Evidence for Production of Single Top Quarks

Boosted Decision Trees (DT)  σ(ppbar→ tb + X, tqb + X) = 4.9 ± 1.4 pb 
Matrix Elements (ME)  σ(ppbar→ tb + X, tqb + X) = 4.6 +1.81.5 pb 
Bayesian Neural Networks (BNN)  σ(ppbar→ tb + X, tqb + X) = 5.0 ± 1.9 pb 
The DT result corresponds to a 3.4 standard deviation significance from the
backgroundonly hypothesis. The ME and BNN measurements correspond to 2.9 and 2.4
standard deviations, respectively. We use the cross section measurement to directly
determine the CKM matrix element that describes the Wtb coupling and find
0.68 < V_{tb} ≤ 1 at 95% C.L. within the
standard model.
The two dominant single top production channels at the Tevatron are shown below. We have
tb (schannel) with a SM cross section of 0.88 pb, and tqb (tchannel) with
cross section 1.98 pb.
Single top schannel, tb
Single top tchannel, tqb
Note: Clicking on a plot will give the .eps version. Right click and "View Image" will get the full resolution .png version.
The experimental signal for single top events is one isolated highp_{T} central lepton and missing transverse energy from the decay of a W boson from the top quark decay, accompanied by a b jet from the top decay, and a second jet which is sometimes also from the decay of a b hadron. Since the trigger jet thresholds are quite high, and since there may be significant initialstate or finalstate radiation, we include in our search events with between two and four jets. We use data collected with triggers that include an electron or a muon, and a jet.
We divide the selected events into 12 nonoverlapping samples depending on the flavor of the lepton (e or mu), the number of jets (2,3,4), and the number of btagged jets (1,2). The signal:background ratios and fractions of expected signal in each set differ significantly, as illustrated below.
Signal fraction and S:B ratios in each subsample
Event yield after final event selection
Three signals were considered:
The background includes Monte Carlo events for ttbar → lepton+jets, ttbar → dilepton+jets and W+jets (consisting of the separate subsamples: Wbb+Nlp, Wcc+Nlp and W+Nlp, where bb/cc stands for a b/c quarkantiquark pair and Nlp stands for N light partons, 0 ≤ N ≤ 5. W+Nlp includes processes with one (massless c parton.). Each background component is represented in proportion to its expected fraction in the background model.
The dominant background is W+jets events. We model this background using Monte Carlo events normalized to data before b tagging. We also use a Monte Carlo model to simulate the background from ttbar events. Finally, we use data events with fake leptons to model the multijet component where a jet is misidentified as a lepton (electron channel) or a muon in a jet from b decay is misidentified as a muon from a W boson decay.
We have used three different multivariate discriminants on the same dataset to measure the single top cross section:
(Click on the method names for details of each analysis.)
The first two methods use a list of 49 and 24 discriminating variables respectively. The Matrix Element method uses the fourvectors of the reconstruted objects to perform a fully differential crosssection calculation to build an eventbyevent probability.
We form a binned likelihood as a product over all bins and channels (lepton flavor, jet multiplicity, and tag multiplicity) of the discriminant output, separately for the tb+tqb, tqb, and tb analyses. We assume a Poisson distribution for the observed counts and flat nonnegative prior probabilities for the signal cross sections. Systematic uncertainties and their correlations are taken into account by integrating over the signal acceptances, background yields, and integrated luminosity with Gaussian priors for each systematic uncertainty. The final posterior probability density is computed as a function of the production cross section. For each analysis, we measure the cross section using the position of the posterior density peak and we take the 68% asymmetric interval about the peak as the uncertainty on the measurement.
Summary table
Exp pvalue (std.dev.) 
Obs pvalue (std.dev.) 
pvalue SM (std.dev.) 
Frequency 

DT 
0.019 (2.1) 
0.00035 (3.4) 
0.11 (1.2) 
60% 
ME 
0.037 (1.8) 
0.0021 (2.9) 
0.21 (0.8) 
62% 
BNN 
0.097 (1.3) 
0.0089 (2.4) 
0.175 (0.9) 
59% 
We use the decision tree measurement of the tb+tqb cross section to derive a first direct measurement of the strength of the VA coupling V_{tb} f_{1}^{L} in the Wtb vertex, where f_{1}^{L} is an arbitrary lefthanded form factor. We measure:
V_{tb}f_{1}^{L} = 1.3 ± 0.2.
This measurement assumes V_{td}^{2} + V_{ts}^{2} ≪ V_{tb}^{2} and a pure VA and CPconserving Wtb interaction. Assuming in addition that f_{1}^{L}=1 and using a flat prior for V_{tb}^{2} from 0 to 1, we obtain:
0.68 < V_{tb} ≤ 1
at 95% C.L. These measurements make no
assumptions about the number of quark families or CKM matrix
unitarity.
V_{tb}f_{1}^{L}^{2} posterior (using a nonnegative prior) 
V_{tb}^{2} posterior (using a flat prior between 0 and 1 and assuming f_{1}^{L}=1) 
Answers to frequently asked questions are here.
Email the single top subgroup leaders: Arán GarcíaBellido, Ann Heinson
Last modified: