A search is presented for flavour-changing neutral-current interactions involving the top quark, the Higgs boson and an up-type quark ($q=u,c$) with the ATLAS detector at the Large Hadron Collider. The analysis considers leptonic decays of the top quark along with Higgs boson decays into two $W$ bosons, two $Z$ bosons or a $\tau^{+}\tau^{-}$ pair. It focuses on final states containing either two leptons (electrons or muons) of the same charge or three leptons. The considered processes are $t\bar{t}$ and $Ht$ production. For the $t\bar{t}$ production, one top quark decays via $t\to Hq$. The proton-proton collision data set analysed amounts to 140 fb$^{-1}$ at $\sqrt{s}=13$ TeV. No significant excess beyond Standard Model expectations is observed and upper limits are set on the $t\to Hq$ branching ratios at 95% confidence level, amounting to observed (expected) limits of $\mathcal{B}(t\to Hu)<2.8\,(3.0) \times 10^{-4}$ and $\mathcal{B}(t\to Hc)<3.3\,(3.8) \times 10^{-4}$. Combining this search with other searches for $tHq$ flavour-changing neutral-current interactions previously conducted by ATLAS, considering $H\to b\bar{b}$ and $H\to\gamma\gamma$ decays, as well as $H\to\tau^{+}\tau^{-}$ decays with one or two hadronically decaying $\tau$-leptons, yields observed (expected) upper limits on the branching ratios of $\mathcal{B}(t\to Hu)<2.6\,(1.8) \times 10^{-4}$ and $\mathcal{B}(t\to Hc)<3.4\,(2.3) \times 10^{-4}$.
Measurements of both the inclusive and differential production cross sections of a top-quark-top-antiquark pair in association with a $Z$ boson ($t\bar{t}Z$) are presented. Final states with two, three or four isolated leptons (electrons or muons) are targeted. The measurements use the data recorded by the ATLAS detector in $pp$ collisions at $\sqrt{s}=13$ TeV at the Large Hadron Collider during the years 2015-2018, corresponding to an integrated luminosity of $140$ fb$^{-1}$. The inclusive cross section is measured to be $\sigma_{t\bar{t}Z}= 0.86 \pm 0.04~\mathrm{(stat.)} \pm 0.04~\mathrm{(syst.)}~$pb and found to be in agreement with the most advanced Standard Model predictions. The differential measurements are presented as a function of a number of observables that probe the kinematics of the $t\bar{t}Z$ system. Both the absolute and normalised differential cross-section measurements are performed at particle level and parton level for specific fiducial volumes, and are compared with NLO+NNLL theoretical predictions. The results are interpreted in the framework of Standard Model effective field theory and used to set limits on a large number of dimension-6 operators involving the top quark. The first measurement of spin correlations in $t\bar{t}Z$ events is presented: the results are in agreement with the Standard Model expectations, and the null hypothesis of no spin correlations is disfavoured with a significance of $1.8$ standard deviations.
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