A search for flavor-changing neutral-current couplings between a top quark, an up or charm quark and a $Z$ boson is presented, using proton-proton collision data at $\sqrt{s} = 13$ TeV collected by the ATLAS detector at the Large Hadron Collider. The analyzed dataset corresponds to an integrated luminosity of 139 fb$^{-1}$. The search targets both single-top-quark events produced as $gq\rightarrow tZ$ (with $q = u, c$) and top-quark-pair events, with one top quark decaying through the $t \rightarrow Zq$ channel. The analysis considers events with three leptons (electrons or muons), a $b$-tagged jet, possible additional jets, and missing transverse momentum. The data are found to be consistent with the background-only hypothesis and 95% confidence-level limits on the $t \rightarrow Zq$ branching ratios are set, assuming only tensor operators of the Standard Model effective field theory framework contribute to the $tZq$ vertices. These are $6.2 \times 10^{-5}$ ($13\times 10^{-5}$) for $t\rightarrow Zu$ ($t\rightarrow Zc$) for a left-handed $tZq$ coupling, and $6.6 \times 10^{-5}$ ($12\times 10^{-5}$) in the case of a right-handed coupling. These results are interpreted as 95% CL upper limits on the strength of corresponding couplings, yielding limits for $|C_{uW}^{(13)*}|$ and $|C_{uB}^{(13)*}|$ ($|C_{uW}^{(31)}|$ and $|C_{uB}^{(31)}|$) of 0.15 (0.16), and limits for $|C_{uW}^{(23)*}|$ and $|C_{uB}^{(23)*}|$ ($|C_{uW}^{(32)}|$ and $|C_{uB}^{(32)}|$) of 0.22 (0.21), assuming a new-physics energy scale $\Lambda_\text{NP}$ of 1 TeV.
Summary of the signal strength $\mu$ parameters obtained from the fits to extract LH and RH results for the FCNC tZu and tZc couplings. For the reference branching ratio, the most stringent limits are used.
Observed and expected 95% CL limits on the FCNC $t\rightarrow Zq$ branching ratios and the effective coupling strengths for different vertices and couplings (top eight rows). For the latter, the energy scale is assumed to be $\Lambda_{NP}$ = 1 TeV. The bottom rows show, for the case of the FCNC $t\rightarrow Zu$ branching ratio, the observed and expected 95% CL limits when only one of the two SRs, either SR1 or SR2, and all CRs are included in the likelihood.
Comparison between data and background prediction before the fit (Pre-Fit) for the mass of the SM top-quark candidate in SR1. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The four FCNC LH signals are also shown separately, normalized to five times the cross-section corresponding to the most stringent observed branching ratio limits. The first (last) bin in all distributions includes the underflow (overflow). The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).
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