DOI 10.1393/ncc/i2018-18148-x
Colloquia: LaThuile 2018
Top quark physics at the Tevatron
S. Leone for the CDF and D0 Collaborations
INFN, Sezione di Pisa - Pisa, Italy
received 6 September 2018
Summary. — A selection of the most recent CDF and D0 results in the top quark sector is presented. The most recent top quark mass measurements, including the pole mass measurements obtained from cross section measurements, are discussed. The Tevatron combined t¯t charge asymmetry results are shown. The recent top
quark polarization measurements are reviewed.
1. – Introduction
The Tevatron Collider provided p¯p collisions at a center of mass energy of √s =
1.96 TeV until it ceased operating in September 2011. Data corresponding to approxi-mately 10 fb−1 were recorded by the CDF and D0 experiments. The top quark was first observed at the Tevatron. On 2 March 1995, physicists at CDF and D0 announced the discovery of the top quark [1]. Since then, the top sector has been actively explored by the Tevatron and LHC experiments.
At the Tevatron center of mass energy top quarks are primarily produced in t¯t pairs,
with q ¯q → t¯t being the dominant process. This is distinct from the production at the
LHC, where the dominant process is gluon fusion gg→ t¯t. Therefore the Tevatron is the right place to study the t¯t production via q ¯q annihilation.
However, the production cross section is small: the top quark discovery happened with a few hundred of top quarks produced per experiment, and even in 10 fb−1 the number of produced events is much smaller than at the LHC, which can be considered a top factory.
The standard model of elementary particles (SM) predicts that each top quark decays almost exclusively into a real W and a b quark. Each W subsequently decays into either a charged lepton and a neutrino or two quarks. For top quark pair production, events can thus be identified by means of different combinations of leptons (e or μ) and jets. Two decay modes are used in the analyses described in this report: the dilepton mode, where both W ’s decay to a charged lepton and a neutrino, and the lepton plus jets mode, where one W decays leptonically and the other one decays hadronically to a pair of quarks.
) 2 (GeV/c t m 150 160 170 180 190 200 2.66 ! 12.40 !(1.50 ! 2.20) Tevatron combination * 174.30 ±0.65 (±0.35 ± 0.54) syst) ± stat ± ( CDF-II MET+Jets 173.93 ±1.85 (±1.26 ± 1.35) CDF-II Lxy 166.90 ±9.43 (±9.00 ± 2.80) CDF-II all-jets 175.07 ±1.95 (±1.19 ± 1.55) CDF-I all-jets 186.0 ±11.5 (±10.0 ± 5.7) D0-II lepton+jets 174.98 ±0.75 (±0.41 ± 0.63) CDF-II lepton+jets 172.85 ±1.12 (±0.52 ± 0.99) D0-I lepton+jets 180.1 ± 5.3 (± 3.6 ± 3.9) CDF-I lepton+jets 176.1 ± 7.3 (± 5.1 ± 5.3) D0-II dilepton * 173.50 ±1.56 (±1.31 ± 0.84) CDF-II dilepton 171.5 ± 3.2 (± 1.9 ± 2.5) D0-I dilepton 168.4 ±12.8 (±12.3 ± 3.6) CDF-I dilepton 167.4 ±11.4 (±10.3 ± 4.9)
Mass of the Top Quark (* preliminary)
July 2016
/dof = 10.8/11 (46%)
2
χ
Fig. 1. – Summary of the CDF and D0 top quark mass measurements used for the 2016 Tevatron top mass combination.
The top quark is the most massive of the known elementary particles. As a conse-quence of its large mass it is the only quark that decays before hadronizing, thus offering a chance to study a bare quark. The top quark properties can be inferred from the kinematic distributions of its decay products. More than 20 years ago CDF and D0 as-sembled all the pieces needed to discover the quark top. The standard strategy to study the top quark properties remains the same today.
All the analyses described in the following are based on the full Tevatron Run 2 dataset.
2. – Top quark mass measurement
The most measured top quark property is its mass, which is a free parameter of the SM. Several methods have been used to obtain precise top quark mass measurements. Most of them are based on the comparison of kinematic observables in data and in Monte Carlo (MC) samples generated at different top quark masses.
Figure 1 shows a summary of the CDF and D0 top quark mass measurements obtained in all the decay channels and used for the latest Tevatron combination mtop= 174.30±
0.35(stat.)± 0.54(syst.) GeV, which was produced in summer 2016 and has a relative uncertainty of less than 0.4% [2].
D0 recently published a combination of the measurements of the top quark mass in Run 1 and Run 2 in the lepton plus jets and dilepton channels. The systematic uncertainties are grouped into sources of the same or similar origin to form uncertainty
Top quark pole mass (GeV) 160 170 180 190 (pb) tt σ 4 6 8 10 12 +X) t t → p (p σ Measured σ Measured dependence of NNLO+NNLL -1 D0 9.7 fb [GeV] t m 160 170 180 190 ) top T ), pt (m(t 2 χ Combined 0 50 100 -1 (b) D0 Preliminary, 9.7fb Data vs. NNLO (MSTW2008) Scale uncertainties : 2.39 min 2 χ Fit
Fig. 2. – (a): D0 measured t¯t production cross section dependence on the top quark mass
(points) parametrized by a quartic function (solid black line) and compared to the dependence provided by a NNLO+NNLL calculation (red curves); (b) D0 χ2 distribution for the differential
cross sections in terms of ptopT and mt¯t calculated at NNLO, as a function of the top quark
mass.
categories. The dominant sources of uncertainty are the statistical uncertainty, the jet energy scale calibration, which has statistical origin, and the modeling of the signal. The resulting combined value for the top quark mass is: mtop= 174.95± 0.40(stat.) ±
0.64(syst.) GeV. With a relative precision of 0.43% this measurement constitutes the legacy Run 1 and Run 2 measurement of the top quark mass in the D0 experiment [3].
Given the continuous reduction of the experimental error on the top quark mass measurement, in the last few years a lot of theoretical work was devoted to studies aimed to translate the MC top quark mass into a definition of mass in a well defined renormalization scheme [4].
From the experimental point of view, alternative ways of measuring the top quark mass were investigated, with the goal of having less inputs from MC, or depending on different systematic effects, with respect to the standard methods.
In this perspective D0 obtained a top quark pole mass measurement from the inclusive cross section measurement. In this analysis the experimental t¯t cross section measurement
is compared to the theory computation.
Figure 2(a) shows the measured and theoretical mass dependence of the inclusive t¯t
production cross section. The measured t¯t cross section only changes by 0.7% for a change
of 1 GeV in the assumed top quark mass. The experimentally measured dependence is parametrized with a fourth-order polynomial function.
The most probable top quark mass value and uncertainty are extracted by employing a normalized likelihood function, which takes into account the total experimental un-certainty, the theoretical uncertainties on the renormalization and factorization scales, and the PDF uncertainties. Employing the quartic parametrization and the the-ory predictions at next-to-next-to leading order (NNLO) perturbative QCD mtop =
172.8± 1.1(theo.)+3.3−3.1(exp.) GeV is found [5]. The experimental uncertainties dominate the precision of the measurement.
D0 also measured the top quark pole mass from a comparison of the differential t¯t
cross sections measured as a function of the transverse momentum of the top quark
ptopT and the invariant mass of the t¯t system mt¯twith the differential distributions
pre-dicted by perturbative QCD. This measurement was made possible thanks to the recent availability of NNLO differential predictions [6]. The measured top quark pole mass is
Top Quark Mass (GeV)
150 160 170 180 190 200
World average (preliminary 2014) 173.34 ±0.27 ± 0.71 GeV
± 0.76 GeV cross section t Run II t 9.7 fb-1 172.8 ±0.7 ± 3.2 GeV ± 3.3 GeV D0 combined 174.95 0.40 ± ± 0.64 GeV ± 0.75 GeV
luminosity mt ± stat ± syst
Run I Dileptons 0.1 fb-1 168.4 ±12.3 ± 3.6 GeV
± 12.8 GeV
Run I Lepton+jets 0.1 fb-1 180.1 ±3.6 ± 3.9 GeV
± 5.3 GeV
Run II Dileptons 9.7 fb-1 173.50 ±1.31 ± 0.84 GeV
± 1.56 GeV
Run II Lepton+jets 9.7 fb-1 174.98 ±0.41 ± 0.63 GeV
± 0.76 GeV D0
150 160 170 180 190 200
Fig. 3. – Summary of the D0 top quark mass measurements.
mtop = 169.1± 2.5(total)GeV [7]. Figure 2(b) shows the combined χ2 distribution for
the differential cross sections in terms of ptopT and mt¯tcalculated at NNLO, as a function
of the top quark mass. The shaded band indicates the theoretical scale uncertainties. Figure 3 shows a summary of the top quark mass measurements used in the recent D0 combination along with the D0 final result and the top quark pole mass extracted from the D0 inclusive cross section measurement. The latter is not used in the combination. 3. – t¯t charge asymmetry
The t¯t production mechanism has been investigated in detail by studying the charge
production asymmetry. The forward-backward asymmetry is such that the top quark is preferentially emitted in the direction of the incoming light quark, while the antitop quark follows the direction of the incoming antiquark, and it is due to the q ¯q annihilation
process. A recent QCD NNLO calculation evaluates an asymmetry of 9.5% [8]. The gg initial state does not contribute to the asymmetry but dilutes the average value. On the other hand, new physics could give rise to an enhanced asymmetry.
Experimentally the asymmetry is defined relying either on the fully reconstructed top quarks, or on leptons from the W decay. In the first case it uses the rapidity difference Δy of the top (antitop) quark decaying semileptonically t→ lνb and the antitop (top) decaying hadronically ¯t → jjb. It requires reconstruction of top and antitop quarks
using all the available information associated with the final-state particles. Background contributions are subtracted from the yield of selected candidates, thereby providing the
t¯t signal, which is then corrected for detector effects, to unfold from the reconstructed
top and antitop to the parton level.
In the second case the lepton asymmetry in t¯t decay is parametrized as a function of qy where q is the charge and yis the pseudorapidity of the charged lepton from the W
decay. This asymmetry, while smaller in magnitude, does not need unfolding but must be corrected for acceptance effects, and it is insensitive to biases from the top quark reconstruction procedure.
When the t¯t forward-backward asymmetry measurements were first performed in
Tevatron Run 2 in the lepton plus jets channel, a small departure from the SM ex-pectations was observed, which brought a lot of excitement in the field [9]. Both CDF
350 450 550 650 mt¯tGeV/c2 − 0 .4 − 0 .2 0 .0 0 .2 0 .4 0 .6 A t¯t FB D0 + jets, 9.7 fb−1 CDF + jets, 9.4 fb−1 Tevatron combination, ≤ 9.7 fb−1 mt¯t= (9.71 ± 3.28) × 10−4GeV−1c2 NNLO QCD + NLO EW [Czakon et al.]
0.0 0.4 0.8 1.2 1.6 2.0 |Δyt¯t| − 0 .4 − 0 .2 0 .0 0 .2 0 .4 0 .6 0 .8 A t¯t FB
Tevatron combination: Δyt¯t= 0.187 ± 0.038 NNLO QCD + NLO EW [Czakon et al.]
D0 + jets, 9.7 fb−1 CDF + jets, 9.4 fb−1 CDF , 9.1 fb−1
Fig. 4. – (a): Results for At¯F Bt vs. mt¯tfor the individual CDF and D0 measurements and for their
combination. (b) Measurements of the differential asymmetries At¯F Bt vs. |Δyt¯t|. In both plots
the inner error bar indicates the statistical uncertainty, while the outer error bar corresponds to the total uncertainty. The linear dependence of the combined result is given by the solid black line, with the 1 SD total uncertainty of the two-parameter (one-parameter) fit given by the shaded gray area. The dashed orange area shows the NNLO QCD + NLO EW prediction with its 1 SD uncertainty.
and D0 then completed their measurements program on the full Run 2 dataset, and with a more refined analysis they found, in some cases, lower values of the asymmetry [10]. Furthermore, the theory predictions were improved by including higher-order QCD and electro-weak (EW) corrections, and, as a result, the new expectations are higher than they were before [8].
Recently CDF and D0 published the combination of their asymmetry measurements obtained with the BLUE method accounting for all uncertainties and their correla-tions [11]. The combination is performed for the three asymmetries, based either on the reconstructed rapidities of the top and antitop, or on the lepton pseudorapidities, or on the difference between lepton pseudorapidities for the dilepton channel. The com-bined inclusive asymmetry is At¯F Bt = 0.128± 0.021(stat.) ± 0.014(syst.), consistent with the NNLO QCD + next-to-leading order (NLO) EW prediction of 0.095± 0.007 within 1.3 standard deviations (SD).
The values of At¯t
F Bas a function of mt¯tfor each experiment and their combination are
shown in fig. 4(a), together with the NNLO QCD + NLO EW predictions. The predicted slope parameter agrees with the combined experimental results to within 1.3 SD. The linear dependence of the combined result is given by the solid black line together with the 1 SD total uncertainty of the two-parameter fit given by the shaded gray area.
The differential t¯t asymmetry as a function of|Δyt¯t| is available from CDF for both the
lepton plus jets and the dilepton channels, and from D0 for the lepton plus jets channel. The choice of binning differs for these measurements. A simultaneous least-squares fit to a linear function for all available measurements is performed. The prediction and the combined result differ by 1.5 SD. Figure 4(b) shows the individual measurements and the result of the linear fit.
The combined fit to the CDF and D0 inclusive single-lepton asymmetry gives A
F B =
0.073± 0.016(stat.) ± 0.012(syst.) and is consistent with the NLO QCD + NLO EW prediction of 0.038± 0.003 to within 1.6 SD.
−15 0 15 30 Asymmetry [%] t¯tΔy AsymmetryAt¯t FB CDF + jets, 9.4 fb−1 PRD 87, 092002 (2013) 16.4 ± 4.7 CDF , 9.1 fb−1 PRD 93, 112005 (2016) 12 ± 13 D0 + jets, 9.7 fb−1 PRD 90, 072011 (2014) 10.6 ± 3.0 D0 , 9.7 fb−1 PRD 92, 052007 (2015) 17.5 ± 6.3 Tevatron combination 12.8 ± 2.5 Lepton qη AsymmetryA FB CDF + jets, 9.4 fb−1 PRD 88, 072003 (2013) 10.5 ± 3.2 2.9 CDF , 9.1 fb−1 PRL 113, 042001 (2014) 7.2 ± 6.0 D0 + jets, 9.7 fb−1 PRD 90, 072001 (2014) 5.0 ± 3.4 3.7 D0 , 9.7 fb−1 PRD 88, 112002 (2013) 4.4 ± 3.9 Tevatron combination 7.3 ± 2.0 Lepton Δη AsymmetryAFB CDF , 9.1 fb−1 PRL 113, 042001 (2014) 7.6 ± 8.2 D0 , 9.7 fb−1 PRD 88, 112002 (2013) 12.3 ± 5.6 Tevatron combination 10.8 ± 4.6
NNLO QCD + NLO EW [Czakon et al.] NLO SM [Bernreuther and Si]
Fig. 5. – Summary of inclusive forward-backward asymmetries in t¯t events in percents at the
Tevatron.
rapidity of the 2 leptons yields A
F B= 0.108±0.043(stat.)±0.016(syst.) and is consistent
with the NLO QCD + NLO EW prediction of 0.048± 0.004 to within 1.3 SD.
All measurements favor somewhat larger positive asymmetries than the predictions, but none of the observed differences are larger than 2 standard deviations. Hence, we conclude that the measurements and their combinations, shown in fig. 5, are consistent with each other and with the SM predictions.
4. – Top quark polarization
The SM predicts that top quarks produced at the Tevatron collider are almost unpo-larized, while some models beyond the standard model (BSM) predict enhanced polar-ization [12]. The top quark polarpolar-izations at the Tevatron and LHC are expected to be different because of the different initial states, which motivates the measurement of the top polarization in Tevatron data.
The top quark polarization can be measured in the top quark rest frame through the angular distributions of the top quark decay products relative to some chosen axis. The
TableI. – D0 measured the top quark polarization from the lepton plus jets channel along the
beam, helicity, and transverse axes. The total uncertainties are obtained by adding the statistical and systematic uncertainties in quadrature.
Axis Measured polarization SM prediction
Beam +0.070± 0.055 −0.002 Helicity −0.102 ± 0.061 −0.004 Transverse +0.040± 0.035 +0.011 P α 0.3 − −0.2 −0.1 0 0.1 0.2 0.3
Top Quark Polarization Measurement in Dilepton Channel at Tevatron
0.111 (syst.) ± (stat.) 0.109 − +0.114 = -0.130 CPC P α 0.040 (syst.) ± 0.123 (stat.) ± = -0.046 CPV P α 0.098 (syst.) ± 0.177 (stat.) ± = -0.077 CPC P α (syst.) 0.056 − +0.055 (stat.) 0.145 − +0.146 = -0.111 CPV P α 0.042 (syst.) ± 0.105 (stat.) ± = 0.072 CPC P α 0.019 (syst.) ± 0.091 (stat.) ± = 0.113 CPC P α Helicity Basis • αPSM = -0.0039±0.0004 * Transverse Basis • αPSM≈ +0.011 ** Beamline Basis • αPSM = -0.0019 ±0.0005 * * PRD 78, 017503 (2008) ** JHEP. 08 (2013) 072. *** PRD 92, 052007 (2015) ) -1 CDF ( 9.1fb ) -1 CDF ( 9.1fb ) *** -1 D0 ( 9.4fb constraint) FB (without A constraint) FB (with A CDF Run II Prelim + θ cos 1 − −0.8−0.6−0.4−0.2 0 0.2 0.4 0.6 0.8 1 Events/0.2 0 20 40 60 80 100 120 140 Data Backgrounds P= -0.4) α CPC( P= 0.0) α CPC( P= +0.4) α CPC( ) -1 CDF Run II Prelim ( 9.1 fb T E + 2jets + -l + l → t t Transverse (a)
Fig. 6. – (a) cos θ data distribution (black dots) for positive leptons in the tranverse basis, compared to expectations for three different polarization values; (b) summary of top quark polarization measurements in the dilepton channel at the Tevatron.
mean polarizations of the top and antitop quarks are expected to be identical because of
CP conservation.
D0 published a measurement of top quark polarization in t¯t production in the lepton
plus jets final state [13]. The polarization is measured along three quantization axes: i) the beam axis, given by the direction of the proton beam; ii) the helicity axis, given by the direction of the parent top or antitop quark; and iii) the transverse axis, given as perpendicular to the production plane defined by the proton and parent top quark directions. The measured polarizations for the three spin-quantization axes are listed in table I. The polarizations are consistent with SM predictions. The transverse polarization is measured for the first time.
Very recently CDF presented a new measurement of the top quark polarization in the dilepton channel [14]. The measurement is performed assuming that the polariza-tion is generated by either a CP -conserving (CPC) or a CP -violating (CPV) producpolariza-tion amplitude. The top quark polarization is measured using the two-dimensional angular distributions of leptons with respect to the helicity axis and the transverse axis. Fig-ure 6(a) shows, as an example, the one-dimensional cos θ distribution for positive leptons in the transverse basis assuming CPC and comparing data to two extreme polarization values in the allowed physical region. Figure 6(b) shows a summary of the measurements of top quark polarization in the dilepton channel at the Tevatron, compared to SM pre-diction (red vertical line). The measured polarizations are consistent between CDF and D0 and with the SM predictions.
5. – Conclusions
Several years after the end of Run 2, Tevatron experiments continue to provide valu-able top physics results. CDF and D0 are in the process of producing the last Tevatron legacy measurements. D0 evaluated a combined top quark mass and presented pole mass measurements based on the inclusive and differential cross section measurements. The final Tevatron combined production asymmetry AF B was just published. Both
experi-ments measured the top quark polarization in the lepton plus jets and dilepton channels. All measurements are in agreement with the SM predictions.
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