Measurements of Spin Correlation in ttbar Events at D0
PProceedings of the DPF-2011 Conference, Providence, RI, August 8-13, 2011 Measurements of Spin Correlation in t ¯ t Events at D0
Kenneth Bloom (for the D0 Collaboration)
Department of Physics and Astronomy, University of Nebraska-Lincoln, Lincoln, NE, USA
Two recent measurements by the D0 Collaboration of spin correlation in t ¯ t production using 5.4 fb − of Teva-tron p ¯ p collider data are presented. Both rely on the dilepton final state of t ¯ t . One measurement relies on fullreconstruction of the top quark kinematics, and the other makes use of leading-order matrix elements to char-acterize the kinematics. The latter measurement is the first ever to have sufficient analyzing power to excludethe no-correlation hypothesis.
1. Introduction
In the p ¯ p → q ¯ q process, the quarks that are produced are unpolarized, but their spins are correlated. Thisis required by angular momentum conservation in the strong interaction. In general, this correlation is unob-servable, as the hadronization process involves the emission of gluons that can flip the spins of the quarks. Butthe top quark provides a laboratory for studying the correlation. The short lifetime of top, about 5 × − s,is shorter than the timescale for strong processes, so top decays before fragmentation and spin flips can oc-cur. Thus, the original spin orientation is preserved, and is passed to the decay products. It should then beobservable through a study of the kinematics of the decay products.A measurement of top-quark spin correlation is a test of top-quark properties and also a probe of new physics.The very observation of the correlation could in principle be used to set an upper limit on the top lifetime.Should top have a non-standard decay (such as t → H + b ), or non-standard production mechanism (throughdecays of stop pairs, or a Z (cid:48) resonance), a non-standard correlation would be observed. The correlation isultimately a subtle effect – the theme of this presentation – but there is now enough Tevatron data to exploreit.
2. About correlation
At the Tevatron, the primary production mode of t ¯ t is through q ¯ q → t ¯ t with an s -channel gluon. (This isin contrast to the LHC, where the initial state is primarily gg ). The q and ¯ q must have opposite helicity tocouple to that gluon, and that forces the t and ¯ t to have their spins pointing along the beamline. A correlationstrength can be defined based on the number of t ¯ t pairs with their spins pointing in the same direction, A = N ↑↑ + N ↓↓ − N ↑↓ − N ↓↑ N ↑↑ + N ↓↓ + N ↑↓ + N ↓↑ . (1)But the spin orientation must be defined with respect to a quantization axis. In the measurements describedhere, the beamline axis, defined as the direction of the colliding hadrons in the zero-momentum frame of the t ¯ t system, is used. This choice is intuitive, easy to construct, and optimal for t ¯ t produced at threshold. With thischoice of quantization axis, next-to-leading order QCD calculations predict A = 0 . +0 . − . [1].The spin orientation of the top is then passed to its decay products. The differential angular decay distribu-tions of the top daughters is given by 1Γ d Γ d cos θ i = 12 (1 + α i cos θ i ) , (2)where cos θ i is the angle between the i th top daughter and the spin of the top. Different decay products havedifferent correlation strengths, as indicated by α i . This is illustrated in Figure 1. In the case of a leptonic W decay, the lepton has the greatest analyzing power, and for a hadronic W decay it is the down-type quark . Inboth cases, α (cid:39) In the original observation of parity violation, it was the angular distribution of electrons from nuclear beta decay that wereobserved. What would the history of our understanding of the weak interaction have been had the correlation with the nuclearspin direction not been so strong? a r X i v : . [ h e p - e x ] S e p Proceedings of the DPF-2011 Conference, Providence, RI, August 8-13, 2011
Figure 1: Illustration of the top decay angles (left) and dependence of the decay rate on the angles (right) [2].
Thus, the doubly-differential cross section as a function of the decay angles of decay products from twodifferent quarks in t ¯ t is given by 1 σ d σd cos θ d cos θ = 14 (1 − Aα α cos θ cos θ ) . (3)To study the spin correlation, one looks for correlation between the directions of decay products from the twodifferent top decays. In the case of both tops decaying leptonically, α α (cid:39)
1, and we write Aα α ≡ C (cid:39) A .
3. Experimental situation The measurements described below were performed at the Fermilab Tevatron, a p ¯ p collider operating at √ s = 1 .
96 TeV. Run II of the collider has been in progress since 2001, with almost 12 fb − of integratedluminosity delivered. The spin-correlation measurements make use of 5.4 fb − . The data was recorded by theD0 detector, which consists of silicon and fiber trackers inside a 2 T solenoid, a liquid argon-uranium calorimeter,and muon trackers and scintillators inside toroids.At the Tevatron, 85% of t ¯ t production arises from q ¯ q annihilation and the remaining 15% from gg interactions.Each top quark decays to W b nearly 100% of the time, and the final states are characterized by the W decaymodes. The three final states are all-hadronic, lepton plus jets and dilepton. In the order listed, the final stateshave decreasing rate and increasing number of neutrinos and signal purity.The dilepton state in particular is characterized by two high- p T leptons, missing momentum due to theescaping neutrinos, two hadronic jets from b decays, and perhaps additional jets due to initial- and final-state radiation. For the purpose of the spin-correlation measurements, the dilepton state has the best analyzingpower and most accurate measurement of the decay-product (lepton) directions, but the worst statistical power,compared to other final states that could be considered.
4. Event selection
The two measurements described have the same event selection. A t ¯ t -enriched sample is chosen by selectingevents with two high- p T , isolated, opposite-charge leptons. Only electrons and muons are considered as leptons,so the dilepton pairs can be either ee , eµ or µµ .. There must also be at least two high- p T jets. To suppressbackgrounds, a large scalar sum of the lepton and jet p T values is required in the eµ channel, and significantmissing energy in the ee and µµ channels. Backgrounds from Z/γ ∗ (diboson) events are modeled by leading-order Monte Carlo samples, and normalized to next-to-next-to-leading (next-to-leading) order cross sections. This presentation was given at the very end of a long day of top-physics talks, and by unanimous consent of the audience most ofthe material in this section was not presented, as it was deemed redunant. roceedings of the DPF-2011 Conference, Providence, RI, August 8-13, 2011 π and η decays in electron samples and real muons in jetsthat appear to be isolated in muon samples; both of these are modeled with complementary data samples. Theselected data sample is about 70% pure in t ¯ t events, as shown in Table I. Table I: Estimates of contributions of various physics processes to the selected dilepton sample. t ¯ t Z/γ ∗ Diboson Instrumental Total Observed341 ±
30 93 ±
15 19 ± ± ±
39 485
5. Analysis I: Template-based
D0 has performed two different measurements of the spin correlation with this event sample. The firstis template-based, in which the decay angles are calculated in each event, and the distribution of angles ismodeled by a sum of templates representing the distributions for correlated and uncorrelated spins [3]. Thistechnique has been used before [4], but with a much smaller data sample.To observe the correlation, one must measure the angle between the lepton and the beamline (which is used asthe top spin quantization axis) in the zero-momentum frame of the t ¯ t system, which requires a full reconstructionof the decay. A total of eighteen quantities are needed to specify the final-state configuration, but because ofthe two undetected neutrinos only twelve are measured. Constraining the decay kinematics to the values of thetop and W masses provides four additional pieces of information, but that still leaves two missing.The “neutrino weighting” technique is used to solve the remaining kinematics. Two values of the neutrino η (where η = − ln tan( θ/
2) and θ is the polar angle measured from the beamline) are randomly sampled fromthe neutrino η distribution as predicted from t ¯ t Monte Carlo simulations. These values are then used to solvefor the implied t ¯ t kinematics. This allows a determination of the product of decay angles cos θ cos θ and ofthe neutrino momenta. The cos θ cos θ value is then weighted by the consistency of the determined neutrinomomenta with the measured missing transverse energy in the event. The sampling is repeated many times, andweighted mean of all solutions obtained is then used as the estimator of cos θ cos θ . t ¯ t events are simulated using the MC@NLO generator [6], in which the spin correlation can be turned on oroff straightforwardly. Then, with the appropriate weighting of simulated samples, cos θ cos θ distributions forany value of C can be generated. The left panel of Figure 2 shows the expected distribution of cos θ cos θ at parton level for t ¯ t with no spin correlation ( C = 0) and standard-model (SM) spin correlation ( C = 0 . θ cos θ when there is correlation. θ cos θ cos -1 -0.5 0 0.5 1 N o r m a li z ed No spin corr.SM spin corr. DØ θ cos θ cos -1 -0.5 0 0.5 1 E v en t s -1 DØ L=5.4 fb
Figure 2: Left: The distribution in cos θ cos θ for a sample including the NLO QCD spin correlation (C = 0.78) (reddashed line) and with no spin correlation (C = 0) (blue solid line) at the parton level, generated using MC@NLO. Right:The distribution in cos θ cos θ for the entire dilepton event sample. The summed signal, including NLO QCD spincorrelation (C = 0.78) (red) and all backgrounds (blue) are compared to data. The open histogram is the predictionwithout spin correlation (C = 0). The right panel of Figure 2 shows the distribution observed in the data, along with the appropriately-normalized background distribution and the distributions expected for the cases of no correlation and SM
Proceedings of the DPF-2011 Conference, Providence, RI, August 8-13, 2011 correlation. On the face of it, it seems hard to distinguish the two cases. To make a quantitative statement,the most likely value of C is obtained with a binned maximum-likelihood fit. Systematic uncertainties areincorporated to the fit as nuisance parameters, and the overall t ¯ t cross section is treated as a free parameter toavoid biases.A Feldman-Cousins-based frequentist approach [5] is used to set confidence limits on C as a function of themeasured value. These are shown in Figure 3. The measured value is C meas = 0 . ± .
45, which can be comparedwith the expected value of C = 0 .
78. We find − . < C < .
81 at 95% confidence level. Uncertainties on thecentral value are shown in Table II. Statistical uncertainties dominate by far; the leading systematic uncertaintyarises from the limited Monte Carlo statistics in generating the templates. This can obviously be remediedwhen statistical uncertainties are reduced with more data.
Figure 3: The 68% (inner), 95% (middle), and 99% (outer) C.L. bands of C as a function of C meas from likelihood fitsto MC events for all channels combined. The yellow line indicates the most probable value of C as a function of C meas ,and represents the calibration of the method. The vertical dashed black line depicts the measured value C meas = 0 . C = 0 . +0 . − . . While the measured value of C agrees with the predicted value within two standard deviations, it is alsoconsistent with no spin correlation at all. A more powerful technique is required to observe the effect with thedata sample in hand.
6. Analysis II: Matrix-element-based
The second measurement makes use of the leading-order matrix element for t ¯ t production and decay, usingthe full event kinematics to determine the fraction of t ¯ t events in the sample that the spin correlation that isexpected in the SM [7]. Matrix elements have never been used in spin-correlation measurements before, andtheir implementation leads to a significant improvement in sensitivity.On an event by event basis, we can characterize whether the kinematics are consistent with the SM or withno correlation at all. This is done by calculating a probability for consistency of the event with spin correlationor non-correlation. The probability is given by P sgn ( x ; H ) = 1 σ obs (cid:90) f PDF ( q ) f PDF ( q )d q d q · (2 π ) |M ( y, H ) | q q s W ( x, y ) dΦ . (4)Here, σ obs denotes the leading order cross section including selection efficiency, q and q the energy fractionof the incoming quarks from the proton and antiproton, respectively, f PDF the parton distribution function, s the center-of-mass energy squared of the p ¯ p system and dΦ the infinitesimal volume element of the 6-body roceedings of the DPF-2011 Conference, Providence, RI, August 8-13, 2011 Table II: Summary of uncertainties on C meas .Source +SD − SDMuon identification 0.01 − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . − . phase space. The detector resolution is taken into account through a transfer function W ( x, y ) that describesthe probability of a partonic final state y to be measured as x = (˜ p , . . . , ˜ p n ), where ˜ p i denotes the measuredfour-momenta of the final state particles. H represents the correlation hypothesis – H = c corresponds to SMcorrelation and H = u corresponds to no correlation. The appropriate matrix element is used for each case. Incontrast to the template measurement, the full event kinematics plus theoretical models of t ¯ t production anddecay are used, not just the lepton angles, and by adding this information, the sensitivity of the measurementis increased.For each event, we compute R = P sgn ( H = c ) P sgn ( H = u ) + P sgn ( H = c ) , (5)Events more consistent with having SM spin correlation will tend to have R close to one, while those lessconsistent will have R closer to zero. A value of R (cid:39) . R for MC@NLO t ¯ t events generatedwith and without spin correlation. In fact, R (cid:39) . R observed in the data, along with the distributionexpected for the background events and those for t ¯ t with and without spin correlation. By eye, one can see thatthe data are more consistent with the hypothesis of correlation.The fraction of events that are consistent with SM spin correlation, f , is obtained from a binned likelihood fitthat is very similar to that of Analysis I. This fraction is of course expected to be 100%. The confidence bandsare shown in Figure 5. We find f = 0 . +0 . − . , which is consistent with the SM. A value of f = 0 is excludedat the 97.7% confidence level. (From ensemble testing, the measurement was expected to exclude f = 0 atthe 99.6% confidence level; if the correlation exists as expected in the SM, this measurement was “unlucky”in finding a value less than 100%.) The uncertainties on the measured value of f are listed in Table III; onceagain, statistical uncertainties greatly dominate.
7. Summary
Quark spin correlation is a phenomenon that can only be seen in t ¯ t production, thanks to the short toplifetime. However, it is a subtle effect that requires large data samples and sophisticated analysis techniques to Proceedings of the DPF-2011 Conference, Providence, RI, August 8-13, 2011 R N o r m a li z e d SM spin corr.tt no spin corr.tt DØ R eve n t s N Data SM spin corr.tt no spin corr.tt tmeasured tBackground -1 DØ, L=5.4 fbR eve n t s N R eve n t s N R eve n t s N R eve n t s N R eve n t s N R eve n t s N Figure 4: Left: Comparison of the discriminant R between SM spin correlation H = c and no spin correlation H = u atparton level. The first and last bin include also the contributions from R < .
29 and
R > .
63. Right: The predicteddiscriminant distribution R for the combined dilepton event sample for the fitted σ t ¯ t and f meas compared to the data.The prediction with spin correlation ( f = 1) and without spin correlation ( f = 0) is shown including background.Figure 5: The 68.0% (inner), 95.0% (central), and 99.7% (outer) C.L. bands of f as a function of f meas from likelihoodfits to MC events. The thin yellow line indicates the most probable value of f as a function of f meas , and thereforerepresents the calibration of the method. The vertical dashed black line indicates the measured value f meas = 0 . observe. Indeed, the matrix-element technology is perhaps the most powerful, and most complex, analysis toolthat is currently available for Tevatron data analyses, and it was required here to have the hope of observingthe effects of interest. Two analyses of t ¯ t dilepton events at D0 have been performed. One was a template-basedanalysis using full reconstruction of top decays, giving a result within two standard deviations of the NLO QCDprediction, but also compatible with the no-correlation hypothesis. The other one was a matrix-element-basedanalysis that gives a result consistent with the SM hypothesis, and powerful enough to exclude the no-correlationhypothesis for the first time ever. Both analyses are statistics limited, with only about half of the final D0 Run IIdata sample analyzed so far. Thus, there is great potential for improving the precision of the measurements inthe near future. Acknowledgments
I thank the D0 “spinners” (Alexander Grohsjean, Tim Head, Yvonne Peters and Christian Schwanenberger)for their advice while I was preparing this presentation, and the D0 Collaboration for giving me the opportunity roceedings of the DPF-2011 Conference, Providence, RI, August 8-13, 2011 Table III: Summary of uncertainties on f meas .Source +SD − SDMuon identification 0.01 -0.01Electron identification and smearing 0.02 -0.02PDF 0.06 -0.05 m t to present these interesting results. I also thank the organizers of the DPF 2011 conference for an engaging andenjoyable week. References
B539 , 235 (2002).2 Figure lifted from Greg Mahlon’s presentation at the 3rd International Workshop on Top-Quark Physics,Brussels, Belgium, June 2010. See also M. Jezabek and J.H. Kuhn, Phys. Lett.
B329 , 317 (1994) and Refer-ence 1.3 V.M. Abazov et al. (D0 Collaboration), Phys. Lett.
B702 , 16 (2011).4 B. Abbott et al. (D0 Collaboration), Phys. Rev. Lett , 256 (2000).5 G. Feldman and R. Cousins, Phys. Rev. D57 , 3873 (1998).6 S. Frixione and B.R. Webber, J. High Energy Phys. , 29, (2002).7 V.M. Abazov et al. (D0 Collaboration), Phys. Rev. Lett.107