Search for a new $Z^{\mathrm{\prime }}$ gauge boson via the $pp\to W^{\pm (\ast )}\to Z^{\mathrm{\prime }}{\mu }^{\pm }\nu \to {\mu }^{\pm }{\mu }^{\mp }{\mu }^{\pm }\nu$ process in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

A search for a new $Z^{\mathrm{\prime }}$ gauge boson predicted by $L_{\mu }-L_{\tau }$ models, based on charged-current Drell-Yan production, $pp\to W^{\pm (\ast )}\to Z^{\mathrm{\prime }}{\mu }^{\pm }\nu \to {\mu }^{\pm }{\mu }^{\mp }{\mu }^{\pm }\nu$, is presented. The data sample used corresponds to an integrated luminosity of 140 fb${}^{-1}$ of proton-proton collisions at $\sqrt{s}=13$ TeV recorded by the ATLAS detector at the Large Hadron Collider. The search examines a final state of $3\mu$ plus large missing transverse momentum. Upper limits are set on the $Z^{\mathrm{\prime }}$ production cross-section times branching ratio in the mass range of 5-81 GeV. After combining with the previous $Z^{\mathrm{\prime }}$ search using the neutral-current Drell-Yan production with a $4\mu$ final state, the most stringent exclusion limits to date are achieved in the parameter space of the $Z^{\mathrm{\prime }}$ coupling strength and mass.