \sigma$ access with respect to the SM prediction. We show that in a 2HDM for the 4th generation (the 4G2HDM), which we view as a low energy effective theory for dynamical electroweak symmetry breaking, with one of the Higgs doublets coupling only to the 4th family leptons and quarks (thus effectively addressing their large masses), the loop exchanges of the heavy 4th generation neutrino can account for the measured value of the muon anomalous magnetic moment. We also discuss the sensitivity of the lepton flavor violating decays $\mu \to e \gamma$ and $\tau \to \mu \gamma$ and of the decay $B_s \to \mu \mu$ to the new couplings which control the muon g-2 in our model.