Measurement of $t$-channel production of single top quarks and antiquarks in $pp$ collisions at 13 TeV using the full ATLAS Run 2 dataset

The production of single top quarks and top antiquarks via the $t$-channel exchange of a virtual $W$ boson are measured in proton--proton collisions at a centre-of-mass energy of 13 TeV. The full Run 2 dataset recorded with the ATLAS detector in the years 2015-2018 is used. The total cross-sections are determined to be $\sigma(tq)=137\pm 8\,\mathrm{pb}$ and $\sigma(\bar{t}q)=84^{+6}_{-5}\,\mathrm{pb}$ for top-quark and top-antiquark production, respectively. The combined cross-section is found to be $\sigma(tq+\bar{t}q)=221\pm13\,\mathrm{pb}$ and the cross-section ratio is $R_{t}=\sigma(tq)/\sigma(\bar{t}q)=1.636^{+0.036}_{-0.034}$. The measured cross-sections are in good agreement with predictions made at next-to-next-to-leading order in perturbation theory. The measured value of $R_{t}$ is compared to predictions using different sets of parton distribution functions, demonstrating the potential to further constrain the functions when using this result in global fits. The measurements of $\sigma(tq)$ and $\sigma(\bar{t}q)$ are interpreted in an effective field theory approach, setting limits on the strength of a four-quark operator: $-0.25 < C_{qQ}^{(1,3)} < 0.12$. The measured total cross-section is used to derive the constraint $|V_{tb}|>0.95$ at the 95% confidence level. In a more general approach, pairs of CKM matrix elements involving top quarks are simultaneously constrained, leading to confidence contours in the corresponding two-dimensional parameter spaces.