Measurement of top-quark pair production in association with charm quarks in proton-proton collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

Inclusive cross-sections for top-quark pair production in association with charm quarks are measured with proton-proton collision data at a center-of-mass energy of 13 TeV corresponding to an integrated luminosity of 140 fb$^{-1}$, collected with the ATLAS experiment at the LHC between 2015 and 2018. The measurements are performed by requiring one or two charged leptons (electrons and muons), two $b$-tagged jets, and at least one additional jet in the final state. A custom flavor-tagging algorithm is employed for the simultaneous identification of $b$-jets and $c$-jets. In a fiducial phase space that replicates the acceptance of the ATLAS detector, the cross-sections for $t\bar{t}+ {\geq} 2c$ and $t\bar{t}+1c$ production are measured to be $1.28^{+0.27}_{-0.24}\;\text{pb}$ and $6.4^{+1.0}_{-0.9}\;\text{pb}$, respectively. The measurements are primarily limited by uncertainties in the modeling of inclusive $t\bar{t}$ and $t\bar{t}+b\bar{b}$ production, in the calibration of the flavor-tagging algorithm, and by data statistics. Cross-section predictions from various $t\bar{t}$ simulations are largely consistent with the measured cross-section values, though all underpredict the observed values by 0.5 to 2.0 standard deviations. In a phase-space volume without requirements on the $t\bar{t}$ decay products and the jet multiplicity, the cross-section ratios of $t\bar{t}+ {\geq} 2c$ and $t\bar{t}+1c$ to total $t\bar{t}+\text{jets}$ production are determined to be $(1.23 \pm 0.25) \%$ and $(8.8 \pm 1.3) \%$.