A search for a new pseudoscalar $a$-boson produced in events with a top-quark pair, where the $a$-boson decays into a pair of muons, is performed using $\sqrt{s} = 13$ TeV $pp$ collision data collected with the ATLAS detector at the LHC, corresponding to an integrated luminosity of $139\, \mathrm{fb}^{-1}$. The search targets the final state where only one top quark decays to an electron or muon, resulting in a signature with three leptons $e\mu\mu$ and $\mu\mu\mu$. No significant excess of events above the Standard Model expectation is observed and upper limits are set on two signal models: $pp \rightarrow t\bar{t}a$ and $pp \rightarrow t\bar{t}$ with $t \rightarrow H^\pm b$, $H^\pm \rightarrow W^\pm a$, where $a\rightarrow\mu\mu$, in the mass ranges $15$ GeV $ < m_a < 72$ GeV and $120$ GeV $ \leq m_{H^{\pm}} \leq 160$ GeV.
Comparison between data and expected background for the on-$Z$-boson control region in the $e\mu\mu$ final state. The bins correspond to different jet and $b$-jet multiplicities. Rare background processes include $ZZ+$jets, $WWZ$, $WZZ$, $ZZZ$, and $t\bar{t}t\bar{t}$.
Comparison between data and expected background for the on-$Z$boson control region in the $\mu\mu\mu$ final state. The bins correspond to different jet and $b$-jet multiplicities. Rare background processes include $ZZ+$jets, $WWZ$, $WZZ$, $ZZZ$, and $t\bar{t}t\bar{t}$.
Di-muon mass distribution for the $e\mu\mu$ signal region for data and expected background. The expected signal distribution for $m_a = 35$ GeV is shown assuming $\sigma(t\bar{t}a)\times \text{Br}(a\rightarrow\mu\mu) = 4$ fb. Rare background processes include $ZZ+$jets, $WWZ$, $WZZ$, $ZZZ$, and $t\bar{t}t\bar{t}$.
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