Search for ${\mathrm{Z}}^{\prime}$ bosons decaying to pairs of heavy Majorana neutrinos in proton-proton collisions at $\sqrt{s} = 13 ~\mathrm{TeV}$

A search for pair production of heavy Majorana neutrinos (${\mathrm{N}}_{\ell}$) from the decays of ${\mathrm{Z}}^{\prime}$ bosons is performed using the CMS detector at the LHC. The data were collected in proton-proton collisions at a center-of-mass energy of $\sqrt{s} = 13 ~\mathrm{TeV}$, with an integrated luminosity of $138 ~\text{fb}^\text{$-$1}$. The signature of this search is two same-flavor leptons ($\mathrm{e}$ or $\mu$) and at least two jets. We do not observe any significant excess of events beyond the expected background. Upper limits at the $95\%$ CL are set on the cross section times branching ratio for the pair production of ${\mathrm{N}}_{\ell}$ as a function of ${\mathrm{N}}_{\ell}$ and ${\mathrm{Z}}^{\prime}$ boson masses (${m}_{{\mathrm{N}}_{\ell}}$ and ${m}_\mathrm{{Z}^{\prime}}$, respectively) for ${m}_\mathrm{{Z}^{\prime}}$ from $400 ~\mathrm{GeV}$ to $4.4 ~\mathrm{TeV}$ and ${m}_{{\mathrm{N}}_{\ell}}$ from $100 ~\mathrm{GeV}$ to $\frac{{m}_\mathrm{{Z}^{\prime}}}{2}$. In the theoretical framework of a left-right symmetric model, exclusion bounds on the ${m}_{{\mathrm{N}}_{\ell}}$-${m}_\mathrm{{Z}^{\prime}}$ plane are presented in both the electron and muon channels.