# Properties of the top quark

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## Introduction

The top quark is the most massive known fundamental particle to date (PDG). It is an up-type quark (charge +2/3e) in the 3rd family of elementary particles. Its mass is 173 GeV/c2. The top quark – together with its antiparticle, the antitop quark – has been discovered in 1995 by the CDF and D0 experiments at the proton-antiproton collider Tevatron in Fermiab near Chicago. With its high mass, the top quark is particularly interesting for searches for physics beyond the Standard Model – be it through precision measurements of its properties, or being a decay product from a more massive state. These are the topics at the ongoing physics programme at the Large Hadron Collider(LHC) at CERN.

## Predicting the Top Quark

The top quark's existence was predicted indirectly by Makoto Kobayashi and Toshihide Maskawa in 1973, 22 years before its experimental observation. After the discovery of CP violation in the Kaon system in 1964, the existence of a third generation of quarks was postulated in order to allow for a CP-violating phase in the quark sector. The observation of the bottom quark in 1977 at Fermilab gave strong support for the existence of a sixth quark. With the discovery of the carriers of Weak Interactions W and Z at CERN in 1984, the new theory of particles and interactions, the Standard Model (SM), became established and the existence of the top quark unquestioned. This theory relates a variety of physical properties of particles and forces, including their mass, through its mathematical framework. Basing on this theory, it became clear that the top quark had to be extremely massive. This explains that the search for it at the most powerful particle accelerators in the Eighties - DESY, KEK and at CERN - remained unsuccessful.

In 1989, two new powerful particle accelerators, the Large Electron Positron Collider LEP at CERN and the Tevatron proton antiproton collider at Fermilab came into operation. With the accumulation of electroweak precision data in particular from LEP, a prediction of the top quark mass with an increasing accuracy was possible (Figure 1). At the same time, the sensitivity for the observation of the top quark by the experiments CDF and D0 increased with the amount of data taken over the years of collider operation.

## Towards finding the Top Quark

“Finding” a massive particle means it has to be produced on-shell with an accelerator and identified – usually through its decay products – with a suited detector. Since production stems from conversion of energy into a particle and an antiparticle, for a ttbar system about 350 GeV of energy will be needed at minimum. In 1992 only the Tevatron was sufficiently powerful for this: 900 GeV protons were smashed head-on against 900 GeV antiprotons which were produced beforehand in proton-tungsten interactions and stored. The available energy in the system of the colliding fundamental partons amounts to typically 1/6 of the total energy of the proton and antiproton, which is just sufficient to produce ttbar pairs. The main production mechanisms of the top quark at hadron colliders are via the strong interaction as top-antitop quark (ttbar) pair production (Figure 2), and via electroweak processes for single top quark production (Figure 3). The top quark will decay almost instantaneously to a W boson and a down-type quark "x" with the probabilities given by the CKM matrix elements |Vtx|2. The main decay happens into a W boson and a b quark with a probability of 99.9%. The final states of the decay, which are used to study the top quark, are usually classified according to the W decay modes. Due to its high mass and electroweak coupling, the top quark has some special properties. In particular, its decay time of 5 10-25s is about 20 times shorter than the time for hadronization, making the top quark the only known quark not to form bound states. Furthermore, the top quark's decay time is shorter than the time for spin-decorrelation, thus enabling the access of the top quark's spin information via its decay products.

The Tevatron is a proton-antiproton collider, while the LHC is a proton-proton collider (see box below). Due to the different initial hadrons and the different collision energy, the main production mechanisms contributing to ttbar or single top quark production differ at Tevatron and LHC. While at the Tevatron ttbar production happens via valence quark-antiquark annihilation (at about 85%), at the LHC the main production of ttbar events happens via gluon-gluon fusion (at about 90% at 13 TeV centre-of-mass energies). This difference arises from the distribution of probabilities finding a pair of partons within the colliding hadrons with sufficient momentum fraction to generate the required center of mass energy of 350 GeV or more. In contrast to the pair production through strong interaction (QCD processes), the single top production (see Figure 3) proceeds through electroweak processes. Their cross sections are not so much smaller than the ones of the QCD process as one would expect, simply because the sub system has about half the mass as in the case of pair production. Tables Table 1 and Table 2 give an overview of the calculated production cross section for top-antitop pair production and single top production, respectively.

Table 1: Predicted cross sections for top pair production at the Fermilab collider and at the LHC at various collision energies. The predictions base on next-to-next-to leading order calculations (NNLO).
Top-antitop production cross sections
Collider Cross section (pb)
Tevatron (1.96 TeV) $$7.2^{+0.1+0.2}_{-0.2-0.1}$$
LHC (7 TeV) $$177^{+5}_{-6}\pm 9$$
LHC (8 TeV) $$253^{+6}_{-9}\pm 12$$
LHC (13 TeV) $$832^{+20}_{-29}$$

Table 2: Predicted cross sections for single top at the Fermilab collider and at the LHC at various collision energies. The predictions base on next-to-next-to leading order calculations (NNLO).
Single top production cross section
Collider Cross section t-channel (pb) Cross section Wt-channel (pb) Cross section s-channel (pb)
Tevatron (1.96 TeV) $$2.06\pm 0.13$$ $$0.22$$ $$1.03 \pm 0.05$$
LHC (7 TeV) $$64^{+0.8}_{-0.4}$$ $$15.5 \pm 1.2$$ $$4.5 \pm 0.2$$
LHC (8 TeV) $$84.6^{+1.0}_{-0.5}$$ $$22.1 \pm 1.5$$ $$5.5 \pm 0.2$$
LHC (13 TeV) $$215^{+2.1}_{-1.3}$$ $$71.7 \pm 1.8 \pm 3.4$$ $$10.3^{+0.6}_{-0.5}$$

The Tevatron was a proton-antiproton collider at Fermilab, close to Chicago, US. Two multi-purpose experiments, CDF and D0, were located at different interaction points of the Tevatron. The Tevatron was commissioned in 1984, with first collisions in 1985 recoded by CDF. The D0 experiment was constructed later, seeing its first collisions in 1992. Tevatron's Run I with a collision energy of 1.8 TeV lasted from 1992 to 1996, during which time about 20 pb-1 of data were recorded by CDF and D0. During this time, the top quark was discovered. After an upgrade of the detectors and the accelerator system, Tevatron had its second data-taking period (run 2) with a collision energy of 1.96 TeV from 2001 until September 30th, 2011. During run 2 about 10 fb-1 of data were recoded per experiment, enabling an extensive top quark physics programme, which allowed for deep insights into the Standard Model and in particular a prediction of the mass of the Higgs boson. The Large Hadron Collider(LHC) on the other hand was discussed as early as 1984 as the ultimate discovery machine, to be installed in the LEP tunnel. Following a design phase starting in 1988, machine and the four experiments ALICE, ATLAS, CMS and LHCb were commissioned in 2009. The following proton-proton collision runs 1 and 2 were carried out at centre-of-mass energies of 5,7, 8 and 13 TeV – ending at the end of 2018. A highlight of the LHC was the Higgs boson discovery in 2012.

## Discovery

The cross section of a ttbar pair at the Tevatron lies in the range of 6 pb at 1.8 TeV CM energy. This is in contrast to the huge inelastic collision cross section of about 55 mb (diffractive processes included) and also to the large cross section of background processes which resemble a ttbar pair. To separate a ttbar system from background, specific decay channels are selected. Figure 4 gives an overlook for all decay modes in a ttbar system. The cleanest discovery channels were the modes where both W bosons decayed into leptons (dilepton channel) or where one of the bosons decayed into a pair of light quarks which fragment (lepton+jets channel). In case of the latter, in addition at least one of the four jets in the system needs to be identified as a jet from fragmentation of a bottom quark. The large detectors CDF and D0 were constructed in a way that their particle-identification capabilities allowed to select such channels. Figure 5: Reconstructed invariant mass distribution of top quarks as they were discovered by CDF. The solid line represents the measurement, the dotted the simulated signal. The dashed histogram shows the distribution of background events.

It took until 1994 for the first evidence of a top quark signal at CDF and until 1995 for the announcement of the official discovery by the CDF and D0 experiments ( Reference Abe, Abachi, et al.). The discovery of the top quark happened with only few dozens of events found in each experiment (see Figure 5), using about 67pb-1 of data by CDF and 50 pb-1 of data by D0. CDF and D0 had pursued different strategies for their search for the top quark. While CDF used an approach of b-tagging (b-tagging allows to identify jets from the hadronization of a b quark), D0 used topological variables in the jet plus lepton channels. The cross section was measured to be 6.8+3.8-2.4pb by CDF and 6.4±2.2pb by D0. The mass was measured to be 176±13GeV and 199±30GeV resp. by CDF and D0 in these first analyses of the top quark. It took until 2009 when single top quark production through weak processes were discovered by CDF and D0. Because the single top quark process has a smaller production cross section than ttbar production, and given that the signature of single top production is quite similar to its main background, only with a much larger data set and with highly dedicated analyses techniques single top production could be discovered. It was the first time in particle physics that multivariate analyses techniques like boosted decision trees and neural networks came into use.

After its discovery, the top quark became the centre of attention for many precision measurements and searches for new physics. The wealth of studies in the top sector focused on its production properties and its decay modes. In the Standard Model, the production of top quarks can happen via strong and electroweak interactions, with the top quark’s decay proceeding via the electroweak force. Measuring precisely the various properties of the top and comparing those to the Standard Model predictions can reveal new physics. For example, the pair of top quark could be produced by a massive exotic object (like a neutral vector boson Z’). This would be manifest in larger cross sections than predicted, or in resonant-like structures in top-pair invariant mass distributions. It could also affect other kinematic distributions, which then would look different in data compared to the Standard Model predictions.

In the following an overview of measurements in the top sector is given, together with some motivation on why they are interesting. It’s by no means a complete list, in particular since the ongoing LHC experiments come up with new measurements all the time – scrutinizing the top sector ever further in the hunt for physics beyond the Standard Model.

## Production properties of the top quark

By comparing the measurement with the theoretical calculation at a given mass, the Standard Model can be probed for deviations. Figure 6 shows the most recent measurements for the cross section of ttbar production at difference CM energies, while Figure 7 shows a similar graph for single top quark production. So far the inclusive cross sections agree very well with the predictions and leave little room for large deviations. For experimentalists this mandates the look into small effects and deviations.

### Top forward-backward asymmetry

When calculating the ttbar cross sections at leading order QCD, one would expect that the emission of the top quark and antitop quark is symmetric in the direction forward and backward of the incoming quarks and antiquarks from the beams. However, when using a next-to-leading order (NLO) description, interference between different processes causes a preferred emission of the top quark in the direction of the incoming quark, and of the antitop quark in direction of the incoming antiquark. Figure 8 shows example diagrams contributing to the interference effects and, hence the asymmetry. This asymmetry is expected to be in the percentage range but can be enhanced from various new physics effects, for example through the additional production of ttbar pairs by massive bosons (Z’) with large chiral couplings to fermions. Figure 9: The different approaches for the measurement of the forward-backward asymmetry at Tevatron and LHC. The letter eta denotes pseudorapidity, which is a measure for the angle of the particle’s flight direction relative to the proton beam direction.

At Tevatron, the direction of the incoming proton or the incoming antiproton can be used directly as a proxy for the direction of the incoming quark or incoming antiquark. Thus, the measurement at Tevatron can simply probe the difference in rapidity of the top and antitop quark to extract the forward-backward asymmetry (see Figure 9). At the LHC, asymmetries should also play a role and reflect the findings of the Tevatron. Two features, however, complicate the analysis. The first complication comes from the fact that at the LHC the main production mechanism of ttbar events is via gluon fusion. In gluon fusion, the described interference effect does not occur, washing out any measurable asymmetry from the small contribution of quark-antiquark annihilation to the total ttbar production. Furthermore, protons collide with protons, so a priory the initial state is symmetric. Figure 10: Forward-backward production asymmetry of top quarks at the Tevatron as a function of their invairant mass. the results are compatible with the Standard Model but leave room for exotic production modes.

As at the Tevatron, in quark-antiquark annihilation top-quarks tend to prefer slightly the direction of the incoming up-quark, and antitop-quarks of the antiup-quarks. The resulting distributions are symmetric but have a different width because the quarks in the protons have a different distribution function (pdf) than the antiquarks. This results in a wider rapidity distribution of top quarks than of antitop quarks, and the difference in the respective distributions is called “charge asymmetry”.

At first, CDF observed an asymmetry value which was considerably larger than predicted by the SM. A strong increase with the invariant mass of the tt system was found. The D0 experiment made no such observation, however. Careful re-analysis of all data taken at the Tevatron gave results in the end which were compatible with the Standard Model - as shown in Figure 10

Should there exist exotic production modes of top quark pairs in hadron collisions, at the LHC they should be exhibited more clearly. So far, however, all results were compatible with the small SM preditions: at 7 TeV CMS Energy, the result of a combination of ATLAS and CMS measurements is Ac=0.005+.0.007±0.006, compatible with the theoretical prediction of 0.012. At 8 TeV, the measurements gives 0.0055±0.0023±0.0025, compared to the SM prediction of 0.011. These values leave little room for exotic production modes of the top quark pairs.

## The properties of the top particle

The top quark has many intrinsic and decay properties that make it an interesting particle to study. The top quark is the most massive of all known fundamental particles. Its lifetime is so small that top quarks decay before they can hadronise. That gives the opportunity to study a bare quark, which transfers its quantum numbers such as spin information directly to the final state decay products. In the following, a selection of some of the most important property measurements is given – the selection is by no means complete though. This includes a measurement of spin correlations in ttbar events, which probe the full production and decay of ttbar events for new physics. Furthermore, top polarization in single top events can be extracted and compared to Standard Model predictions. The top quark charge is predicted to be +2/3 in the SM and can be measured either by extracting information about the jet charges and the lepton charge from the final state objects, or from the cross section of events with photons radiated off the top quark. In the Standard Model, the top quark decays via the weak interaction into a W boson and a down-type quark. Experimentally, the |V_tb| matrix element can be measured, as well as its branching fractions and the helicity of the W boson. Another interesting field of study is the coupling of the top quark to the Higgs boson – the so-called Yukawa coupling which is postulated in the Standard Model.

### The top quark mass Figure 11: Example of a template method used for the top quark mass extraction ( Reference ATLASMass). Here, different assumptions of top quark mass are used in the simulation (as indicated by the different lines), and the reconstruction method is applied in the same way on each of those simulated samples. The difference in shape for each assumption will yield different compatibility with the data and thus allow the extraction of the top quark mass in the data.

The top quark mass is a free parameter in the Standard Model. The first prediction of the top quark mass was extracted using indirect measurements and relying on Standard Model calculations . For instance the W boson mass depends on the top quark mass through electroweak processes at the quantum level. The evolution of these predictions with direct measurements over the years is shown in Figure 1. The direct measurement is carried out by a fit to the kinematics of the decay products.. Many complex methods have been developed to extract the top quark mass to astonishing precision, yielding the highest relative accuracy amongst all quarks. In particular there are various template methods, matrix element methods and hybrid-techniques applied to the mass determination.

The idea of the template method for instance is to extract an observable, as for example the reconstructed top quark mass, using the final state objects, which is sensitive to the mass parameter. By fitting templates with different mass assumptions to the data, the top quark mass can thus be extracted from the best fit. Figure 11 shows an example of how the template method works by analysing ATLAS data. The matrix element method ( Reference MEM) is more complex, but has the advantage to use the most possible kinematic information of each event. The idea here is to calculate matrix elements of the top process, integrating out unknown quantities using multi-dimensional numerical integration. The extraction of the top quark mass then happens via a fitting procedure that takes into account the weights extracted from the calculated matrix elements.

### What makes the top mass measurement so interesting?

• Figure 12: Direct measurements of the top quark and W boson mass compared to the Higgs Boson mass on the one hand and to a SM fit to all parameters except for these measured masses on the other hand ( Reference GFIT).

Over the years, the measurements of the top quark mass reached a high precision with an uncertainty at the sub-percent-level; the world average amounts to 173.34 ±0.27±0.71 GeV/$$c^2$$. At present, this precision is already limited by systematic uncertainties, but within the coming years an overall uncertainty of about 0.15 GeV/$$c^2$$ should be in reach. Within the framework of the Standard Model, different parameters are linked together. In this way, for instance the mass of the top quark together with the mass of the W boson are linked to the mass of the Higgs boson. Any deviation from this connection would indicate new physics. Our present knowledge is quite compatible, as can be seen in Figure 12 from the overlap of the green and the blue ellipse.

### Top quark charge

In the SM, the charge of the top quark is +2/3 of the electron charge. An exotic model about the top quark with a negative 4/3 could also be possible though. To measure the top quark charge, it is necessary to determine the charge of its decay products. Since all of the quarks from top decay hadronize, it is necessary to find a way of extracting the charge of jets. Most measurement use top quarks that decay into a charged lepton, a neutrino and a b-quark. The charge of the lepton can be extracted easily using the curvature of its track in the magnetic fields of the detectors. The charge of the jet from the b quark is harder to extract, requiring techniques like weighted track-sums of the jet components. As a result, these types of measurements excluded the exotic model with charge of -4/3. Another method to gain information on the top quark charge is via events with a photon from the top quark decay. The rate at which photons (chosen to be of high energy) are radiated off a top quark is directly proportional to the square of its charge. First candidate events were found in the existing data, but higher statistics will be needed to make an accurate measurement.

### W helicity in top quark decays Figure 13: W helicity states of the top quark decays. The red arrows indicate the spin direction, while the yellow and blue arrows indicate the direction of the momenta of the respective particles. The top quark is taken to be at rest (not moving).

The decay of the top quark allows us to learn more about the coupling between the W boson, top quark and b quark. The W boson only couples to left-handed particles (so-called V-A structure – see (CHIRAL)). It is therefore expected that the decay products of the W boson from top decay arrange such that the chiral structure of the coupling vertex is fulfilled (see Figure 13). In the SM about 30% of the events have a negative W boson helicity, 70% longitudinal helicity, and just a negligible amount a positive helicity of the W boson. Measurements at Tevatron and LHC have confirmed the SM to high precision. This sets stringent constraints on new physics models that require a change in the coupling structure of the top quark decay. Figure 14: Angular distributions from the decay leptons of W bosons in top quark decays at three individual helicities, compared to the standard model mixture.

The helicity fractions are extracted from fits to angular distributions of the decay leptons of the respective W bosons (see Figure 14). As an example, below are shown the results from 8 TeV data taken by CMS: F0=0.681±0.012 (stat)±0.023 (syst), FL=0.323±0.008 (stat)±0.014 (syst), FR=−0.004±0.005 (stat)±0.014 (syst)

### Top quark polarization and spin correlation

The top quark is a fermion with a half-integer spin (1/2). Due to its short lifetime, the spin information of the top quark is directly transferred to its decay products, thus enabling the measurement of the top quark's polarization. In hadron collisions, top quark pairs are produced unpolarized (in QCD processes). However, the correlation between the spins of the top and the antitop quarks is an interesting quantity to measure, as it is predicted to be non-zero. Figure 15: Spin configurations of the top quark pair. The red arrows indicate the spin of the respective particles, while the green and black arrows are indicating the momenta of the top quarks and the particles from the beam (quarks or gluons).

Example configurations are shown in Figure 15. The measurement of the ttbar spin correlation is a probe of new physics from production to decay, as any new physics contribution within the ttbar production can change the correlation of the top and antitop quark spin. For example, if the top quark would decay into a scalar (spin-zero) charged Higgs boson, the structure of the top decay would change from V-A to V+A. This would change the way the spin information from the top quark is transferred to its decay products and therefore result in a different spin correlation coefficient than in case of a Standard Model top quark decay.

The way to measure spin correlations or top polarizations is to measure angular distributions. These in general take one of the final state particles from the top decay and use the angle relative to a spin quantization axis, boosted into the top quark rest frame. The challenge of such measurements is that the ttbar event needs to be fully reconstructed, which is inaccurate. Another, simpler variable can be used to extract information on spin correlations, namely in dileptonic events where the difference in azimuthal angles between the two charged leptons from the W can be used. This allowed observation of spin correlations in ttbar already at the early LHC runs. Figure 16: Measurement of the azimuthal angle between electrons and muons at the ATLAS expeeriment, showing sensitivity to spin correlations of top-antitop quark pairs.

In Figure 16, a new result of top quark spin correlations from ATLAS ( Reference Atlasspin) is shown. The figure shows the measurement of the azimuthal angle between the electron and the muon, divided by pi to normalise the axis. The label “parton” level means that the measurement is corrected for detector and resolution effects, making it directly comparable to theory predictions. The y-axis shows the differential distribution as function of the measured angle. All distributions are normalised. In the fugure, the measured values are shown in black dots, and are compared to two theory predictions: one with spin correlations as predicted by the Standard Model, and the other assuming no spin correlations. The green dashed line represents the fitted result. This result is quite interesting: it shows that the fitted spin correlations are larger than expected by the Standard Model calculations. The same is seen in other measurements by ATLAS, and by CMS. Currently, studies are ongoing to understand why the messured values are larger than expected. One way to try to understand this, is to calculate theory predictions in higher orders of perturbative calculations. Only once Standard Model effects can be excluded, one can gain certainty of whether an effect comes from new physics or not.

### Top quark couplings

The top quark couples to all known bosons: the W and Z bosons, the photon, the gluon and the Higgs boson. These coupling strengths are well predicted by the Standard Model. Thus, measuring processes of associated production of top quarks and a boson (for example ttbar+boson) provide an important test of the Standard Model. With the large available data samples at the LHC at hand, all mentioned processes have been observed, albeit with large uncertainties so far. The most important result is the direct observation of the ttbar+Higgs process in 2018 by ATLAS and CMS. This is particularly interesting, as it allows to probe the Yukawa sector of the mass generation through the Higgs mechanism. Off course, there has been an indirect determination of the Higgs Youkawa coupling to the top quark since the discovery of the Higgs boson through the measurement of the production cross section, since the production procedes largely via a virtual top loop in the collision. But this bases on model assumptions (for instance the result relies on the absence of BSM objects in the loop. Hence, the rate of Higgs radiation off a top quark is the only direct way to measure the coupling. Our very first measurements are in rough agreement with the SM within 50% or so, so for a more detailed value an overall combination of all results from ATLAS and CMS form the past runs will be needed.

## Concluding remarks

This article only covers some of the interesting properties the top quark has and gives a status of our present knowledge. Top physics is an active area of research, with new results becoming available every year. Thanks to the great performance of the LHC, the data samples containing top quarks still increase, enabling an ever-deeper look into the heaviest elementary particle we know. The large amount of data also allows for a shift in the main measurements that are done: while in the beginning more emphasis was set on inclusive cross-section measurements, or extraction of a given parameter, the trend now goes more towards extracting full spectra of kinematic distributions, so-called differential measurements. These can be used to search for new physics in a more model-independent way and thus challenge the Standard Model as best as we can. Currently, plans are being discussed for future colliders beyond the LHC. The discussions include lepton colliders, as for example electron-positron colliders. Lepton colliders provide the benefit of a clear initial state, with known collision energy of the initial partons, (basically) no underlying event and low pile-up. This yields a variety of precision measurements possible in many different areas, including in the top sector. For example, a threshold scan could provide a precision measurement of the top quark mass beyond what is possible with the LHC. Furthermore, the top-Higgs Yukawa coupling could be measured to a precision not reachable with current hadron colliders. The next years will show if any of those future colliders will be planned officially to pursue this goal.
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