Right-handed heavy neutrinos in the littlest Higgs model

In this paper we discuss the consequences of including a new heavy right-handed neutrino singlet $N_R$ in the littlest Higgs model. This new state is not connected with the light neutrinos {\it via} the seesaw mechanism. A very interesting property of this extended model is the full coupling of the new neutral gauge boson $A_H$ to $N_R$, giving large total cross sections and suggesting a wide range of experimental search for the $N_R$ at the p p collider CERN-LHC and future electron-positron collider ILC.