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We revisit the sensitivity to non-resonant, heavy Majorana neutrinos $N$ insame-sign $W^\pm W^\pm$ scattering at the $\sqrt{s}=13$ TeV LHC and itshigh-luminosity upgrade. As a benchmark scenario, we work in the context of thePhenomenological Type I Seesaw model, relying on a simulation up tonext-to-leading order in QCD with parton shower matching. After extensivelystudying the phenomenology of the $pp\to\mu^\pm\mu^\pm j j$ process at theamplitude and differential levels, we design a simple collider analysis withremarkable signal-background separation power. At 95\% confidence level we findthat the squared muon-heavy neutrino mixing element $\vert V_{\mu N} \vert^{2}$can be probed down to about $0.06-0.3 ~ (0.03-0.1)$ for $m_N = 1-10~{\rm TeV}$with $\mathcal{L}=300$ fb$^{-1}~(3$ ab$^{-1})$. For heavier masses of $m_N =20~{\rm TeV}$, we report sensitivity for $\vert V_{\mu N} \vert^{2}\gtrsim0.5~(0.3)$. The $W^\pm W^\pm$ scattering channel can greatly extend the massrange covered by current LHC searches for heavy Majorana neutrinos andparticularly adds invaluable sensitivity above a few hundred GeV. We comment onareas where the analysis can be improved as well as on the applicability toother tests of neutrino mass models.

Majorana Neutrinos in Same-Sign $W^\pm W^\pm$ Scattering at the LHC: Breaking the TeV Barrier