- Email: [email protected]
Top-Quark Physics at the Tevatron
Nuclear Physics B (Proc. Suppl.) 183 (2008) 67–74 www.elsevierphysics.com
Top-Quark Physics at the Tevatron Wolfgang Wagnera a
Institut f¨ ur Experimentelle Kernphysik, Universit¨ at Karlsruhe, 76128 Karlsruhe, Germany
The Tevatron experiments, CDF and DØ have by now analysed collision data corresponding an integrated luminosity of more than 2 fb−1 and the selected data sets comprise several hundreds of reconstructed tt¯ pairs. Run II of the Tevatron has thus paved the way for a new era in top quark physics focussing on the precise measurement of top quark properties. This article gives a concise overview on the status of measurements in the top quark sector by CDF and DØ including tt¯ cross section measurements, the measurement of the charge asymmetry in top-antitop events, the search for top-antitop resonances, the measurement of the W helicity in top quark decays, and the search for flavor-changing neutral current top quark decays. The measurements of intrisic top quark properties, mass, width and charge, are discussed. The article concludes with a presentation of first measurements of single top-quark production.
1. Introduction The top quark is the heaviest elementary particle observed by particle physics experiments. With a mass of mt = 172.6 ± 1.4 GeV/c2 the top quark is as heavy as an Ytterbium nucleus (172 Yb), i.e. more than 40 times heavier than its weak-isospin partner, the bottom quark. Due to its large mass the top quark gives rise to large radiative corrections, for example to the W propagator, which causes a strong correlation between mW , mt , and the Higgs boson mass mH . To predict mH a precise measurement of mt is crucial. The large mass leads also to a very short lifetime of the top quark, τt 0.5 · 1024 s, such that top hadrons are not formed. The top quark thus offers the unique possibility to study a quasi-free quark and as a consequence polarization effects are accessible in the angular distributions of top quark decay products. Since mt is close to the energy scale at which the electroweak symmetry breaks down (vacuum expectation value of the Higgs field v = 246 GeV), it has been argued that the top quark may be part of a special dynamics causing the break down of the symmetry [1]. Furthermore, it is important to test all facets of top quark physics to establish the particle discovered thirteen years at the Tevatron as the standard model top quark and obtain a consistent and complete picture. This includes in partic0920-5632/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2008.09.084
ular measurements of the charge, the branching ratios and polarization effects. Finally, the top quark offers the chance to find new, unexpected physics, for example heavy resonances that decay into tt¯ pairs. In the past years the Fermilab Tevatron was the only place to produce and observe top quarks under laboratory conditions. The Tevatron is a synchrotron colliding protons √ and antiprotons at a center-of-mass energy of s = 1.96 TeV. Tevatron Run 2 started in 2002 and in the meanwhile the accelerator has delivered collisions corresponding to an integrated luminosity of 4.3 fb−1 . The improvement of the accelerator performance over the past years is illustrated in figure 1. The initial luminosity of the Tevatron is now regulary in the design range of 1.6 to 2.7 · 1032 cm−2 s−1 . The record initial luminosity of 3.1·1032 cm−2 s−1 was reached in March 2008. The proton and antiproton beams are brought to collision at two interaction points where two general-purpose detectors, CDF and DØ, are located. Both detectors feature azimuthal and forward-backward symmetry with a barrel structure in the center and two endcaps, yielding nearly full 4π coverage. Near the interaction region silicon tracking devices provide precise measurements of the impact parameters of tracks, which is essential for the identification of secondary vertices originating from heavy flavor
68
W. Wagner / Nuclear Physics B (Proc. Suppl.) 183 (2008) 67–74
-1
Delivered Luminosity (pb )
1200 1000 800
2007
2005
600
2006
400
2004 2003 2002 2001
200
2008 0 0
50
100
150
200
250 300
350 Day
Figure 1. Integrated luminosity delivered by the Tevatron per calendar year from 2002 to 2008 as a function of the day in the year.
hadrons. While the main tracking instrument of CDF is an open-cell drift chamber that covers the radial range from 40 cm to 137 cm, the DØ detector utilizes scintillating fibres. In CDF hadronic jets are measured in a sandwich calorimeter using polystyrene or plastic scintillators as active media and lead and iron sheets as absorber material. DØ has a sampling calorimeter based on depleted uranium, lead and copper as absorber materials and liquid argon as a sampling medium. Both detectors feature an √ energy resolution for jets of approximately 80%/ E. The detectors are completed by extended muon systems covering the pseudorapidity range of |η| < 1.5 in CDF and |η| < 2.0 in DØ. 2. Top-Antitop Production The main source of top quarks at the Tevatron is the pair production via the strong interaction. According to the standard model top quarks decay with a branching ratio of nearly 100% to a bottom quark and a W -boson. The tt¯ final states are therefore classified according to the decay modes of the W -bosons. The most important (or golden) channel is the so-called lepton+jets
channel where one W -boson decays leptonically into a charged lepton plus neutrino, while the second W -boson decays into jets. The lepton+jets channel features a large branching ratio of about 30%, manageable backgrounds, and allows for the full reconstruction of the event kinematics. Other accessible channels are the dilepton channel, where both W -bosons decay to leptons and the all-hadronic channel, where both W -bosons decay hadronically. The experimental signature of lepton+jets tt¯ events comprises on reconstructed isolated lepton candidate, large missing transverse energy and at least four jets with large transverse energy ET ≡ E · sin θ. Two jets originate from b-quarks. Typical selection cuts ask for a charged lepton with pT > 20 GeV/c, E / T > 20 GeV, at least four jets with ET > 20 GeV and |η| < 2.0, one of them identified as a b-quark jet. The most commonly used algorithm to identify b-quark jets is based on the reconstruction of secondary vertices in jets, exploiting the relatively long lifetime of b-hadrons and a large Lorentz boost. The typical decay length of b-hadrons in high-pT b-quark jets is on the order of a few millimeters. The requirement of a secondary vertex within one of the jets leads to a large reduction of the W +jets background by roughly a factor of 50, while the selection efficiency for tt¯ events is about 50% to 60%. 2.1. Top-Antitop Cross Section The most single precise measurement of the tt¯ cross section at CDF is based on secondary vertex b-quark jet identification [2]. The analysis is a counting experiment in which the background rate is estimated using a combination of simulated events and data driven methods. The signal region is defined as the data set with a leptonic W candidate plus ≥ 3 jets. The jet multiplicity distribution for the W +jets data set is shown in figure 2. The subset with one or two jets is used as a control region to check the validity of the background estimate and its systematic uncertainty. The cross section measurement yields σ(tt¯) = 8.2 ± 0.5 ± 0.9 pb, where the first error is statistical, the second is systematic including the luminosity uncertainty. The combina-
W. Wagner / Nuclear Physics B (Proc. Suppl.) 183 (2008) 67–74
69
Figure 2. Jet multiplicity distribution for the W plus jets data set, where the W boson is reconν ). structed in its leptonic decay W ± → ± νe ll(¯ Figure 3. Overview of the most precise tt¯ cross section measurements at the Tevatron. tion of all CDF cross section measurements gives σ(tt¯) = 7.3 ± 0.5 ± 0.7 pb. Figure 3 summarizes of the most precise tt¯ cross section results by CDF and DØ [4]. At the present precision a good agreement between the theoretical prediction [5] and the experimental measurements is found. 2.2. Production Mechanism Calculations in perturbative QCD predict that the dominating subprocess of the production of tt¯ pairs is q q¯ annihilation (85%), while gluon-gluon fusion contributes 15%. One analysis idea to measure the fraction of tt¯ pairs originating from a gg initial state uses the proportionality of the mean ¯trk , and number of low-pT tracks in an event, N the gluon content. The physical reason for this is that gg initial states produce more initial-state radiation than q q¯ initial states. The linear re¯trk and the average number of lation between N hard initial-state gluons is calibrated in W +jets and dijet data samples. Using simulated events ¯trk distribution are calculated templates for the N for gg → tt¯ and q q¯ → tt¯ events. These templates are fit to the distribution observed in collision data, resulting in a measurement of σ(gg → tt¯)/σ(q q¯ → tt¯) = 0.07 ± 0.14 (stat.) ± 0.07 (syst.) [6]. An alternative method exploits the spin information in the top decay products employing neural networks and sets an upper limit on the
gg initiated fraction of tt¯ events of 0.61 at the 95% confidence level (C.L.) [7]. 2.3. Charge Asymmetry At present, all available experimental data support the notion that the strong interaction conserves charge partiy C and spatial parity P individually. However, due to interference effects at next-to-leading order (NLO) QCD predicts a charge asymmetry AC =
Nt (p) − Nt¯(p) = (5.0 ± 1.5)% Nt (p) + Nt¯(p)
at the Tevatron [8], where Nt (p) is the number of top quarks moving in proton direction and Nt¯(p) is the number of antitop quarks moving in proton direction. Top quarks are thus more likely to be produced in proton direction, while antitop quarks are more likely to be produced in antiproton direction. Using events of the lepton+jets topology CDF and DØ have investigated the charge asymmetry. There are two CDF analyses, one measuring the asymmetry in the quantity ΔY ≡ Q · (Yt − Yth ), i.e. the rapidity difference of the semileptonically and hadronically decaying top quark times the lepton charge, and one analysis using cos θ ≡ Q · cos αp with
70
W. Wagner / Nuclear Physics B (Proc. Suppl.) 183 (2008) 67–74
αp being the polar angle between the hadronically decaying top quark and the proton beam [9]. CDF corrects both measurements for background contributions, acceptance bias, and migration effects due to the reconstruction, and finds AΔY = 0.24 ± 0.13 ± 0.04 as well as Acos θ = 0.17 ± 0.07 ± 0.04, where the uncertainties are statistical and systematic, respectively. DØ also uses ΔY as an observable, applies a background correction and obtains A = 0.12 ± 0.08 ± 0.01 [10]. To compare this value with the CDF measurements or with the theory prediction it has to be corrected for acceptance and migration effects. A prescription for this is provided in reference [10].
b-tagged events
2.4. Top-Antitop Resonances The tt¯ candidate samples offer the possibility to search for a narrow resonance X 0 decaying into tt¯ pairs by investigating the tt¯ invariant mass. In an analysis using data corresponding to 2.1 fb−1 the DØ collaboration found no evidence for such a resonance as can be seen in figure 4. The re-
70
DØ, L=2.1 fb-1
60
Preliminary
505 Data
Z’(650 45.9 GeV)
50
343.7 tt Single 6.8 top
40
3.9 Diboson
W+jets 59.9
30
Z+jets 9.2
20
Multijet 22.3
10 00
200
400
600
800
1000 1200 Mtt [GeV]
Figure 4. Invariant mass distribution of the topantitop-pair.
sulting upper limits on σX · BR(X 0 → tt¯) range from 1.9 pb at MX = 350 GeV/c2 to 0.2 pb at MX = 1000 GeV/c2 . If interpreted in the frame of a topcolor-assisted technicolor model these limits can be used to derive mass limits on a narrow lepto-phobic Z : M (Z ) > 760 GeV/c2 at the 95% C.L., assuming Γ(Z ) = 0.012 M (Z ) [11].
A very similar analysis was performed by CDF, yielding slightly lower mass limits [12]. 3. Top Quark Decay According to the standard model the top quark decays with a branching ratio of nearly 100% to W + boson and a bottom quark via the weak interaction. The charged current weak interaction has a pure V − A structure and thereby strongly suppresses the production of right-handed W + bosons in top quark decays. Only left-handed and longitudinally polarized W -bosons are allowed, the production of the later being enhanced due to the large Yukawa coupling of the top quark to the Higgs boson. The fraction of longitudinally polarized W -bosons is predicted to be f0 = 0.70, the left-handed fraction f− = 0.30. 3.1. W Helicity CDF and DØ have measured the W helicity fractions in fully reconstructed tt¯ lepton+jets events. A suitable sensitive variable to determine the W helicity fractions is the angle θ∗ between the charged lepton and the negative direction of the top quark in the W rest frame. Assuming f+ = 0 CDF obtains f0 = 0.66 ± 0.10 ± 0.06, assuming f0 = 0.70 the measurement yields f+ = 0.01 ± 0.05 ± 0.03 [13]. Similar analyses reach compatible results [14]. After unfolding acceptance and migration effects the measured cos θ∗ distribution can be compared to the theoretical prediction, see figure 5. Performing a two-dimensional and thereby model independent fit DØ obtains f0 = 0.43 ± 0.17 ± 0.10 and f+ = 0.12 ± 0.09 ± 0.05 [15]. 3.2. Branching Ratio The DØ collaboration has recently also measured the ratio of branching ratios R = BR(t → W b)/BR(t → W q), an analysis which tests the hypothesis whether there is any room for an additional top decay channel t → W + qx into a yet undiscovered quark qx . In the analysis, R and the tt¯ cross section are simultaneously measured [16]. The W +jets data set is split in various disjoint subsets according to the number of jets (0, 1, or ≥ 2), the charged lepton type (electron or muon), and most importantly the number of
dσ [pb] d(cos θ*)
W. Wagner / Nuclear Physics B (Proc. Suppl.) 183 (2008) 67–74
3
CDF II Preliminary
F0 = 0.66 ± 0.10 SM
-1
Lint = 1.9 fb
is used to derive an upper limit on the branching ratio: BR(t → Zq) < 3.7% at the 95% C.L. [17]. 4. Intrinsic Properties
2
1
0 -1
71
-0.5
0
0.5
1 cos θ*
Intrinsic properties that have been measured or tested using collision data are the mass, the width and the charge of the top quark. The spin has only been indirectly infered, for example from cross section measurements. By now, the mass is the most precisely measured quantity regarding the top quark. Figure 6 gives an overview of the current status of mt mea-
Figure 5. Differential cross section dσ/d cos θ∗ [13]. In this fit the right-handed fraction is fixed to f+ = 0.
b-tagged jets. The fit results are: R = 0.97+0.09 −0.08 +0.90 and σ(tt¯) = 8.18−0.84 ± 0.50 (lumi) pb, where the statistical and systematic uncertainties have been combined. The lower limit on R is obtained to be R > 0.79 at the 95% C.L. 3.3. FCNC Top Quark Decays In the standard model flavor-changing neutral currents (FCNC) are not present at tree level, but rather occur only through loop processes in higher orders of perturbation theory. In the top sector in particular FCNC are strongly suppressed with branching ratios of O ≈ 10−14 . The CDF collaboration has searched for non-SM top quark decays of the type tt¯ → ZqW −¯b → (+ − q)(q q¯¯b). TopAntitop candidates are reconstructed in events with four high-pT jets and two isolated leptons using kinematic constraints. Within their experimental resolutions determined from simulated events the reconstructed mass of the hadronically decaying W -boson, Mqq , has to be equal to mW , the mass of the reconstructed hadronic top quark, Mbqq , and the mass of semileptonically decaying top quark, MZq , have to resemble mt . A χ2 formed from these conditions is used to determine the most likely combination of physics objetcs and measure its tt¯-likeness under the anomalous hypothesis. A fit to the χ2 distribution in combination with a Feldman-Cousins technique
Figure 6. Overview of top quark mass measurements.
surements. The combination of all Tevatron results yields mt = 172.6 ± 1.4 GeV/c2 . A wide range of measurement techniques has been employed to obtain these results. The traditional method uses an event reconstruction based on kinematic fitting and template fits to the reconstructed top quark mass distribution Mtrec [18]. Methods developed in the recent years exploit the entire event kinematics to measure mt either by utilizing leading order matrix elements, the ideogram method or neural networks [19]. To reduce the systematic uncertainty due to the jet en-
72
W. Wagner / Nuclear Physics B (Proc. Suppl.) 183 (2008) 67–74
ergy scale these methods use constraints on the reconstructed mass of the hadronically decaying W -boson in the event. The top quark mass and the jet energy scale are thereby simultaneously determined. Due to these precise measurements the relative precision on mt is 0.8% and mt is thus the most precisely known quark mass. The measurement is already dominated by systematic uncertainties, but some of those scale with the square root of the integrated luminosity that characterizes the amount of data used for the analysis because the relevant control samples grow in size as well. Thus, some further improvement on the precision of mt is foreseen and the final uncertainty may reach the 1 GeV/c2 level. All measurements, however, are calibrated against the input mass to the leading order Monte Carlo programs used for the analyses. In the past it has always been assumed that the quantity mt determined in this way is equal to the pole mass of the top quark. Fits to electroweak precision data use mt in this way. With uncertainties dropping below 1 GeV/c2 this may be a questionable assumption. Certainly, further discussion of this issue between experimentalists and phenomenologists will be needed in the future [20]. Using the template method from the top quark mass measurement CDF has made an attempt to measure the top quark width Γt which is predicted to be Γt 1.5 GeV in the standard model. The measurement is not yet sensitive at this level, but sets an upper limit of Γt < 12.7 GeV at the 95% C.L. [21]. While even the final data set of tt¯ candidates at the Tevatron will not be sufficient to obtain an experimental sensitivity at the level of the predicted width, this technique shows an avenue one can proceed at the LHC where much bigger top quark samples will be available. Analysing dilepton and lepton+jets events the CDF collaboration has also investigated the top quark charge [22]. The analysis is done in the form of a hypothesis test where the standard model prediction of Qt = +2/3 is compared with an exotic model assigning Qt = −4/3. To distinguish the two hypotheses a b-jet flavor tagging algorithm based on computing the jet charge has been developed. The algorithm determines
whether a jet with a reconstructed secondary vertex is more likely to originate from a b-quark or a ¯b-quark. In total 225 tt¯ candidates are subjected to the flavor-assignment and 124 pairs are found to be standard model like, while 101 pairs are exotic-like, favoring the standard model in the statistical analysis. 5. Single Top-Quark Production While tt¯ pair production via the strong interaction is the main source to top quarks at the Tevatron, the standard model also predicts the production of single top-quarks via charged current weak interactions, in which a virtual W -boson is either exchanged in the t- or in the s-channel. While Run I and early Run II searches for single top-quarks at CDF and DØ [23] could only set upper limits on the production cross section, recent analysis have produced first evidence for single top-quark production [24]. Even though the single top-quark production cross section is predicted [25] to amount to about 40% of the cross section for tt¯ production, the signal has been obscured for a long time due to the difficult background situation. After a cut based event selection requiring one isolated high-pT charged lepton, missing transverse energy, and two or three energetic jets the signalto-background ratio is only about 5 to 6%. Further kinematic cuts on the event topology proofed to be prohibitive, since the number of signal events in the resulting data set would be too small. Given this challenging situation the analysis groups in both Tevatron collaborations turned towards the use of multivariate techniques in order to exploit as much information on the observed events as possible. The explored techniques comprise Bayesian neural networks, leading order matrix elements, boosted decision trees and likelihood ratios. An example of a final discriminant separating single top-quark events from background is shown in figure 7. After preforming a binned likelihood fit to the output distributions the analyses determine the single topquark production cross section as presented in figure 8. Both experiments see evidence for single top-quark production, CDF at a level of 3.7 σ
W. Wagner / Nuclear Physics B (Proc. Suppl.) 183 (2008) 67–74
73
Figure 7. Neural network discriminant to isolate single top-quark events from background [26]. The observed distribution is compared to the prediction of background and signal events assuming the predicted single top-quark cross section of 2.9 pb.
Figure 8. Summary of measured single top-quark production cross sections. (5.1 σ expected), while DØ observes an excess corresponding to a fluctuation at the level of 3.6 σ (2.3 σ expected). Using the theoretical prediction one can determine the CKM matrix element |Vtb |. CDF obtains |Vtb | = 0.88 ± 0.14 (exp) ± 0.07 (theory), DØ sets a lower limit of |Vtb | > 0.68 at the 95% C.L. If one extrapolates the current analyses to a data set corresponding to 4 fb−1 , one expects a measurement of |Vtb | with an experimental precision of 8%. Once single top-quark production is established it is also important to measure the cross sections of the t-channel and s-channel processes separately. At CDF a separate search based on neu+0.7 pb ral network discriminants gives σt = 0.8−0.6 +0.9 and σs = 1.6−0.8 pb [26], while DØ obtains σt = 4.2+1.8 −1.4 pb and σs = 1.0 ± 0.9 pb. Both measurements are in agreement with the theoretical prediction of σt = 1.98 ± 0.25 pb and σs = 0.88 ± 0.11 pb [25]. With more Run II data these measurements will allow for testing alternative, non-standard-model sources of single topquark production [27].
6. Conclusions The large data sets available in Run II of the Tevatron have propelled top quark physics in a new era in which precise investigations of top quark properties are possible. The most striking result is the precise mass measurement of mt = 172.6 ± 1.4 GeV/c2 with a relative uncertainty of 0.8%. In the last year many properties have been examined for the first time, including measurements of the width and charge. The measurements of top quark decay show impressive progress, most importantly the measurement of the W helicity fractions in top decay. The search for single top-quark production has been a tremendous challenge for many years, but recently first evidence for this process was found by CDF and DØ. Many more interesting results are yet to come from the Tevatron and are paving the way for high precision measurements at the LHC where tens of thousands of reconstructed tt¯
74
W. Wagner / Nuclear Physics B (Proc. Suppl.) 183 (2008) 67–74
pairs and single top-quarks will be available for examination. REFERENCES 1. R.D. Peccei, S. Peris, and X. Zhang, Nucl. Phys. B 349 (1991) 305–322. 2. A. Abulencia et al. (CDF Collaboration), Phys. Rev. Lett. 97, 082004 (2006). Public conference note No. 8795. 3. A. Abulencia et al. (CDF Collaboration), public conference note no. 8148. 4. V. M. Abazov et al. (DØ Collaboration), Phys. Rev. Lett. 100, 192004 (2008); Phys. Rev. D 76, 052006 (2007); Public conference note no. 5477 (2007). 5. S. Moch and P. Uwer, arXiv:0804.1476 [hep-ph] (2008). N. Kidonakis, R. Vogt, arXiv:0805.3844 [hep-ph] (2008). M. Cacciari et al., arXiv:0804.2800 [hep-ph] (2008). 6. T. Aaltonen et al. (CDF Collaboration), arXiv:0712.3273 [hep-ex]. 7. T. Aaltonen et al. (CDF Collaboration), public conference note no. 8811 (2007). 8. J.H. K¨ uhn and G. Rodrigo, Phys. Rev. D 59, 054017 (1999); Phys. Rev. Lett. 81, 49 (1998). O. Antunano, J.H. K¨ uhn, and G. Rodrigo, Phys. Rev. D 77, 014003 (2008). 9. T. Aaltonen et al. (CDF Collaboration), arXiv: 0806.2472 [hep-ex]. 10. V.M. Abazov et al. (DØ Collaboration), Phys. Rev. Lett. 100, 142002 (2008). 11. V.M. Abazov et al. (DØ Collaboration), public conference note no. 5600 (2008). 12. T. Aaltonen et al. (CDF Collaboration), public conference note no. 8675 (2007); Phys. Rev. Lett. 100, 231801 (2008). 13. A. Abulencia et al. (CDF Collaboration), Phys. Rev. D 75, 052001 (2007); public conference note no. 9114. 14. T. Aaltonen et al. (CDF Collaboration), public conference note no. 9215 and no. 9144. 15. V.M. Abazov et al. (DØ Collaboration), Phys. Rev. Lett. 100, 062004 (2008). 16. V.M. Abazov et al. (DØ Collaboration), FERMILAB-PUB-04/08-010-E. 17. T. Aaltonen et al. (CDF Collaboration), public conference note no. 9202.
18. A. Abulencia et al. (CDF Collaboration), Phys. Rev. Lett. 96, 022004 (2006; Phys. Rev. D 73, 032003 (2006). 19. V.M. Abazov et al. (DØ Collaboration), Phys. Rev. D 74, 092005 (2006); Phys. Rev. D 75, 092001 (2007). A. Abulencia et al. (CDF Collaboration) Phys. Rev. Lett. 96 022004 (2006); Phy. Rev. D 73, 092002 (2006); Phys. Rev. D 75, 031105 (2007). T. Aaltonen et al. (CDF Collaboration), Phys. Rev. Lett. 99, 182002 (2007). 20. W. Bernreuther, J. Phys. G 35, 083001 (2008). P. Skands and D. Wicke, Eur. Phys. J. C 52, 133 (2007). 21. T. Aaltonen et al. (CDF Collaboration), public conference note no. 8953 (2007). 22. T. Aaltonen et al. (CDF Collaboration), public conference note no. 8967 (2007). 23. D. Acosta et al. (CDF Collaboration), Phys. Rev. D 65, 091102 (2002); Phys. Rev. D 69, 052003 (2004); Phys. Rev. D 71, 012005 (2005). W. Wagner et al. (CDF Collaboration), hep-ex/0610074. B. Abbott et al. (DØ Collaboration), Phys. Rev. D 63, 031101 (2001). V.M. Abazov et al. (DØ Collaboration), Phys. Lett. B 517, 282 (2001); Phys. Lett. B 622, 265 (2005); Phys. Rev. D 75, 092007 (2007). 24. V.M. Abazov et al. (DØ Collaboration), Phys. Rev. Lett. 98:181802, 2007; FERMILAB-PUB-08/056-E. T. Aaltonen et al. (CDF Collaboration), public conference note no. 9251. 25. B.W. Harris et al., Phys. Rev. D 66, 054024 (2002). Z. Sullivan, Phys. Rev. D 70, 114012 (2004). J. Campbell, R.K. Ellis, F. Tramontano, Phys. Rev. D 70, 094012 (2004). N. Kidonakis, Phys. Rev. D 74, 114012 (2006). 26. T. Aaltonen et al. (CDF Collaboration), public conference note no. 9217 (2008). 27. M. Hosch, K. Whisnant, and B.L. Young, Phys. Rev. D 56, 5725 (1997). T. Tait and C.-P. Yuan, Phys. Rev. D 63, 014018 (2001).
Top-Quark Physics at the Tevatron Wolfgang Wagnera a
Institut f¨ ur Experimentelle Kernphysik, Universit¨ at Karlsruhe, 76128 Karlsruhe, Germany
The Tevatron experiments, CDF and DØ have by now analysed collision data corresponding an integrated luminosity of more than 2 fb−1 and the selected data sets comprise several hundreds of reconstructed tt¯ pairs. Run II of the Tevatron has thus paved the way for a new era in top quark physics focussing on the precise measurement of top quark properties. This article gives a concise overview on the status of measurements in the top quark sector by CDF and DØ including tt¯ cross section measurements, the measurement of the charge asymmetry in top-antitop events, the search for top-antitop resonances, the measurement of the W helicity in top quark decays, and the search for flavor-changing neutral current top quark decays. The measurements of intrisic top quark properties, mass, width and charge, are discussed. The article concludes with a presentation of first measurements of single top-quark production.
1. Introduction The top quark is the heaviest elementary particle observed by particle physics experiments. With a mass of mt = 172.6 ± 1.4 GeV/c2 the top quark is as heavy as an Ytterbium nucleus (172 Yb), i.e. more than 40 times heavier than its weak-isospin partner, the bottom quark. Due to its large mass the top quark gives rise to large radiative corrections, for example to the W propagator, which causes a strong correlation between mW , mt , and the Higgs boson mass mH . To predict mH a precise measurement of mt is crucial. The large mass leads also to a very short lifetime of the top quark, τt 0.5 · 1024 s, such that top hadrons are not formed. The top quark thus offers the unique possibility to study a quasi-free quark and as a consequence polarization effects are accessible in the angular distributions of top quark decay products. Since mt is close to the energy scale at which the electroweak symmetry breaks down (vacuum expectation value of the Higgs field v = 246 GeV), it has been argued that the top quark may be part of a special dynamics causing the break down of the symmetry [1]. Furthermore, it is important to test all facets of top quark physics to establish the particle discovered thirteen years at the Tevatron as the standard model top quark and obtain a consistent and complete picture. This includes in partic0920-5632/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2008.09.084
ular measurements of the charge, the branching ratios and polarization effects. Finally, the top quark offers the chance to find new, unexpected physics, for example heavy resonances that decay into tt¯ pairs. In the past years the Fermilab Tevatron was the only place to produce and observe top quarks under laboratory conditions. The Tevatron is a synchrotron colliding protons √ and antiprotons at a center-of-mass energy of s = 1.96 TeV. Tevatron Run 2 started in 2002 and in the meanwhile the accelerator has delivered collisions corresponding to an integrated luminosity of 4.3 fb−1 . The improvement of the accelerator performance over the past years is illustrated in figure 1. The initial luminosity of the Tevatron is now regulary in the design range of 1.6 to 2.7 · 1032 cm−2 s−1 . The record initial luminosity of 3.1·1032 cm−2 s−1 was reached in March 2008. The proton and antiproton beams are brought to collision at two interaction points where two general-purpose detectors, CDF and DØ, are located. Both detectors feature azimuthal and forward-backward symmetry with a barrel structure in the center and two endcaps, yielding nearly full 4π coverage. Near the interaction region silicon tracking devices provide precise measurements of the impact parameters of tracks, which is essential for the identification of secondary vertices originating from heavy flavor
68
W. Wagner / Nuclear Physics B (Proc. Suppl.) 183 (2008) 67–74
-1
Delivered Luminosity (pb )
1200 1000 800
2007
2005
600
2006
400
2004 2003 2002 2001
200
2008 0 0
50
100
150
200
250 300
350 Day
Figure 1. Integrated luminosity delivered by the Tevatron per calendar year from 2002 to 2008 as a function of the day in the year.
hadrons. While the main tracking instrument of CDF is an open-cell drift chamber that covers the radial range from 40 cm to 137 cm, the DØ detector utilizes scintillating fibres. In CDF hadronic jets are measured in a sandwich calorimeter using polystyrene or plastic scintillators as active media and lead and iron sheets as absorber material. DØ has a sampling calorimeter based on depleted uranium, lead and copper as absorber materials and liquid argon as a sampling medium. Both detectors feature an √ energy resolution for jets of approximately 80%/ E. The detectors are completed by extended muon systems covering the pseudorapidity range of |η| < 1.5 in CDF and |η| < 2.0 in DØ. 2. Top-Antitop Production The main source of top quarks at the Tevatron is the pair production via the strong interaction. According to the standard model top quarks decay with a branching ratio of nearly 100% to a bottom quark and a W -boson. The tt¯ final states are therefore classified according to the decay modes of the W -bosons. The most important (or golden) channel is the so-called lepton+jets
channel where one W -boson decays leptonically into a charged lepton plus neutrino, while the second W -boson decays into jets. The lepton+jets channel features a large branching ratio of about 30%, manageable backgrounds, and allows for the full reconstruction of the event kinematics. Other accessible channels are the dilepton channel, where both W -bosons decay to leptons and the all-hadronic channel, where both W -bosons decay hadronically. The experimental signature of lepton+jets tt¯ events comprises on reconstructed isolated lepton candidate, large missing transverse energy and at least four jets with large transverse energy ET ≡ E · sin θ. Two jets originate from b-quarks. Typical selection cuts ask for a charged lepton with pT > 20 GeV/c, E / T > 20 GeV, at least four jets with ET > 20 GeV and |η| < 2.0, one of them identified as a b-quark jet. The most commonly used algorithm to identify b-quark jets is based on the reconstruction of secondary vertices in jets, exploiting the relatively long lifetime of b-hadrons and a large Lorentz boost. The typical decay length of b-hadrons in high-pT b-quark jets is on the order of a few millimeters. The requirement of a secondary vertex within one of the jets leads to a large reduction of the W +jets background by roughly a factor of 50, while the selection efficiency for tt¯ events is about 50% to 60%. 2.1. Top-Antitop Cross Section The most single precise measurement of the tt¯ cross section at CDF is based on secondary vertex b-quark jet identification [2]. The analysis is a counting experiment in which the background rate is estimated using a combination of simulated events and data driven methods. The signal region is defined as the data set with a leptonic W candidate plus ≥ 3 jets. The jet multiplicity distribution for the W +jets data set is shown in figure 2. The subset with one or two jets is used as a control region to check the validity of the background estimate and its systematic uncertainty. The cross section measurement yields σ(tt¯) = 8.2 ± 0.5 ± 0.9 pb, where the first error is statistical, the second is systematic including the luminosity uncertainty. The combina-
W. Wagner / Nuclear Physics B (Proc. Suppl.) 183 (2008) 67–74
69
Figure 2. Jet multiplicity distribution for the W plus jets data set, where the W boson is reconν ). structed in its leptonic decay W ± → ± νe ll(¯ Figure 3. Overview of the most precise tt¯ cross section measurements at the Tevatron. tion of all CDF cross section measurements gives σ(tt¯) = 7.3 ± 0.5 ± 0.7 pb. Figure 3 summarizes of the most precise tt¯ cross section results by CDF and DØ [4]. At the present precision a good agreement between the theoretical prediction [5] and the experimental measurements is found. 2.2. Production Mechanism Calculations in perturbative QCD predict that the dominating subprocess of the production of tt¯ pairs is q q¯ annihilation (85%), while gluon-gluon fusion contributes 15%. One analysis idea to measure the fraction of tt¯ pairs originating from a gg initial state uses the proportionality of the mean ¯trk , and number of low-pT tracks in an event, N the gluon content. The physical reason for this is that gg initial states produce more initial-state radiation than q q¯ initial states. The linear re¯trk and the average number of lation between N hard initial-state gluons is calibrated in W +jets and dijet data samples. Using simulated events ¯trk distribution are calculated templates for the N for gg → tt¯ and q q¯ → tt¯ events. These templates are fit to the distribution observed in collision data, resulting in a measurement of σ(gg → tt¯)/σ(q q¯ → tt¯) = 0.07 ± 0.14 (stat.) ± 0.07 (syst.) [6]. An alternative method exploits the spin information in the top decay products employing neural networks and sets an upper limit on the
gg initiated fraction of tt¯ events of 0.61 at the 95% confidence level (C.L.) [7]. 2.3. Charge Asymmetry At present, all available experimental data support the notion that the strong interaction conserves charge partiy C and spatial parity P individually. However, due to interference effects at next-to-leading order (NLO) QCD predicts a charge asymmetry AC =
Nt (p) − Nt¯(p) = (5.0 ± 1.5)% Nt (p) + Nt¯(p)
at the Tevatron [8], where Nt (p) is the number of top quarks moving in proton direction and Nt¯(p) is the number of antitop quarks moving in proton direction. Top quarks are thus more likely to be produced in proton direction, while antitop quarks are more likely to be produced in antiproton direction. Using events of the lepton+jets topology CDF and DØ have investigated the charge asymmetry. There are two CDF analyses, one measuring the asymmetry in the quantity ΔY ≡ Q · (Yt − Yth ), i.e. the rapidity difference of the semileptonically and hadronically decaying top quark times the lepton charge, and one analysis using cos θ ≡ Q · cos αp with
70
W. Wagner / Nuclear Physics B (Proc. Suppl.) 183 (2008) 67–74
αp being the polar angle between the hadronically decaying top quark and the proton beam [9]. CDF corrects both measurements for background contributions, acceptance bias, and migration effects due to the reconstruction, and finds AΔY = 0.24 ± 0.13 ± 0.04 as well as Acos θ = 0.17 ± 0.07 ± 0.04, where the uncertainties are statistical and systematic, respectively. DØ also uses ΔY as an observable, applies a background correction and obtains A = 0.12 ± 0.08 ± 0.01 [10]. To compare this value with the CDF measurements or with the theory prediction it has to be corrected for acceptance and migration effects. A prescription for this is provided in reference [10].
b-tagged events
2.4. Top-Antitop Resonances The tt¯ candidate samples offer the possibility to search for a narrow resonance X 0 decaying into tt¯ pairs by investigating the tt¯ invariant mass. In an analysis using data corresponding to 2.1 fb−1 the DØ collaboration found no evidence for such a resonance as can be seen in figure 4. The re-
70
DØ, L=2.1 fb-1
60
Preliminary
505 Data
Z’(650 45.9 GeV)
50
343.7 tt Single 6.8 top
40
3.9 Diboson
W+jets 59.9
30
Z+jets 9.2
20
Multijet 22.3
10 00
200
400
600
800
1000 1200 Mtt [GeV]
Figure 4. Invariant mass distribution of the topantitop-pair.
sulting upper limits on σX · BR(X 0 → tt¯) range from 1.9 pb at MX = 350 GeV/c2 to 0.2 pb at MX = 1000 GeV/c2 . If interpreted in the frame of a topcolor-assisted technicolor model these limits can be used to derive mass limits on a narrow lepto-phobic Z : M (Z ) > 760 GeV/c2 at the 95% C.L., assuming Γ(Z ) = 0.012 M (Z ) [11].
A very similar analysis was performed by CDF, yielding slightly lower mass limits [12]. 3. Top Quark Decay According to the standard model the top quark decays with a branching ratio of nearly 100% to W + boson and a bottom quark via the weak interaction. The charged current weak interaction has a pure V − A structure and thereby strongly suppresses the production of right-handed W + bosons in top quark decays. Only left-handed and longitudinally polarized W -bosons are allowed, the production of the later being enhanced due to the large Yukawa coupling of the top quark to the Higgs boson. The fraction of longitudinally polarized W -bosons is predicted to be f0 = 0.70, the left-handed fraction f− = 0.30. 3.1. W Helicity CDF and DØ have measured the W helicity fractions in fully reconstructed tt¯ lepton+jets events. A suitable sensitive variable to determine the W helicity fractions is the angle θ∗ between the charged lepton and the negative direction of the top quark in the W rest frame. Assuming f+ = 0 CDF obtains f0 = 0.66 ± 0.10 ± 0.06, assuming f0 = 0.70 the measurement yields f+ = 0.01 ± 0.05 ± 0.03 [13]. Similar analyses reach compatible results [14]. After unfolding acceptance and migration effects the measured cos θ∗ distribution can be compared to the theoretical prediction, see figure 5. Performing a two-dimensional and thereby model independent fit DØ obtains f0 = 0.43 ± 0.17 ± 0.10 and f+ = 0.12 ± 0.09 ± 0.05 [15]. 3.2. Branching Ratio The DØ collaboration has recently also measured the ratio of branching ratios R = BR(t → W b)/BR(t → W q), an analysis which tests the hypothesis whether there is any room for an additional top decay channel t → W + qx into a yet undiscovered quark qx . In the analysis, R and the tt¯ cross section are simultaneously measured [16]. The W +jets data set is split in various disjoint subsets according to the number of jets (0, 1, or ≥ 2), the charged lepton type (electron or muon), and most importantly the number of
dσ [pb] d(cos θ*)
W. Wagner / Nuclear Physics B (Proc. Suppl.) 183 (2008) 67–74
3
CDF II Preliminary
F0 = 0.66 ± 0.10 SM
-1
Lint = 1.9 fb
is used to derive an upper limit on the branching ratio: BR(t → Zq) < 3.7% at the 95% C.L. [17]. 4. Intrinsic Properties
2
1
0 -1
71
-0.5
0
0.5
1 cos θ*
Intrinsic properties that have been measured or tested using collision data are the mass, the width and the charge of the top quark. The spin has only been indirectly infered, for example from cross section measurements. By now, the mass is the most precisely measured quantity regarding the top quark. Figure 6 gives an overview of the current status of mt mea-
Figure 5. Differential cross section dσ/d cos θ∗ [13]. In this fit the right-handed fraction is fixed to f+ = 0.
b-tagged jets. The fit results are: R = 0.97+0.09 −0.08 +0.90 and σ(tt¯) = 8.18−0.84 ± 0.50 (lumi) pb, where the statistical and systematic uncertainties have been combined. The lower limit on R is obtained to be R > 0.79 at the 95% C.L. 3.3. FCNC Top Quark Decays In the standard model flavor-changing neutral currents (FCNC) are not present at tree level, but rather occur only through loop processes in higher orders of perturbation theory. In the top sector in particular FCNC are strongly suppressed with branching ratios of O ≈ 10−14 . The CDF collaboration has searched for non-SM top quark decays of the type tt¯ → ZqW −¯b → (+ − q)(q q¯¯b). TopAntitop candidates are reconstructed in events with four high-pT jets and two isolated leptons using kinematic constraints. Within their experimental resolutions determined from simulated events the reconstructed mass of the hadronically decaying W -boson, Mqq , has to be equal to mW , the mass of the reconstructed hadronic top quark, Mbqq , and the mass of semileptonically decaying top quark, MZq , have to resemble mt . A χ2 formed from these conditions is used to determine the most likely combination of physics objetcs and measure its tt¯-likeness under the anomalous hypothesis. A fit to the χ2 distribution in combination with a Feldman-Cousins technique
Figure 6. Overview of top quark mass measurements.
surements. The combination of all Tevatron results yields mt = 172.6 ± 1.4 GeV/c2 . A wide range of measurement techniques has been employed to obtain these results. The traditional method uses an event reconstruction based on kinematic fitting and template fits to the reconstructed top quark mass distribution Mtrec [18]. Methods developed in the recent years exploit the entire event kinematics to measure mt either by utilizing leading order matrix elements, the ideogram method or neural networks [19]. To reduce the systematic uncertainty due to the jet en-
72
W. Wagner / Nuclear Physics B (Proc. Suppl.) 183 (2008) 67–74
ergy scale these methods use constraints on the reconstructed mass of the hadronically decaying W -boson in the event. The top quark mass and the jet energy scale are thereby simultaneously determined. Due to these precise measurements the relative precision on mt is 0.8% and mt is thus the most precisely known quark mass. The measurement is already dominated by systematic uncertainties, but some of those scale with the square root of the integrated luminosity that characterizes the amount of data used for the analysis because the relevant control samples grow in size as well. Thus, some further improvement on the precision of mt is foreseen and the final uncertainty may reach the 1 GeV/c2 level. All measurements, however, are calibrated against the input mass to the leading order Monte Carlo programs used for the analyses. In the past it has always been assumed that the quantity mt determined in this way is equal to the pole mass of the top quark. Fits to electroweak precision data use mt in this way. With uncertainties dropping below 1 GeV/c2 this may be a questionable assumption. Certainly, further discussion of this issue between experimentalists and phenomenologists will be needed in the future [20]. Using the template method from the top quark mass measurement CDF has made an attempt to measure the top quark width Γt which is predicted to be Γt 1.5 GeV in the standard model. The measurement is not yet sensitive at this level, but sets an upper limit of Γt < 12.7 GeV at the 95% C.L. [21]. While even the final data set of tt¯ candidates at the Tevatron will not be sufficient to obtain an experimental sensitivity at the level of the predicted width, this technique shows an avenue one can proceed at the LHC where much bigger top quark samples will be available. Analysing dilepton and lepton+jets events the CDF collaboration has also investigated the top quark charge [22]. The analysis is done in the form of a hypothesis test where the standard model prediction of Qt = +2/3 is compared with an exotic model assigning Qt = −4/3. To distinguish the two hypotheses a b-jet flavor tagging algorithm based on computing the jet charge has been developed. The algorithm determines
whether a jet with a reconstructed secondary vertex is more likely to originate from a b-quark or a ¯b-quark. In total 225 tt¯ candidates are subjected to the flavor-assignment and 124 pairs are found to be standard model like, while 101 pairs are exotic-like, favoring the standard model in the statistical analysis. 5. Single Top-Quark Production While tt¯ pair production via the strong interaction is the main source to top quarks at the Tevatron, the standard model also predicts the production of single top-quarks via charged current weak interactions, in which a virtual W -boson is either exchanged in the t- or in the s-channel. While Run I and early Run II searches for single top-quarks at CDF and DØ [23] could only set upper limits on the production cross section, recent analysis have produced first evidence for single top-quark production [24]. Even though the single top-quark production cross section is predicted [25] to amount to about 40% of the cross section for tt¯ production, the signal has been obscured for a long time due to the difficult background situation. After a cut based event selection requiring one isolated high-pT charged lepton, missing transverse energy, and two or three energetic jets the signalto-background ratio is only about 5 to 6%. Further kinematic cuts on the event topology proofed to be prohibitive, since the number of signal events in the resulting data set would be too small. Given this challenging situation the analysis groups in both Tevatron collaborations turned towards the use of multivariate techniques in order to exploit as much information on the observed events as possible. The explored techniques comprise Bayesian neural networks, leading order matrix elements, boosted decision trees and likelihood ratios. An example of a final discriminant separating single top-quark events from background is shown in figure 7. After preforming a binned likelihood fit to the output distributions the analyses determine the single topquark production cross section as presented in figure 8. Both experiments see evidence for single top-quark production, CDF at a level of 3.7 σ
W. Wagner / Nuclear Physics B (Proc. Suppl.) 183 (2008) 67–74
73
Figure 7. Neural network discriminant to isolate single top-quark events from background [26]. The observed distribution is compared to the prediction of background and signal events assuming the predicted single top-quark cross section of 2.9 pb.
Figure 8. Summary of measured single top-quark production cross sections. (5.1 σ expected), while DØ observes an excess corresponding to a fluctuation at the level of 3.6 σ (2.3 σ expected). Using the theoretical prediction one can determine the CKM matrix element |Vtb |. CDF obtains |Vtb | = 0.88 ± 0.14 (exp) ± 0.07 (theory), DØ sets a lower limit of |Vtb | > 0.68 at the 95% C.L. If one extrapolates the current analyses to a data set corresponding to 4 fb−1 , one expects a measurement of |Vtb | with an experimental precision of 8%. Once single top-quark production is established it is also important to measure the cross sections of the t-channel and s-channel processes separately. At CDF a separate search based on neu+0.7 pb ral network discriminants gives σt = 0.8−0.6 +0.9 and σs = 1.6−0.8 pb [26], while DØ obtains σt = 4.2+1.8 −1.4 pb and σs = 1.0 ± 0.9 pb. Both measurements are in agreement with the theoretical prediction of σt = 1.98 ± 0.25 pb and σs = 0.88 ± 0.11 pb [25]. With more Run II data these measurements will allow for testing alternative, non-standard-model sources of single topquark production [27].
6. Conclusions The large data sets available in Run II of the Tevatron have propelled top quark physics in a new era in which precise investigations of top quark properties are possible. The most striking result is the precise mass measurement of mt = 172.6 ± 1.4 GeV/c2 with a relative uncertainty of 0.8%. In the last year many properties have been examined for the first time, including measurements of the width and charge. The measurements of top quark decay show impressive progress, most importantly the measurement of the W helicity fractions in top decay. The search for single top-quark production has been a tremendous challenge for many years, but recently first evidence for this process was found by CDF and DØ. Many more interesting results are yet to come from the Tevatron and are paving the way for high precision measurements at the LHC where tens of thousands of reconstructed tt¯
74
W. Wagner / Nuclear Physics B (Proc. Suppl.) 183 (2008) 67–74
pairs and single top-quarks will be available for examination. REFERENCES 1. R.D. Peccei, S. Peris, and X. Zhang, Nucl. Phys. B 349 (1991) 305–322. 2. A. Abulencia et al. (CDF Collaboration), Phys. Rev. Lett. 97, 082004 (2006). Public conference note No. 8795. 3. A. Abulencia et al. (CDF Collaboration), public conference note no. 8148. 4. V. M. Abazov et al. (DØ Collaboration), Phys. Rev. Lett. 100, 192004 (2008); Phys. Rev. D 76, 052006 (2007); Public conference note no. 5477 (2007). 5. S. Moch and P. Uwer, arXiv:0804.1476 [hep-ph] (2008). N. Kidonakis, R. Vogt, arXiv:0805.3844 [hep-ph] (2008). M. Cacciari et al., arXiv:0804.2800 [hep-ph] (2008). 6. T. Aaltonen et al. (CDF Collaboration), arXiv:0712.3273 [hep-ex]. 7. T. Aaltonen et al. (CDF Collaboration), public conference note no. 8811 (2007). 8. J.H. K¨ uhn and G. Rodrigo, Phys. Rev. D 59, 054017 (1999); Phys. Rev. Lett. 81, 49 (1998). O. Antunano, J.H. K¨ uhn, and G. Rodrigo, Phys. Rev. D 77, 014003 (2008). 9. T. Aaltonen et al. (CDF Collaboration), arXiv: 0806.2472 [hep-ex]. 10. V.M. Abazov et al. (DØ Collaboration), Phys. Rev. Lett. 100, 142002 (2008). 11. V.M. Abazov et al. (DØ Collaboration), public conference note no. 5600 (2008). 12. T. Aaltonen et al. (CDF Collaboration), public conference note no. 8675 (2007); Phys. Rev. Lett. 100, 231801 (2008). 13. A. Abulencia et al. (CDF Collaboration), Phys. Rev. D 75, 052001 (2007); public conference note no. 9114. 14. T. Aaltonen et al. (CDF Collaboration), public conference note no. 9215 and no. 9144. 15. V.M. Abazov et al. (DØ Collaboration), Phys. Rev. Lett. 100, 062004 (2008). 16. V.M. Abazov et al. (DØ Collaboration), FERMILAB-PUB-04/08-010-E. 17. T. Aaltonen et al. (CDF Collaboration), public conference note no. 9202.
18. A. Abulencia et al. (CDF Collaboration), Phys. Rev. Lett. 96, 022004 (2006; Phys. Rev. D 73, 032003 (2006). 19. V.M. Abazov et al. (DØ Collaboration), Phys. Rev. D 74, 092005 (2006); Phys. Rev. D 75, 092001 (2007). A. Abulencia et al. (CDF Collaboration) Phys. Rev. Lett. 96 022004 (2006); Phy. Rev. D 73, 092002 (2006); Phys. Rev. D 75, 031105 (2007). T. Aaltonen et al. (CDF Collaboration), Phys. Rev. Lett. 99, 182002 (2007). 20. W. Bernreuther, J. Phys. G 35, 083001 (2008). P. Skands and D. Wicke, Eur. Phys. J. C 52, 133 (2007). 21. T. Aaltonen et al. (CDF Collaboration), public conference note no. 8953 (2007). 22. T. Aaltonen et al. (CDF Collaboration), public conference note no. 8967 (2007). 23. D. Acosta et al. (CDF Collaboration), Phys. Rev. D 65, 091102 (2002); Phys. Rev. D 69, 052003 (2004); Phys. Rev. D 71, 012005 (2005). W. Wagner et al. (CDF Collaboration), hep-ex/0610074. B. Abbott et al. (DØ Collaboration), Phys. Rev. D 63, 031101 (2001). V.M. Abazov et al. (DØ Collaboration), Phys. Lett. B 517, 282 (2001); Phys. Lett. B 622, 265 (2005); Phys. Rev. D 75, 092007 (2007). 24. V.M. Abazov et al. (DØ Collaboration), Phys. Rev. Lett. 98:181802, 2007; FERMILAB-PUB-08/056-E. T. Aaltonen et al. (CDF Collaboration), public conference note no. 9251. 25. B.W. Harris et al., Phys. Rev. D 66, 054024 (2002). Z. Sullivan, Phys. Rev. D 70, 114012 (2004). J. Campbell, R.K. Ellis, F. Tramontano, Phys. Rev. D 70, 094012 (2004). N. Kidonakis, Phys. Rev. D 74, 114012 (2006). 26. T. Aaltonen et al. (CDF Collaboration), public conference note no. 9217 (2008). 27. M. Hosch, K. Whisnant, and B.L. Young, Phys. Rev. D 56, 5725 (1997). T. Tait and C.-P. Yuan, Phys. Rev. D 63, 014018 (2001).