Search for a light CP-odd Higgs boson decaying into a pair of $\tau$-leptons in proton-proton collisions at $\sqrt{s} = 13$ TeV with the ATLAS detector

This paper reports a search for a light CP-odd scalar resonance with a mass of 20 GeV to 90 GeV in 13 TeV proton-proton collision data with an integrated luminosity of 140 fb$^{-1}$ collected with the ATLAS detector at the Large Hadron Collider. The analysis assumes the resonance is produced via gluon-gluon fusion and decays into a $\tau^{+}\tau^{-}$ pair which subsequently decays into a fully leptonic $\mu^{+}\nu_{\mu} \bar{\nu}_{\tau} e^{-} \bar{\nu}_{e} \nu_{\tau}$ or $e^{+}\nu_{e}\bar{\nu}_{\tau} \mu^-\bar{\nu}_{\mu}\nu_{\tau}$ final state. No significant excess of events above the predicted Standard Model background is observed. The results are interpreted within a flavour-aligned two-Higgs-doublet model, and a model-independent cross-section interpretation is also given. Upper limits at 95$%$ confidence level between 3.0 pb and 68 pb are set on the cross-section for producing a CP-odd Higgs boson that decays into a $\tau^+\tau^-$ pair.