Evidence for Production of Single Top Quarks
and First Direct Measurement of |Vtb|

The DØ Collaboration

December 2006

[Abstract]   [Introduction]   [Analysis Method]   [Results]   [|Vtb|]   [FAQ]   [Talks]   [People]


The DØ Collaboration presents first evidence for the production of single top quarks at the Fermilab Tevatron ppbar collider. We apply three multivariate analyses to separate signal from background in the same 0.9 fb-1 dataset, and measure:

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 +1.8-1.5 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 background-only 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 < |Vtb| ≤ 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 (s-channel) with a SM cross section of 0.88 pb, and tqb (t-channel) with cross section 1.98 pb.

Single top Feynmann diagrams
Single top s-channel, tb              Single top t-channel, tqb

Note: Clicking on a plot will give the .eps version. Right click and "View Image" will get the full resolution .png version.

Analysis Method


The experimental signal for single top events is one isolated high-pT 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 initial-state or final-state 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 b-tagged 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
Percent of signal

Event yield after final event selection


Three signals were considered:

  • s-channel single top only (tb)
  • t-channel single top only (tqb)
  • s and t-channel single top signals combined (tb+tqb), where s and t contribute in their standard model ratio.

The background includes Monte Carlo events for ttbar → lepton+jets, ttbar → dilepton+jets and W+jets (consisting of the separate sub-samples: Wbb+Nlp, Wcc+Nlp and W+Nlp, where bb/cc stands for a b/c quark-antiquark 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.

Background measurement

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.

Background measurement


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 four-vectors of the reconstruted objects to perform a fully differential cross-section calculation to build an event-by-event 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.


Three results

Summary table

Exp p-value (std.dev.)
Obs p-value (std.dev.)
p-value SM (std.dev.)
0.019  (2.1)
0.00035   (3.4)
0.11  (1.2)
0.037  (1.8)
0.0021  (2.9)
0.21  (0.8)
0.097  (1.3)
0.0089  (2.4)
0.175 (0.9)

  • Expected p-value: Fraction of zero-signal pseudo-datasets above SM cross section (2.9 pb)
  • Observed p-value: Fraction of zero-signal pseudo-datasets above measured cross section
  • p-value SM: Fraction of SM-signal pseudo-datasets (including 16% uncertainty on the signal cross section) above measured cross section
  • Frequency: Fraction of measured-cross-section signal pseudo-datasets (including 16% uncertainty on the signal cross section) that fall within the 1 standard deviation error bands of the observed value

|Vtb| Measurement

We use the decision tree measurement of the tb+tqb cross section to derive a first direct measurement of the strength of the V-A coupling |Vtb f1L| in the Wtb vertex, where f1L is an arbitrary left-handed form factor. We measure:

|Vtbf1L| = 1.3 ± 0.2.

This measurement assumes |Vtd|2 + |Vts|2 ≪ |Vtb|2 and a pure V-A and CP-conserving Wtb interaction. Assuming in addition that f1L=1 and using a flat prior for |Vtb|2 from 0 to 1, we obtain:

0.68 < |Vtb| ≤ 1

at 95% C.L. These measurements make no assumptions about the number of quark families or CKM matrix unitarity.

Vtb squared Vtb squared
|Vtbf1L|2 posterior
(using a non-negative prior)
|Vtb|2 posterior
(using a flat prior between 0 and 1
and assuming f1L=1)

Frequently Asked Questions

Answers to frequently asked questions are here.


  1. Evidence for production of single top quarks and first direct measurement of |Vtb| at DØ
    Dugan O'Neil. Wine and Cheese seminar. Fermilab, Batavia, IL. December 8, 2006.
  2. Evidence for production of single top quarks and first direct measurement of |Vtb| at DØ   (odp)
    Aran Garcia-Bellido. HEP seminar, Universidad Autonoma de Madrid, Spain. January 8, 2007.
  3. Evidence of single top production at the Tevatron
    Yann Coadou. Aspen Winter Conference, Aspen, CO. January 10, 2007.
  4. Evidence for single top quark production at DØ    (ppt)
    Gordon Watts. SLAC seminar series, Menlo Park, CA. January 16, 2007.
  5. Statistical methods used in the search for single top at DØ
    Brigitte Vachon. ATLAS statistics workshop, CERN, Geneva, Switzerland. January 18, 2007.
  6. Evidence for single top quark production at DØ   (ppt)
    Ann Heinson. CERN Particle Physics seminar, Geneva, Switzerland. January 30, 2007.
  7. Evidence for production of single top quarks and first direct measurement of |Vtb| at DØ
    Yann Coadou. IPP seminars, Canada. January 2007.
  8. First evidence for rare single top quark production at the DØ experiment
    Brigitte Vachon. Winter Nuclear and Particle Physics Conference, Banff, Canada. February 16, 2007.
  9. Evidence for single top quark production at DØ
    Dag Gillberg. Lake Louise Winter Institute, Lake Louise, Canada. February 19, 2007.
  10. Single top quark production at the Tevatron
    Aurelio Juste. Les Rencontres de Physique de la Vallée d'Aoste, La Thuile, Italy. March 7, 2007.
  11. Evidence for single top quark production at DØ
    Aran Garcia-Bellido. 42nd Rencontres de Moriond: Electroweak Interactions and Unified Theories,
    La Thuile, Aosta Valley, Italy. March 11, 2007.
  12. Evidence for single top quark production at DØ
    Shabnam Jabeen. HEP seminar, Kansas University, March 13, 2007, and Kansas State University, March 14, 2007.
  13. Evidence for single top quark production at DØ
    Len Christofek. 42nd Rencontres de Moriond: QCD and High Energy Hadronic Interactions,
    La Thuile, Italy. March 20, 2007.
  14. Evidence for single top quark production at DØ
    Yann Coadou. CERN Experimental Physics seminar, CERN, Geneva, Switzerland. July 30, 2007.

E-mail the single top subgroup leaders: Arán García-Bellido, Ann Heinson

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