This paper presents a search for exotic decays of the Higgs boson into a pair of new pseudoscalar particles, $H\rightarrow aa$, where one pseudoscalar decays into a $b$-quark pair and the other decays into a $\tau$-lepton pair, in the mass range $12\leq m_{a}\leq 60$ GeV. The analysis uses $pp$ collision data at $\sqrt{s} = 13$ TeV collected with the ATLAS detector at the LHC, corresponding to an integrated luminosity of 140 ${fb}^{-1}$. No significant excess above the Standard Model (SM) prediction is observed. Assuming the SM Higgs boson production cross-section, the search sets upper limits at 95% confidence level on the branching ratio of Higgs bosons decaying into $b\bar{b}\tau^+\tau^-$, $\mathcal{B}(H \rightarrow aa \rightarrow b\bar{b}\tau^+\tau^-)$, between 2.2% and 3.9% depending on the pseudoscalar mass.
Visible mass $m^{\mathrm{vis}}(\mu\tau_{\mathrm{had}})$ and distribution for signal and the expected background. In order to compare the shapes, the expected signal distribution is shown assuming ten times the production cross section of the Higgs boson and a 100% branching ratio to $b\bar{b}\tau^+\tau^-$. Overflow events are included in the last bins.
Sum of the transverse mass $\Sigma m_T$ distributions for signal and the expected background. Events with high $m^{\mathrm{vis}}(\mu\tau_{\mathrm{had}})$ and high $\Sigma m_T$ are included in the $t\bar{t}$ region. In order to compare the shapes, the expected signal distribution is shown assuming ten times the production cross section of the Higgs boson and a 100% branching ratio to $b\bar{b}\tau^+\tau^-$. Overflow events are included in the last bins.
The pNN input variable visible mass $m^{\mathrm{vis}}(\mu\tau_{\mathrm{had}})$ is shown in the SR with no cut on the pNN discriminant. The signal shape is normalized to the same integral as the total background prediction. Overflow events are included in the last bins.
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