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A search for a new pseudoscalar $a$-boson produced in events with a top-quarkpair, 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 atthe LHC, corresponding to an integrated luminosity of $139\, \mathrm{fb}^{-1}$.The search targets the final state where only one top quark decays to anelectron or muon, resulting in a signature with three leptons $e\mu\mu$ and$\mu\mu\mu$. No significant excess of events above the Standard Modelexpectation is observed and upper limits are set on two signal models: $pp\rightarrow t\bar{t}a$ and $pp \rightarrow t\bar{t}$ with $t \rightarrow H^\pmb$, $H^\pm \rightarrow W^\pm a$, 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.

Search for a new pseudoscalar decaying into a pair of muons in events with a top-quark pair at $\sqrt{s} = 13$ TeV with the ATLAS detector