A search for a new <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>Z</a:mi><a:mo>′</a:mo></a:msup></a:math> gauge boson predicted by <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>L</c:mi><c:mi>μ</c:mi></c:msub><c:mo>−</c:mo><c:msub><c:mi>L</c:mi><c:mi>τ</c:mi></c:msub></c:math> models, based on charged-current Drell–Yan production, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>p</e:mi><e:mi>p</e:mi><e:mo stretchy="false">→</e:mo><e:msup><e:mi>W</e:mi><e:mrow><e:mo>±</e:mo><e:mo stretchy="false">(</e:mo><e:mo>*</e:mo><e:mo stretchy="false">)</e:mo></e:mrow></e:msup><e:mo stretchy="false">→</e:mo><e:msup><e:mi>Z</e:mi><e:mo>′</e:mo></e:msup><e:msup><e:mi>μ</e:mi><e:mo>±</e:mo></e:msup><e:mi>ν</e:mi><e:mo stretchy="false">→</e:mo><e:msup><e:mi>μ</e:mi><e:mo>±</e:mo></e:msup><e:msup><e:mi>μ</e:mi><e:mo>∓</e:mo></e:msup><e:msup><e:mi>μ</e:mi><e:mo>±</e:mo></e:msup><e:mi>ν</e:mi></e:math>, is presented. The data sample used corresponds to an integrated luminosity of <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mn>140</l:mn><l:mtext> </l:mtext><l:mtext> </l:mtext><l:msup><l:mi>fb</l:mi><l:mrow><l:mo>−</l:mo><l:mn>1</l:mn></l:mrow></l:msup></l:math> of proton–proton collisions at <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msqrt><n:mi>s</n:mi></n:msqrt><n:mo>=</n:mo><n:mn>13</n:mn><n:mtext> </n:mtext><n:mtext> </n:mtext><n:mi>TeV</n:mi></n:math> recorded by the ATLAS detector at the Large Hadron Collider. The search examines a final state of <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mn>3</p:mn><p:mi>μ</p:mi></p:math> plus large missing transverse momentum. Upper limits are set on the <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:msup><r:mi>Z</r:mi><r:mo>′</r:mo></r:msup></r:math> production cross section times branching ratio in the mass range of 5–81 GeV. After combining with the previous <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:msup><t:mi>Z</t:mi><t:mo>′</t:mo></t:msup></t:math> search using the neutral-current Drell–Yan production with a <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mn>4</v:mn><v:mi>μ</v:mi></v:math> final state, the most stringent exclusion limits to date are achieved in the parameter space of the <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:msup><x:mi>Z</x:mi><x:mo>′</x:mo></x:msup></x:math> coupling strength and mass. © 2024 CERN, for the ATLAS Collaboration 2024 CERN