jats:titleAbstract</jats:title>jats:pA search for Majorana neutrinos in same-sign jats:italicWW</jats:italic> scattering events is presented. The analysis uses jats:inline-formulajats:alternativesjats:tex-math$$\sqrt{s}= 13$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:msqrt mml:mis</mml:mi> </mml:msqrt> mml:mo=</mml:mo> mml:mn13</mml:mn> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> TeV proton–proton collision data with an integrated luminosity of 140 fbjats:inline-formulajats:alternativesjats:tex-math$$^{-1}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msup mml:mrow/ mml:mrow mml:mo-</mml:mo> mml:mn1</mml:mn> </mml:mrow> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula> 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 jats:italicWW</jats:italic> scattering and jats:italicWZ</jats:italic> 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 jats:inline-formulajats:alternativesjats:tex-math$$\vert V_{\mu N} \vert ^{2}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:mrow mml:mo|</mml:mo> </mml:mrow> mml:msub mml:miV</mml:mi> mml:mrow mml:miμ</mml:mi> mml:miN</mml:mi> </mml:mrow> </mml:msub> mml:msup mml:mrow mml:mo|</mml:mo> </mml:mrow> mml:mn2</mml:mn> </mml:msup> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> as a function of the heavy Majorana neutrino’s mass jats:inline-formulajats:alternativesjats:tex-math$$m_N$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msub mml:mim</mml:mi> mml:miN</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula>, and on the effective jats:inline-formulajats:alternativesjats:tex-math$$\mu \mu $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:miμ</mml:mi> mml:miμ</mml:mi> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> Majorana neutrino mass jats:inline-formulajats:alternativesjats:tex-math$$|m_{\mu \mu }|$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:mrow mml:mo|</mml:mo> </mml:mrow> mml:msub mml:mim</mml:mi> mml:mrow mml:miμ</mml:mi> mml:miμ</mml:mi> </mml:mrow> </mml:msub> mml:mrow mml:mo|</mml:mo> </mml:mrow> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula>.</jats:p>