Study of the production of a new $Z^{\prime }$ boson and its decay into Majorana neutrinos in $\mathrm{pp}$ collisions at $\sqrt{s}=14\mathrm{}\hspace{0.5em}\mathrm{TeV}$ and in $e^{+}{e}^{-}$ collisions at $\sqrt{s}=3\mathrm{}\hspace{0.5em}\mathrm{TeV}$

In the theoretical framework of the left-right symmetric model with the seesaw mechanism, we first report on the possibility of observing the decay of a new neutral gauge boson $Z^{\prime }$ into a pair of heavy right-handed Majorana neutrinos $N_e$ at the future CERN LHC, in the ATLAS detector. We then study the $Z^{\prime }\to N_e{N}_e$ process at a possible next-generation $e^{+}{e}^{-}$ multi-TeV collider, such as CLIC, and we show that an accurate measurement of $m_{Z^{\prime }}$ and $m_{N_e}$ can be performed with a resonance scan.