Fourth standard model family neutrino at future linear colliders

It is known that flavor democracy favors the existence of the fourth standard model (SM) family. In order to give nonzero masses for the first three-family fermions flavor democracy has to be slightly broken. A parametrization for democracy breaking, which gives the correct values for fundamental fermion masses and, at the same time, predicts quark and lepton Cabibbo-Kobayashi-Maskawa (CKM) matrices in a good agreement with the experimental data, is proposed. The pair productions of the fourth SM family Dirac $({\ensuremath{\nu}}_{4})$ and Majorana $({N}_{1})$ neutrinos at future linear colliders with $\sqrt{s}=500\text{ }\text{ }\mathrm{GeV}$, 1 TeV, and 3 TeV are considered. The cross section for the process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{4}{\overline{\ensuremath{\nu}}}_{4}({N}_{1}{N}_{1})$ and the branching ratios for possible decay modes of the both neutrinos are determined. The decays of the fourth family neutrinos into muon channels $({\ensuremath{\nu}}_{4}({N}_{1})\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ifmmode\pm\else\textpm\fi{}}{W}^{\ensuremath{\mp}})$ provide cleanest signature at ${e}^{+}{e}^{\ensuremath{-}}$ colliders. Meanwhile, in our parametrization this channel is dominant. $W$ bosons produced in decays of the fourth family neutrinos will be seen in detector as either di-jets or isolated leptons. As an example, we consider the production of 200 GeV mass fourth family neutrinos at $\sqrt{s}=500\text{ }\text{ }\mathrm{GeV}$ linear colliders by taking into account di-muon plus four jet events as signatures.