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

A search for a new ${Z}^{\prime }$ gauge boson predicted by ${L}_{\mu }-{L}_{\tau }$ models, based on charged-current Drell–Yan production, $pp\to {W}^{±\left(*\right)}\to {Z}^{\prime }{\mu }^{±}\nu \to {\mu }^{±}{\mu }^{\mp }{\mu }^{±}\nu $, is presented. The data sample used corresponds to an integrated luminosity of $140\text{}\text{}{\mathrm{fb}}^{-1}$ of proton–proton collisions at $\sqrt{s}=13\text{}\text{}\mathrm{TeV}$ 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 ${Z}^{\prime }$ production cross section times branching ratio in the mass range of 5–81 GeV. After combining with the previous ${Z}^{\prime }$ 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 ${Z}^{\prime }$ coupling strength and mass.