A search for Majorana neutrinos in same-sign $WW$ scattering events is presented. The analysis uses $\sqrt{s}= 13$ TeV proton-proton collision data with an integrated luminosity of 140 fb$^{-1}$ recorded during 2015-2018 by the ATLAS detector at the Large Hadron Collider. The analysis targets final states including exactly two same-sign muons and at least two hadronic jets well separated in rapidity. The modelling of the main backgrounds, from Standard Model same-sign $WW$ scattering and $WZ$ production, is constrained with data in dedicated signal-depleted control regions. The distribution of the transverse momentum of the second-hardest muon is used to search for signals originating from a heavy Majorana neutrino with a mass between 50 GeV and 20 TeV. No significant excess is observed over the background expectation. The results are interpreted in a benchmark scenario of the Phenomenological Type-I Seesaw model. In addition, the sensitivity to the Weinberg operator is investigated. Upper limits at the 95% confidence level are placed on the squared muon-neutrino-heavy-neutrino mass-mixing matrix element $\vert V_{\mu N} \vert^{2}$ as a function of the heavy Majorana neutrino's mass $m_N$, and on the effective $\mu\mu$ Majorana neutrino mass $|m_{\mu\mu}|$.
Observed and expected 95% CL upper limits on the heavy Majorana neutrino mixing element $\vert V_{\mu N} \vert^{2}$ as a function of $m_N$ in the Phenomenological Type-I Seesaw model.
Cutflow for a selection of signal samples used in this analysis. The flavour-aligned scenario (in which $\vert V_{\mu N} \vert^{2}=1$) is considered for heavy Majorana neutrino samples. The event yields include all correction factors applied to simulation, and is normalised to 140 fb$^{-1}$. The `Skim' selection requires 2 baseline muons and 2 jets satisfying the object definitions described in Section 3 and $m_{jj} > 150$ GeV. Uncertainties are statistical only.
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