Light scalars, ($g_{\mu }-2$) muon anomaly and dark matter in a model with a Higgs democracy

We consider isosinglet scalar extension of a model with a Higgs democracy - multihiggs extension of the SM where each quark and lepton has its own Higgs isodoublet. The addition of light isosinglet scalar allows to solve both muon $g_{\mu }-2$ anomaly and dark matter problem. Also we point out that an extension of the model with $L_{\mu }-L_{\tau }$ vector interaction allows not only explain muon $g_{\mu }-2$ anomaly but also dark matter density.