Top Production at the Tevatron: The Antiproton Awakens
IIL NUOVO CIMENTO
Vol. ?, N. ? ? Top Production at the Tevatron: The Antiproton Awakens
Kenneth Bloom for the CDF and D0 Collaborations
Department of Physics and Astronomy, University of Nebraska-Lincoln, Lincoln, Nebraska, USA
Summary. — A long time ago, at a laboratory far, far away, the Fermilab Tevatroncollided protons and antiprotons at √ s = 1 .
96 TeV. The CDF and D0 experimentseach recorded datasets of about 10 fb − . As such experiments may never be re-peated, these are unique datasets that allow for unique measurements. This presen-tation describes recent results from the two experiments on top-quark productionrates, spin orientations, and production asymmetries, which are all probes of the p ¯ p initial state.PACS – top quarks.PACS – polarization in interactions and scattering.PACS – experimental tests of quantum chromodynamics.PACS – hadron-induced high- and super-high-energy interactions. In 2001, the Fermilab Tevatron started colliding protons and antiprotons at √ s =1 .
96 TeV. When operations concluded in September 2011, two experiments, CDF andD0, had each recorded datasets of approximately 10 fb − . As it is possible that therewill never again be a p ¯ p collider, these are unique datasets that allow for unique mea-surements. In particular, the colliding partons were typically quarks and antiquarks, incontrast to the gluon-gluon collisions that predominate at the Large Hadron Collider(LHC). Here we describe a number of recent measurements that probe the productionof top quarks at the Tevatron in ways that cannot easily be explored at the LHC. Forthe sake of brevity, older measurements are only summarized while those that have yetto be published or submitted for publication are described in greater detail.Table I gives the predicted production cross sections for strongly-produced t ¯ t andelectroweakly-produced single top quarks at the Tevatron and at LHC. While the crosssections are generally much larger at the LHC, that is not the case for the s -channelsingle-top production in the tb mode, which is “only” a factor of five larger than at theTevatron. Also, at the Tevatron the q ¯ q initial state provides about 85% of the totalcross section for t ¯ t production, while it is only about 15% (10%) at the LHC in Run 1(Run 2). This allows the Tevatron to compete with the LHC in some areas, and providescomplementarity due to the q ¯ q initial state. c (cid:13) Societ`a Italiana di Fisica a r X i v : . [ h e p - e x ] M a y KENNETH BLOOM FOR THE CDF AND D0 COLLABORATIONS t ¯ t tb tqb tW Tevatron 7.08 1.04 2.08 0.30LHC Run 1 234 5.55 87.2 22.2LHC Run 2 816 10.3 217 71.7
Table
I. –
Cross sections, in picobarns, for the production of different final states including topquarks at the Tevatron ( p ¯ p , √ s = 1 . TeV) and the LHC Run 1 and Run 2 ( pp , √ s = 8 TeVand √ s = 13 TeV), assuming a top-quark mass of 173 GeV [1].
1. – Production
A preliminary measurement from D0, not yet published, gives a precise measurementof the inclusive t ¯ t cross section that makes use of both the dilepton and lepton-plus-jetschannels [2]. The analysis makes heavy use of multivariate techniques, in which thenumeric values of many individual observables from an event are combined to form onesingle quantity, and fits to distributions of those quantities from each different final stateare used to obtain the cross section. The lepton plus jets channel is broken into sixsubsamples based on lepton type (electron or muon) and jet multiplicity (two, three orat least four jets). Each subsample gets its own boosted decision tree with gradientsusing about twenty kinematic variables, plus the output of a multivariate algorithm usedto identify b jets. The dilepton channel is simpler. It is broken into four subsamples ( eµ plus one jet, eµ plus at least two jets, ee plus at least two jets and µµ plus at least twojets), and the b -tag variable of the leading jet is the only one needed for the fit. Somerepresentative distributions from the analysis are shown in Figure 1. The cross section isobtained from a simultaneous log-likelihood fit template fit across all samples, using sys-tematic uncertainties as nuisance parameters. The profiling of systematic uncertaintiesreduces them by cross-calibration (for those that are uncorrelated). Careful attention ispaid to correlations amongst systematic uncertainties in the different subsamples. Theresulting cross section is 7.73 ± ± s -channel pro-duction of single top quarks; at the LHC, the backgrounds (from t ¯ t production) are muchmore significant. The rate for this process is sufficiently small that results from the fulldatasets of both experiments need to be combined to obtain a measurement with suf-ficient statistical significance to be called an observation of the process [3]. The crosssection result, σ s channel = 1 . +0 . − . pb, has 6.3 standard deviations significance. Thismeasurement then allows separate estimates of the s -channel and t -channel cross sections,without any assumptions of the value of σ s /σ t . The results are consistent with the stan-dard model predictions, with no indication of any other contributing process. The twocross section values then leads to a measurement of V tb that makes no assumptions on thenumber of quark generations, unitarity, or σ s /σ t (but does assume standard model topdecays, a pure V − A interaction, and CP conservation). The result is | V tb | = 1 . +0 . − . ,or | V tb | ≥ .
92 at 95% confidence level after applying a flat prior distribution for | V tb | < OP PRODUCTION AT THE TEVATRON: THE ANTIPROTON AWAKENS Fig. 1. – Representative distributions from the D0 inclusive t ¯ t cross section measurement. Left:Output of the boosted decision tree with gradients for the µ plus three jets channel. Right: b -tag discrimination variable for the leading jet in the ee plus at least two jets channel. In bothcases the colored histograms indicate the contributions from different physics proccesses.
2. – Spin orientations
Top quarks produced in the strong interaction are almost entirely unpolarized, butfor electroweak corrections at the 1% level. Thus, a search for top polarization is a searchfor new physics. The polarization of the top quark can be measured in the top rest framethrough angular distributions of decay products i with respect to a given axis n :1Γ d Γ d cos θ i, ˆ n = 12 (1 + P ˆ n κ i cos θ i, ˆ n ) , (1)where P ˆ n is the polarization strength and κ i is the analyzing power of the decay product,which for leptons is nearly unity. There are many axes ˆ n to choose from, such as thebeam axis (the direction of the proton), the helicity axis (the direction of the parent topquark) and the transverse axis (the cross product of the other two which is perpendicularto the production plane).D0 has new measurements of the top-quark polarization that makes use of the leptonplus three or at least four jets samples, in which a kinematic reconstruction is done isperformed to obtain the lepton angles cos θ i, ˆ n [4]. The inclusion of the three-jet sampleincreases the statistical power of the measurement but requires the use of a kinematicfitter developed for the A F B measurement described in Section . Templates in cos θ i, ˆ n for P = +1 and P = − P ˆ n . The cos θ i, ˆ n distributions and fit results areshown in Figure 2 and Table II. The measurements are consistent with both the standardmodel prediction and zero, and the measurement of the transverse polarization is the firstever. A measurement of the polarization in dilepton events is described in Section .While t ¯ t pairs are not produced polarized, their spins are correlated. The measure-ment of this correlation is unique to the t ¯ t system, as the top lifetime is a thousandtimes shorter than the spin decorrelation time. The amount of correlation depends on KENNETH BLOOM FOR THE CDF AND D0 COLLABORATIONS
Fig. 2. – The lepton plus jets cos θ i, ˆ n distributions for data, expected backgrounds and signaltemplates for P = 1 , the initial state, q ¯ q or gg . D0 has measured the spin correlation using the observable O off = σ ( ↑↑ ) + σ ( ↓↓ ) − σ ( ↑↓ ) − σ ( ↓↑ ) σ ( ↑↑ ) + σ ( ↓↓ ) + σ ( ↑↓ ) + σ ( ↓↑ )(2)using the “off-diagonal” spin quantization basis [6] where the correlation is maximized [7].Both dilepton and lepton+jets events are reconstructed with the matrix element methodto create a discriminant distribution that reflects the relative probability for the SM ornull spin correlation hypotheses. The resulting measurement is O off = 0 . ± .
16 (stat) ± .
15 (syst), where the systematic uncertainties are dominated by signal modeling issues.The measured value is in agreement with the SM value of 0.80 [8], and is 4.2 standarddeviations away from zero, giving evidence for spin correlation. In addition, as the q ¯ q and gg initial states lead to different correlation strengths, the fraction from t ¯ t fromeach initial state at next to leading order can be extracted. The result is f gg = 0 . ± OP PRODUCTION AT THE TEVATRON: THE ANTIPROTON AWAKENS Axis Measured polarization P ˆ n SM predictionBeam +0 . ± .
055 -0.002Helicity − . ± .
060 -0.004Transverse +0 . ± .
034 +0.011
Table
II. –
Measured top quark polarization in beam, helicity, and transverse spin quantizationbases along with the standard model (SM) predictions [5] .
12 (stat) ± .
11 (syst), consistent with the SM value of 0 .
135 [8].
3. – Production asymmetries
Due to interference terms that arise at next to leading order in QCD, t ¯ t pairs producedfrom q ¯ q interactions have a forward-backward asymmetry in the direction of the resultingquarks; the t tends to follow the direction of the q and the ¯ t the direction of the ¯ q . Thisasymmetry, defined as A F B = N (∆ y > − N (∆ y < N (∆ y >
0) + N (∆ y < , (3)where ∆ y = y t − y ¯ t , the rapidity difference between the top quark and antiquark, ispredicted to be about 10% [9]. The Tevatron has unique access to this quantity as mostof the t ¯ t pairs are produced in q ¯ q interactions, which is not the case at the LHC.The t ¯ t forward-backward asymmetry has been a topic of great interest for some years,as an anomalously large result could be an indicator of new physics, and some earlymeasurements of this quantity using the amount of Tevatron data that was availableat the time were in fact quite large (and the predicted values had been smaller). Thatspawned an effort to probe the asymmetry through a number of measurements that arebriefly described here.Reconstructing the top direction for A F B is complicated, as it requires a kinematicreconstruction and then an unfolding because the experimental resolution is poor. An-other approach to the problem is to measure the forward-backward asymmetry of thedecay lepton. While the SM prediction for the asymmetry is only 4%, the measurementis relatively simple because of the resolution on the lepton direction. CDF has measured(9 . +2 . − . )% [10] and D0 has measured (4 . ± . A F B should affect b ¯ b production too. Most b ¯ b production is from the gg initial state,but q ¯ q production is enhanced for high-mass pairs. CDF has made two measurementsof the b ¯ b asymmetry. One focuses on high-mass pairs, identifying b jets with secondaryvertices and assigning flavor with the difference in measured jet charges between thetwo jets. Effects that dilute the asymmetry such as mixing, secondary decays, chargemisidentification and non- b backgrounds are accounted for and the result is unfoldedto the particle level. The result is consistent with the SM and is able to exclude someaxigluon models [12]. A more recent search using lower-mass b ¯ b pairs makes use ofsoft-muon tagging to identify the b jets, and is also consistent with SM expectations [13]. KENNETH BLOOM FOR THE CDF AND D0 COLLABORATIONS
But the most fundamental information is obtained from the A F B measurements them-selves, in which the top quark directions are reconstructed. Both Tevatron experimentshave well-established measurements in the lepton plus jets samples. CDF measures A F B = (16 . ± . A F B = (10 . ± . A F B on m t ¯ t and | ∆ y | of the quarks, and find that it is greater than predicted. A F B measurements in the dilepton sample are more challenging because of the twoneutrinos in the final state, and took longer to complete. The recently published D0 anal-ysis [16] measures the production asymmetry simultaneously with the polarization of thetop quark with respect to the beam axis, using a novel application of the matrix-elementtechnique. A full reconstruction of the event kinematics is performed in a probabilisticfashion, and then a likelihood per event for the most probable kinematic value is madefor both the asymmetry and the lepton decay angle with respect to the beam axis in the t ¯ t rest frame. After an appropriate calibration of the method, the relevant quantities canbe extracted from the distributions of these quantities. The systematic uncertainties aredominated by those involved in modeling the t ¯ t signal, in particular hadronization andshowering, and also the calibration of the method.Without constraining either the asymmetry or the polarization, the results are A F B = (15 . ± . ± . κP = (7 . ± . ± . , (5)where the first uncertainty is statistical and the second is systematic, and κ (cid:39) . A F B = (17 . ± . ± . κP = (11 . ± . ± . . (7)The latter result for A F B is combined with that from the lepton plus jets measurementto obtain the final D0 measurement of this quantity, A F B = (11 . ± . ± . A F B in the dilepton final state has recently been submittedfor publication [17]. It is carried out in the same spirit as the D0 measurement. Alikelihood-based algorithm is used to reconstruct the momenta of the two neutrinos, andthus the top momenta, in each event from the observed kinematics. Rather than a singlesolution, a likelihood is formed as a function of the kinematic variables, and both possiblelepton-jet pairings are included. A likelihood-based scheme is used to unfold the resultsback to the parton level. The event selection is optimized to avoid poorly-reconstructedevents, which keeps the migration matrix fairly diagonal. Figure 3 shows the expectedresolution on the measurement of ∆ y , and the posterior probability density obtainedfrom the event sample. The resulting value of A F B is (12 ± ± | ∆ y | dependence of the result, no significant dependence is observed. The resultis then combined with the CDF lepton plus jets result to obtain A F B = (16 . ± . OP PRODUCTION AT THE TEVATRON: THE ANTIPROTON AWAKENS ∆ y (reconstructed) − ∆ y (generated)-4 -2 0 2 4 A r b i t r a r y un i t Powheg -MC sample A t ¯ t FB -1 -0.5 0 0.5 1 P o s t e r i o r - p r o b a b ili t y d e n s i t y A t ¯ t FB = 0 . ± . Fig. 3. – Left: Distribution of | ∆ y (reconstructed)- | ∆ y | (generated) in the CDF dilepton A FB measurement. Right: The resulting posterior probability for A FB . A summary the final Tevatron measurements of A F B , using the full datasets, is givenin Figure 4. The agreement between the results from CDF and D0 is reasonable, as isthe agreement with the predictions from the standard model.
Asymmetry (%)-40 -20 0 20 40
D0 CombinationPRD 92, 052007 (2015) . ± . D0 Dileptons (9 . − )PRD 92, 052007 (2015) . ± . D0 Lepton+jets (9 . − )PRD 90, 072011 (2014) . ± . CDF CombinationarXiv:1602.09015 . ± . CDF Dilepton (9 . − )arXiv:1602.09015 ± CDF Lepton+jets (9 . − )PRD 87, 092002 (2013) . ± . NNLO SM, M. Czakon, P. Fiedler and A. MitovPRL 115, 052001 (2015)
Tevatron A t ¯ t FB Fig. 4. – Summary of A FB measurements from CDF and D0.
4. – Conclusions
Even with the onslaught of data from the LHC, top physics at the Tevatron has re-mained interesting. The complementarity of the proton-antiproton initial state of theTevatron has provided unique opporunities. The production asymmetry cannot be ex-plored as well at the LHC, and the s -channel single-top production is much more difficultto study there too. In addition, CDF and D0 are very mature experiments, with well-understood datasets and well-modeled detectors. This allows for significant creativity indata analyses that have yielded sophisticated measurements. The A F B measurements
KENNETH BLOOM FOR THE CDF AND D0 COLLABORATIONS in particular drove a spectacular effort to fully exploit the capabilities of the two exper-iments. Arguably the LHC has much to learn from the Tevatron experience. The lastfew Tevatron top production measurements should soon be available, bringing this epicadventure to a conclusion. ∗ ∗ ∗
Thousands of physicists worked on the Tevatron and on the CDF and D0 experimentsover decades, and the results presented are due to their efforts. I particularly thank thecurrent top-physics group conveners of the experiments for their input and feedback ontheir presentation. I also thank the conference organizers for the opportunity to enjoyLa Thuile. May the quarks be with you!
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