Physics Highlights from the DØ Experiment (1992--1999)
Fermi National Accelerator Laboratory, Batavia, Illinois, U.S.A.

3. PHYSICS OF THE TOP QUARK

The four lightest quarks (called "up", "down", "strange", and "charm") have been known to us for over 25 years; they come in pairs, with members of each doublet having internal "weak isospin" quantum numbers of ±1/2. In 1977, the "bottom" (or " b") quark was discovered, and found to have weak isospin of -1/2, thus requiring a partner called the "top" quark. Prior to the start of Run 1, the lower limit on the mass of the top quark had been pushed up to about 90 GeV by experiments at CERN and early data from CDF. Physicists had already begun to puzzle over what the large mass difference between the b quark (at about 5 GeV) and the top quark implied, suggesting the possibility of a special role for the top quark in the scheme of particle phenomena.

From the beginning, the search for the top quark was a very high priority at DØ. The Standard Model was explicit in predicting top-production and decay characteristics. Specifically, the production rate for top-antitop pairs could be calculated reliably from on QCD theory, once the top-quark mass was specified. Similarly, the decays of a top (or antitop) quark could be predicted because the top was expected to decay nearly all the time to a W boson and a b quark, giving rise to a final state with two Ws and two b-quark jets. The decays of W bosons (either into charged leptons and their neutrinos or into quark-antiquark pairs) were already well established. Thus the basic classes of final states arising from top and antitop production were the following: (a) six quark jets (four from the Ws and two from b quarks); (b) a lepton and neutrino, accompanied by four quark jets (two from one W and two b jets); or (c) two leptons and neutrinos and two b quark jets (see the diagram in Fig. 5). Other final-state particles were expected from the interactions of the rest of the quarks and gluons in the colliding proton and antiproton, and also from the radiation of gluons from the interacting quarks. Neutrinos could be sensed only through the missing transverse momentum in the detector. Tau leptons are difficult to identify, and consequently the electron and muon channels turned out to be the preferred channels for studying leptonic final states.

The experimental challenges differ for the three classes of events: the six jet class, with no leptons, is the most likely, but suffers from huge backgrounds due to ordinary strong production of jets; the two-lepton class has relatively little background but a small rate. The single lepton class is intermediate in both rate and background. The measurement of jet energies and directions is crucial to the determination of the mass of the top quark; this measurement is complicated by the spatial spreading of particles in the jet, and by the possibility of gluon radiation. It was generally believed that a measurement of the mass could not be performed to better than 10% accuracy, both because of the jet problems and the presence of missing transverse momentum carried by the invisible neutrinos.

Fig. 5: A schematic of top-quark pair production, where both Ws decay leptonically

The first portion of Run 1 (Run 1a) was completed in mid-1993 and yielded an accumulated collider luminosity corresponding to 14 events per 1 pb of production cross section (usually referred to as 14 pb^-1). From these data, DØ published its first search for the top quark in early 1994, using the single lepton, electron (e) and muon (m) channels, and the ee and em channels. The selection criteria were set to optimize the discovery of a top quark with a mass of about 100 GeV. Three events were found: one em candidate, one ee candidate and one single-electron candidate, all with accompanying jets. The expected backgrounds were comparable to the number of observed events. Hence, a lower limit of 131 GeV at the 95% confidence level was set on mass of the top quark, based upon the SM calculations for the expected yield as a function of mass. This was the highest mass limit at the time (and, as it turned out, the last lower limit reported on the mass of the top quark!). There was a spectacular event ("Event 417") in this sample, containing an electron, a muon, and missing transverse momentum, all above 100 GeV, together with two well-identified jets and a small third jet. The probability for background processes to produce this event was extremely small. Our publication reported an analysis of the mass, based on the assumption that this event was a top-antitop production, stating that: "The likelihood distribution is maximized for a top mass of about 145 GeV, but masses as high as 200 GeV cannot be excluded." This event, shown in Fig. 4, survived subsequent signal-selection criteria that were even more restrictive and ended up in our final Run 1 top-quark sample.

With this mass limit in place, and in anticipation of much larger data samples from Run 1b later in 1994, DØ optimized the search for top at higher masses, and developed powerful techniques for determining its mass. Several useful variables were developed to aid in separating signal events from background. One was the "aplanarity" variable that measured the isotropy of energy flow. Top quark pairs are expected to be produced nearly at rest in the center of mass frame and to spray their decay products uniformly in all directions, in contrast to the more back-to-back topology of multi-jet background processes. Another variable was the scalar sum of the transverse momenta of jets and lepton in the event. This variable, resembling a measure of event temperature, distinguished the energetic decay fragments of massive top quarks from typically lower energy background from jet production. Refined methods for estimating background rates were established using the observed rates of background samples, and which decreased exponentially as the number of jets in the sample increased. Simultaneously, methods were developed for determining the mass of the top signal. Using data for background events and Monte Carlo simulation of the top-antitop signal events with a given assumed top mass, templates were made for the expected distributions of reconstructed top masses. The template with which the data agreed best gave the best estimator of true top quark mass.

In late spring of 1994, the CDF experiment submitted for publication a publication showing evidence that the top quark may exist, with a mass near 175 GeV. The CDF excess of events corresponded to a cross section of more than a factor of two above the expected (and currently accepted) value. Although suggestive, these data were insufficient to claim discovery. At the same time, DØ presented its updated results at conferences. New features of the DØ analyses included the use of additional variables and channels in which the b quark was tagged through its decay to a muon (and its accompanying neutrino and other particles). The techniques were now tuned to optimize the discovery of top in the mass range above 160 GeV. The sensitivities of both the CDF and DØ experiments to possible top signal were very similar, but the DØ sample contained only a modest excess over background estimates (7 events with an expected background of 3.2 events), and the top-antitop production rate inferred was consistent with that predicted (and now confirmed) by the Standard Model.

At the beginning of 1995, data samples had increased by a factor of nearly three. On February 24, 1995, DØ and CDF simultaneously submitted papers announcing the discovery of the top quark. The DØ sample had 17 events with an expected background of 3.8, and the odds for the background to fluctuate to the observed sample were only 2 in 1 million. For this sample, the mass of the top quark was estimated to be between 167 and 231 GeV. The cross section was measured to be 6.3 ± 2.2 pb for a mass of about 200 GeV. The CDF results were consistent with those from DØ, favoring a somewhat larger cross section and a lower mass. The discovery of the top quark completed the roster of SM particles comprising matter, and underscored the special nature of the top quark -- an elementary particle as heavy as a gold atom, and with a mass commensurate with the energy scale of electroweak symmetry breaking. These CDF and DØ papers on the discovery of the top quark have now become the second most cited result in experimental high energy physics (after the papers on the J/y discovery).

By the end of Run 1 in early 1996, DØ had recorded about 125 pb^-1 of data. From the full data set, several more improvements were made in understanding the top quark. Searches for anomalous behavior in top production were sought, but none found. Searches for new particles in top decay, such as charged Higgs bosons, came up empty-handed. But several important advances were made in the measurement of the top-antitop production cross section and the mass of the top quark. A comprehensive new study of top production was carried out in the single and two-lepton classes using carefully optimized selection criteria to minimize the uncertainty on the cross section. A sophisticated analysis of the cross section was completed in the six-jet channel, making extensive use of neural networks that were sensitive to the differences between signal and background. The backgrounds were determined from data, without recourse to Monte Carlo simulations. The combination of all analyses of the top-antitop cross section yielded 5.9 ± 1.6 pb, for a top mass of 172 GeV, in excellent agreement with the theoretical prediction from QCD.

Fig. 6: The mass reconstructed for the top-candidate events with one lepton, four jets and missing transverse momentum (yellow histogram). The triangular symbols represent the expected backgrounds, whereas the red circles represent the sum of signal and background for the best fitted value of the top mass. The inset shows the quality of the fit as a function of top mass, with the best value of 173 GeV being at the minimum.

The mass analysis was improved in several ways. For the single-lepton channels, neural networks and a likelihood discriminant were developed to distinguish signal and background without biasing the mass distribution. The final data sample is shown in Fig. 6, where the separate contributions for expected background and total (signal and background) are compared with the observed mass distribution. From this channel alone, the mass was found to be 173.3 ± 7.8 GeV.

Powerful new methods were also devised to estimate the mass for the dilepton samples, where the presence of two neutrinos precluded the direct calculation of a mass. These new techniques were pioneered in DØ at the beginning of 1993, following the excitement over the observation of "Event 417". Probabilities for dilepton events to originate from top production were calculated as a function of the assumed top mass, and a maximum likelihood fit was then used to extract the best value. Taken together with the single lepton channels, the final top mass from DØ analyses is 172.0 ± 7.1 GeV (an uncertainty of about 4%), far exceeding the initial expectation for precision, and making the top mass the most precisely known of all quark masses. Combining all mass measurements from both CDF and DØ, yields a mass of 174.3 ± 5.1 GeV (< 3% uncertainty) for the top quark.

The discovery of the top quark was a major achievement and the highlight of the DØ program in Run 1. Its very large mass suggests that it may well play a special role in the breaking of the electroweak symmetry, and could be partially responsible for the mechanism by which all particles acquire mass. It provides a probe for seeking new forces in which top and antitop quarks combine (annihilate) to make new particles, and a vehicle for the search for new massive particles in its decays. These are the themes that will dominate top-quark studies in the forthcoming Run 2, where at least forty times more top events are expected in a substantially improved detector with greater capability for deciphering these complex signals.

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