# 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.

Figure 1: Prediction and measurement of the mass of the top quark as a function of time (<ref name=Quigg> C. Quigg, Ann. Rev. Nucl. Part. Sci. 59 (2009) 505 </ref>)

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.

Figure 2: Schematics of ttbar production in hadron-hadron collisions through quark-antiquark annihilation (a) and through gluon fusion (b).

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.

Figure 3: Schematics of single top production in hadron-hadron collisions. Three different processes are relevant: s-channel, t-channel and Wt-channel production. As an example, the cross-section values are noted for 7 TeV centre-of-mass energies.

Figure 4: Predicted cross sections for single top and 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).

== Hadron Collider
== 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

Figure 5: Branching fractions of ttbar decay modes.

The cross section of a ttbar pair at the Tevatron lies in the range of 6 pb. This is in contrast to the huge inelastic collision cross section of about 55 mb (where diffractive processes are included) and more specifically the cross section of more serious 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 boson decayed into a pair of light quarks (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 6: 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 (Abe, Abachi). The discovery of the top quark happened with only few dozens of events found in each experiment (see Fig 5), using about 67pb-1 of data by CDF and 50 pb-1 of data by D0. CDF and D0 had different strategies for their search for the top quark. While CDF used an approach of b-tagging (b-tagging allows to identify jets coming from the hadronization of a b quark), D0 used topological variables in the jet plus lepton channels. The cross section was measured to be 6.4+-2.2pb by D0 and 6.8+3.8-2.4pb by CDF. The mass was measured to be 199+-30GeV by D0 and 176+-13GeV by CDF in these first analyses of the top quark. It took until 2009 until top quarks in single top processes were discovered by CDF and D0. Due to the single top quark process having a smaller production cross section compared to ttbar production and given that the signature of single top events is quite similar to its main background, a larger amount of data as well as highly dedicated analyses techniques were required to observe single top production. In particular, the observation of single top quarks was the first observation in particle physics that made use of multivariate analyses techniques like boosted decision trees and neural networks.

After the top quark’s discovery, it 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 the QCD 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. A few measurements performed at the Tevatron and at the LHC are highlighted in the following.

## Production properties of the top quark

When a new process is just being tested at an experiment, the first measurement to carry out is usually the inclusive cross section of that process. 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 different processes from all colliders for ttbar production, while Figure 7 shows a similar graph for single top quark production. So far the inclusive cross sections agree very well with the predictions. This already gives some indication for the possible new physics in the top sector: it cannot be any model that changes the overall top cross section massively. For experimentalists this means to start then looking into more subtle effects and more detailed properties.

Figure 7: ttbar production cross sections at the Tevatron and LHC, status 2018. The two theoretical lines indicate the difference in production mechanisms in ppbar and pp collisions.

Figure 8: Single Top production cross sections measured at the Tevatron and LHC.

### Top forward-backward asymmetry

When calculating the ttbar cross sections at leading order QCD, it is expected that the production of the top quark and antitop quark are symmetric in the direction forward and backward of the incoming quarks and antiquarks from the proton beams. However, when using a next-to-leading order (NLO) description, interference between different diagrams causes a preferred emission of the top quarks in the direction of the incoming quark. Figure 8 shows example diagrams that interfere with each other and cause the asymmetry. This effect can be enhanced from various new physics effects, for example in models giving a preference to a top pair production happening via a new particle that has different coupling strength to particles with different chiralities (CHIRAL).

Figure 9: Quark-antiquark annihilation into a pair of top quarks at NLO.

When the measurement of the forward-backward asymmetry was carried out at the Tevatron experiments, some deviation from the standard model was found. LHC experiments tried to look then for the effect with their larger amount of data, but have not seen any deviation so far. The main challenge with this measurement at the LHC is that it cannot be carried out the same way as at the Tevatron – making the results from the two colliders somewhat complementary. 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.

Figure 10: 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 the LHC, two features complicate the analysis. The first complication comes from the fact that at LHC the main production mechanism of ttbar events is via gluon fusion. In gluon fusion, the described interference effect does not occur, washing out the measurable asymmetry from the tiny contribution of quark-antiquark annihilation to the total ttbar production. Furthermore, protons are collided with protons.

Extracting the information of where the incoming quark or antiquark direction is coming from is not straightforward anymore, requiring the measurement of another quantity, called charge asymmetry. Here, difference in absolute values of top and antitop pseudorapidity is measured, which is sensitive to the same effect. Over the next years, LHC will collect ever more data, with ever improving analysis methods. The forward-backward asymmetry at the Tevatron being measured with some deviation from the standard model will stay an open riddle to be still tackled.

## 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 decay width is very small, resulting in top quarks to decay before they can hadronise. That gives the opportunity to study a bare quark, which transfers its quantum numbers, like its spin information, 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, the non-vanishing 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 connection of the top quark and the Higgs boson. A brief outline will be given on it, as it is a new, upcoming field to test the standard model.

### The top quark mass

The top quark mass is a free parameter in the standard model. The first prediction of the top quark mass was extracted using other quantities, like the W boson mass. 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. Many complex methods have been developed to extract the top quark mass to astonishing precision from Tevatron and LHC data, 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.

Figure 11: Example of a template method used for the top quark mass extraction (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 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 10 shows an example of how the template method works at an ATLAS analysis. The matrix element method (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 mass measurement so interesting?
=== 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/c2. At present, this precision is already limited by systematic uncertainties, but within the coming years an overall uncertainty of about 0.15 GeV/c2 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 11 from the overlap of the green and the blue ellipse.
===


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 (GFIT).

Another, even more interesting aspect lies in considerations of the stability of the vacuum itself – the top quark mass has implications on it and hence on the stability of the universe.

### Top quark charge

In the SM, the charge of the top quark is +2/3 of the electron charge. Given the experimental accessibility of the decay products of the top quark, an exotic model with -4/3 could also be possible though. To measure the top quark charge, it is necessary to access 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. These types of measurements excluded the exotic model with charge of -4/3 already today. 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

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. This can be measured using angular variables. 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 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).

### 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 colliders, top quark pairs are produces unpolarized (in QCD). 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. Example configurations are shown in Figure 13. 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 a scalar boson. This would also change the way the spin information from the top quark is transferred to its decay products and therefore result in a different measured spin correlation 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 reconstructed, which introduces a smearing into the observable. At the LHC, another, simpler variable can be used to extract information on spin correlations, namely in dileptonic events the difference in azimuthal angles between the two leptons can be used. This allowed observation of spin correlations in ttbar already at the early LHC runs.

Figure 14: 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).

### Top quark couplings

The top quark couples to all known bosons: the W and Z bosons, the photon, the gluon and the Higgs boson. Thus, measuring processes of associated production of top quarks and a boson (for example ttbar+boson) is interesting to measure the couplings of those bosons to the top quark and thus probing the coupling of the top quark to different SM processes. With the large available data samples at the LHC, recently great progress on seeing ttbar+boson processes was achieved. In particular, ttbar+Z, ttbar+photon, ttbar+W and ttbar+Higgs all have been observed already. The most recent result is the observation of the ttbar+Higgs process in 2018 by ATLAS and CMS. It is a particularly interesting process, as the top and the Higgs are the heaviest known elementary particles, with the top quark having the largest coupling to the Higgs boson. Due to the top quark mass being the highest fundamental particle mass known today, and due to it being close to the electroweak scale, the top quark is believed to play a special role in the mechanism of electroweak symmetry breaking. The measurement of the top-Higgs Yukawa coupling is therefore one of the main focuses at LHC in the coming years. The top-Higgs Yukawa coupling is predicted to be around 1 in the standard model. Any deviation from 1 would indicate new physics. With the recent observation of the ttbar+Higgs process, in the following years more detailed, more precise measurement in the top-Higgs sector will become available and might hold room for surprises.

## Concluding remarks

This article only covers some of the interesting measurements and properties the top quark has. It is still 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 means a shift in the main measurements that are done: while in early measurements more emphasis was set on inclusive cross-section measurements, or extraction of a given value, the trend 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 come to life and enable ever more precise top physics analyses in the future.

## References

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Note: include link to CMS/LHCb scholarpedia articles