Combinations of single-top-quark production cross-section measurements and $|f_{\rm LV}V_{tb}|$ determinations at $\sqrt{s}=7$ and 8 TeV with the ATLAS and CMS experiments

This paper presents the combinations of single-top-quark production cross-section measurements by the ATLAS and CMS Collaborations, using data from LHC proton-proton collisions at $\sqrt{s}=7$ and 8 TeV corresponding to integrated luminosities of 1.17 to 5.1 fb$^{-1}$ at $\sqrt{s}=7$ TeV, and 12.2 to 20.3 fb$^{-1}$ at $\sqrt{s}=8$ TeV. These combinations are performed per centre-of-mass energy and for each production mode: $t$-channel, $tW$, and $s$-channel. The combined $t$-channel cross-sections are $67.5 \pm 5.7$ pb and $87.7 \pm 5.8$ pb at $\sqrt{s}=7$ and 8 TeV respectively. The combined $tW$ cross-sections are $16.3 \pm 4.1$ pb and $23.1 \pm 3.6$ pb at $\sqrt{s}=7$ and 8 TeV respectively. For the $s$-channel cross-section, the combination yields $4.9 \pm 1.4$ pb at $\sqrt{s}=8$ TeV. The square of the magnitude of the CKM matrix element $V_{tb}$ multiplied by a form factor $f_{\rm LV}$is determined for each production mode and centre-of-mass energy, using the ratio of the measured cross-section to its theoretical prediction. It is assumed that the top-quark-related CKM matrix elements obey the relation $|V_{td}|,|V_{ts}| \ll |V_{tb}|$. All the $|f_{\rm LV}V_{tb}|^2$ determinations, extracted from individual ratios at $\sqrt{s}=7$ and 8 TeV, are combined, resulting in $|f_{\rm LV}V_{tb}|=1.02\pm0.04$ (meas.) $\pm0.02$ (theo.). All combined measurements are consistent with their corresponding Standard Model predictions.