Search for heavy Majorana neutrinos in $e^{\pm }{e}^{\pm }$ and $e^{\pm }{\mu }^{\pm }$ final states via WW scattering in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

A search for heavy Majorana neutrinos in scattering of same-sign $W$ boson pairs in proton-proton collisions at $\sqrt{s}=13$ TeV at the LHC is reported. The dataset used corresponds to an integrated luminosity of 140 fb${}^{-1}$, collected with the ATLAS detector during 2015-2018. The search is performed in final states including a same-sign $ee$ or $e\mu$ pair and at least two jets with large invariant mass and a large rapidity difference. No significant excess of events with respect to the Standard Model background predictions is observed. The results are interpreted in a benchmark scenario of the Phenomenological Type-I Seesaw model. New constraints are set on the values of the $\mathrm{\mid }{V}_{eN}{\mathrm{\mid }}^2$ and $\mathrm{\mid }{V}_{eN}{V}_{\mu N}^{\ast }\mathrm{\mid }$ parameters for heavy Majorana neutrino masses between 50 GeV and 20 TeV, where $V_{\mathrm{\ell }N}$ is the matrix element describing the mixing of the heavy Majorana neutrino mass eigenstate with the Standard Model neutrino of flavour $\mathrm{\ell }=e,\mu$. The sensitivity to the Weinberg operator is investigated and constraints on the effective $ee$ and $e\mu$ Majorana neutrino masses are reported. The statistical combination of the $ee$ and $e\mu$ channels with the previously published $\mu \mu$ channel is performed.