• Figure 1: Feynman diagrams for the electroweak production of single Top quarks in the s-channel (a), in the t-channel (b), and for the W-associated production (c).

  • Figure 2: Cosine of the angle between the lepton and the light quark jet, in the reconstructed Top-quark rest frame (a); pseudorapidity of the light jet (b); boosted decision tree discriminant (c).

The Top quark is the heaviest of the six quarks of the Standard Model and was discovered only 16 years ago by the Tevatron experiments at Fermilab. In addition to the usual production of Top-AntiTop pairs in accordance with quantum chromodynamics (QCD), the electroweak interaction causes three different production channels (Figure 1) for single Top quarks. After many years of intensive search, the Tevatron experiments reported in 2009 an observation of singly produced Top quarks for the first time.

At the LHC, running at a total collision energy of 7 TeV, it is much easier to study single-Top events: the predicted production rates for the dominant t-channel is roughly 30 times more abundant than at the Tevatron. Moreover, background rates rise by a far lower factor with increasing collision energy, leading to an improved signal-to-background ratio. As t-channel events (Figure 1b) are the most abundant and provide a distinctive event signature, they allowed the first "evidence" of singly produced Top quarks at the LHC.

In the Standard Model, the Top quark always decays into a W boson and a lighter quark, a Bottom quark, 99.9% of the time. In roughly a third of the cases, the W boson decays into a charged lepton (with equal probability for electron, muon and tau) plus a neutrino.

After a tight selection based on the cleanest decay channels (those with a muon or an electron in the final state) and the requirement of only two jets, one of which is identified as coming from a Bottom quark, we infer the presence of signal through two complementary methods.

In the simpler of the two ("2D analysis") we rely only on two characteristics of the t-channel single Top: the "left-handedness" of the Top quarks and the typical angular distribution of the light quark (q′ in Figure 1b) recoiling against the Top. The former property comes from the fact that the interaction involving W, Top and Bottom in the same vertex is the weak force, which only involves left-handed fermions. This property becomes apparent when the cosine of the angle between the lepton and the light quark jet is measured in the reconstructed Top-quark rest frame, as shown in Figure 2a: in single-Top events (red histogram) there is a distinct asymmetry, with more leptons going in the direction of the light quark jet (positive values of the cosine) than opposite to that. In contrast, the major backgrounds have a rather flat distribution.

The other method ("BDT analysis") combines the above-mentioned properties with several other kinematic observables via a boosted decision tree, a machine-learning technique which is particularly suited to separate tiny signals from overwhelming backgrounds. Figure 2c shows the discriminant from the boosted decision tree.

In both methods the signal abundance is extracted by comparing the expected shapes for signal and background, with minimal assumptions on the background size.

Although the boosted decision tree has a better sensitivity, and therefore dominates the combination, the simpler "2D" method relies on less modelling assumptions and therefore carries more confidence to the result. And it is remarkable that such a simple method can be used at all, considering that all measurements at Tevatron had to rely on multivariate analyses (boosted decision trees, neural networks, matrix element technique).

The two methods give statistically consistent results, and their combination yields a production rate of 83.6 ± 29.6 (stat.+syst.) ± 3.3 (lumi.) pb.

— Submitted by Andrea Giammanco and Jeannine Wagner-Kuhr