Search for dark mesons decaying to top and bottom quarks with the ATLAS detector in 140 fb$^{-1}$ of proton-proton collisions at $\sqrt{s}=13~$TeV

A search for dark mesons originating from strongly-coupled, $SU(2)$ dark flavour symmetry conserving models and decaying gaugephobically to pure Standard Model final states containing top and bottom quarks in fully hadronic topologies is performed. The analysis of the full Run 2 proton-proton collision data sample corresponding to 140 fb$^{-1}$ collected at $\sqrt{s}=13~$TeV with the ATLAS detector at the Large Hadron Collider yields no significant excess over the Standard Model background expectation. The two-dimensional signal space of dark pion masses $m_{\pi_D}$ and dark rho masses $m_{\rho_D}$ is scanned. For $m_{\pi_D}/m_{\rho_D}=0.35$, dark pions with masses $m_{\pi_D}<434~~$GeV are excluded, while for $m_{\pi_D}/m_{\rho_D}=0.25$ the exclusion covers the mass range $280~\text{GeV}<m_{\pi_D}<522~$GeV.