Calibration of the $b$-tagging efficiency for $c$ jets with the ATLAS detector using events with a $W$ boson produced in association with a single $c$ quark

A novel method is used to measure the $b$-jet tagging efficiency of $c$ jets of the standard MV1 tagging algorithm in proton-proton collisions at $\sqrt{s}=7$ TeV using data collected by the ATLAS experiment at the LHC in the year 2011, corresponding to an integrated luminosity of about 4.6 fb$^{−1}$. The measurement is based on a sample of $c$ jets produced in association with a $W$ boson. The $W$ boson is reconstructed via its decay into an electron and a neutrino, and the $c$ jet is identified via a soft muon stemming from a semileptonic $c$-hadron decay. The charge correlation of the two leptons is exploited to extract a $c$-jet sample with high purity. The results are presented in the form of data-to-simulation efficiency scale factors. The total uncertainties range from 5% to 13%, increasing as the background rejection of the $b$-tagging algorithm increases.