Low scale left-right symmetry and naturally small neutrino mass

We consider the low scale (10-100 TeV) left-right symmetric model with "naturally" small neutrino masses generated through the inverse seesaw mechanism. The Dirac neutrino mass terms are taken to be similar to the masses of charged leptons and quarks in order to satisfy the quark-lepton similarity condition. The inverse seesaw implies the existence of fermion singlets S with Majorana mass terms as well as the "left" and "right" Higgs doublets. These doublets provide the portal for S and break the left-right symmetry. The inverse seesaw allows to realize a scenario in which the large lepton mixing originates from the Majorana mass matrix of S fields which has certain symmetry. The model contains heavy pseudo-Dirac fermions, formed by S and the right-handed neutrinos, which have masses in the 1 GeV-100 TeV range and can be searched for at current and various future colliders such as LHC, FCC-ee and FCC-hh as well as in SHiP and DUNE experiments. Their contribution to neutrinoless double beta decay is unobservable. The radiative corrections to the mass of the Higgs boson and the possibility for generating the baryon asymmetry of the Universe are discussed. Modification of the model with two singlets (S_L and S_R) per generation can provide a viable keV-scale dark matter candidate.