Search for pair-production of vector-like quarks in $pp$ collision events at $\sqrt{s}=13$~TeV with at least one leptonically-decaying $Z$~boson and a third-generation quark with the ATLAS detector

A search for the pair-production of vector-like quarks optimized for decays to a $Z$ boson and a third-generation Standard Model quark is presented, using the full Run 2 dataset corresponding to $139\,\mathrm{fb}^{-1}$ of $pp$ collisions at $\sqrt{s}=13\,\mathrm{TeV}$, collected in 2015-2018 with the ATLAS detector at the Large Hadron Collider. The targeted final state is characterized by the presence of a $Z$ boson with high transverse momentum, reconstructed from a pair of same-flavor leptons with opposite-sign charges, as well as by the presence of $b$-tagged jets and high-transverse-momentum large-radius jets reconstructed from calibrated smaller-radius jets. Events with exactly two or at least three leptons are used, which are further categorized by the presence of boosted $W$, $Z$, and Higgs bosons and top quarks. The categorization is performed using a neural-network-based boosted object tagger to enhance the sensitivity to signal over the background. No significant excess above the background expectation is observed and exclusion limits at 95\% confidence level are obtained on the masses of vector-like partners $T$ and $B$ of the top and bottop quarks, respectively. In the singlet model, limits are set at $m_T > 1.27\,\mathrm{TeV}$ and $m_B > 1.20\,\mathrm{TeV}$. In the doublet model allowed masses are $m_T > 1.46\,\mathrm{TeV}$ and $m_B >1.32\,\mathrm{TeV}$. In the case of 100\% branching ratio for $T\rightarrow Zt$ and 100\% branching ratio for $B\rightarrow Zb$, the limits are $m_T > 1.60\,\mathrm{TeV}$ and $m_B > 1.42\,\mathrm{TeV}$, respectively.