Measurement of the Inclusive and Fiducial Cross-Section of Single Top-Quark $t$-Channel Events in $pp$ Collisions at $\sqrt{s}$ = 8 TeV

This article presents the measurement of a $t$-channel single top-quark production fiducial cross-section in the lepton+jets channel with 20.3 fb${}^{-1}$ of 8 TeV data using a neural-network discriminant. A fiducial cross-section quoted within the detector acceptance of $\sigma_{\rm fid} = 3.37 \pm 0.05 , ($\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}$) \pm 0.47 , ($\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}$) \pm 0.09 , ($\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{i}\mathrm{.}$)~$\text{pb}$$isobtained\mathrm{.}Thetotalinclusive$t$-channel cross-section is calculated using the acceptance predicted by various Monte Carlo generators. If the acceptance from the a MC@NLO + Herwig event generator is used, a value of $\sigma_t = 82.6 \pm 1.2 , ($\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{.}$) \pm 11.4 , ($\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\mathrm{.}$) \pm 3.1 , ($\mathrm{P}\mathrm{D}\mathrm{F}$) \pm 2.3 , ($\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{i}\mathrm{.}$)~$\text{pb}$$ is obtained, consistent with the Standard Model prediction. Using the ratio of the measured inclusive cross-section to the predicted cross-section and assuming that the top-quark-related CKM matrix elements obey the relation $\mathrm{\mid }{V}_{tb}\mathrm{\mid }\gg \mathrm{\mid }{V}_{ts}\mathrm{\mid },\mathrm{\mid }{V}_{td}\mathrm{\mid }$, the coupling strength at the $W$-$t$-$b$ vertex is determined to be $\mathrm{\mid }{V}_{tb}\mathrm{\mid }=0.97_{-0.10}^{+0.09}$. Assuming that $\mathrm{\mid }{V}_{tb}\mathrm{\mid }\le 1$ a lower limit of $\mathrm{\mid }{V}_{tb}\mathrm{\mid }>0.78$ is obtained at the 95% confidence level.