Measurement of the $t$-channel single top-quark and top-antiquark production cross-sections and their ratio in pp collisions at $\sqrt{s}$ = 7 TeV

We present measurements of the single top-quark and top-antiquark cross sections and their ratio in $t$-channel production in $pp$ collisions at the LHC. The collision data recorded with the ATLAS detector correspond to an integrated luminosity of 4.7~fb$^{-1}$. Selected events contain one charged lepton, missing transverse momentum, and two or three jets, one and only one of them $b$-tagged. The background consists of multijets, $W$+jets and $t\bar{t}$ pair events, with smaller contributions from $Z$+jets and diboson events. The top-quark and top-antiquark production cross sections are measured by perfoming a binned maximum likelihood fit to the output distribution of neural networks in the 2-jets and 3-jets data sets that are split according to the charge of the lepton, resulting in $\sigma_t(t)= 53.2\pm 10.8\, \mathrm{pb}$ and $\sigma_t(\bar{t})= 29.5^{+7.4}_{-7.5}\, \mathrm{pb}$. A cross section ratio of $R_{t}= 1.81^{+0.23}_{-0.22}$ is measured. When evaluating the uncertainties of $R_t$ the correlations between the individual cross section measurements are taken into account, leading to a reduction of the uncertainty. The ratio $R_t$ is sensitive to the ratio of the up-quark and down-quark parton density functions (PDF) in the proton. At the current precision, the measurement is in agreement with the predictions based on various global PDF sets that range from 1.86 to 2.07.