Search for $H^{\pm} \rightarrow W^{\pm}A \rightarrow W^{\pm}\mu\mu$ in $pp \rightarrow t\overline{t}$ events using an $e\mu\mu$ signature with the ATLAS detector at $\sqrt{s}=13$ TeV

This note presents a search for a charged Higgs boson ($H^{\pm}$) decaying to a pseudoscalar particle ($A$) and a $W$ boson in top-quark pair events. It selects events with one electron and two muons in the final state and three or more jets, at least one of which is $b$-tagged. The mass range for the $H^{\pm}$ is between 100 GeV and 160 GeV, and that of the $A$ is between 15 GeV and 75 GeV. The study uses 139 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}=13$ TeV collected by the ATLAS detector during Run 2 of the LHC to search for an excess in the $\mu^+\mu^-$ invariant mass spectrum. No significant excess above Standard Model predictions is observed. Upper limits are set at the 95% confidence level on the product of the branching ratios $t\rightarrow bH^\pm$, $H^\pm\rightarrow W^\pm A$ and $A \rightarrow \mu^+\mu^-$. The observed (expected) limits vary from $0.9$ $(1.6)$ $\times 10^{-6}$ to $6.9$ $(9.9)$ $\times 10^{-6}$, depending on the masses of the $H^{\pm}$ and $A$. The results of this search are used to set the first lower limits on $\tan\beta$ in a 2HDM type-I model in the $m_{H^{\pm}}$, $m_A$ parameter space.