*Review* **Charge Asymmetry in Top Quark Pair Production**

## **Roman Lysák**

FZU—Institute of Physics of the Czech Academy of Sciences, Na Slovance 1999/2, 18221 Prague, Czech Republic; lysak@fzu.cz

Received: 16 June 2020; Accepted: 21 July 2020; Published: 2 August 2020

**Abstract:** The top quark is the heaviest elementary particle known. It has been proposed many times that new physics beyond the current theory of elementary particles may reveal itself in top quark interactions. The charge asymmetry in the pair production of a fermion and its antiparticle has been known for many decades. Early measurements of such asymmetry in top quark pair production showed a disagreement with the prediction by more than 3 standard deviations. Many years of an effort on both experimental and theoretical side have allowed to understand the top quark pair charge asymmetry better and to bring back the agreement between the measurements and the theory. In this article, these efforts are reviewed together with the discussion about a potential future of such measurements.

**Keywords:** top quark; pair production; charge asymmetry; forward–backward asymmetry

## **1. Introduction**

The Standard Model (SM) of particles is a quantum field theory which describes strong and electroweak interactions [1–3]. During the past about 40 years, it has been successfully tested in a large number of experiments which performed numerous measurements. However, the SM has its shortcomings. For example, it has too many free parameters, there is an absence of the explanation for the observed amount of dark matter [4], and the prediction for the matter–antimatter asymmetry is way too low compared to the observation [5]. There have been many theoretical attempts to overcome SM shortcomings. On the other hand, the experimentalists have been trying to find a discrepancy between predictions and measurements. This would serve as a hint for a more complex theory going beyond the Standard Model (BSM) framework.

The top quark is one of the fundamental fermions, spin-half particles, in the SM. It has a large mass (*mt* = 173 ± 0.4 GeV [6]), much larger than a mass of any other quark or lepton (the next heaviest quark, *b* quark is about 40 times lighter). This means the top quark may play a special role in BSM theories or the BSM physics may reveal first in the interactions involving the top quark [7,8]. Another consequence of its large mass is that it has a very short lifetime so it has no time to hadronize. Top quark properties are thus transferred to its decay products. From an experimental point of view, it is important that top quark properties can be studied without a complication from the hadronization, unlike with any other quark.

The top quark has been observed in the experiments at only two accelerators: in proton–antiproton (*pp*¯) collisions at the Tevatron in Fermilab, USA and in proton–proton (*pp*) collisions at the Large Hadron Collider (LHC) at the European Organization for Nuclear Research (CERN), Switzerland. The top quark was observed for the first time in 1995 at the Tevatron in a data taking period called 'Run I' at a center-of-mass energy of interactions of <sup>√</sup>*<sup>s</sup>* <sup>=</sup> 1.8 TeV by CDF and D0 experiments [9,10]. The Run I took place during 1992–1996 and the amount of data collected per experiment corresponded to about 100 pb−<sup>1</sup> of the integrated luminosity. Only a few tens of top–antitop (*t*¯*t*) pair candidate events were collected at both experiments. The second data period (Run II) at the Tevatron happened during 2001–2011 at a bit larger energy of <sup>√</sup>*<sup>s</sup>* <sup>=</sup> 1.96 TeV. Overall, about a hundred times more data (10 fb−1)

were collected by each experiment. This amount of data allowed detailed measurements of top quark properties although a lot of the measurements have been statistically limited. The LHC started its operation in 2008, but after the incident a few days later, the first collisions at <sup>√</sup>*<sup>s</sup>* <sup>=</sup> 7 TeV happened only in 2010. The center-of-mass energy of *pp* collisions (and the luminosity) has gradually risen from <sup>√</sup>*<sup>s</sup>* <sup>=</sup> 7 TeV in 2010 (5 fb−1) to <sup>√</sup>*<sup>s</sup>* <sup>=</sup> 8 TeV in 2011–2012 (20 fb−1) and <sup>√</sup>*<sup>s</sup>* <sup>=</sup> 13 TeV in 2015–2018 (150 fb−1) with the shutdown happening in 2013–2014. The data taking period from 2010–2012 is called "Run 1" while the second data taking period between 2015–2018 is called "Run 2". At present, there is another accelerator shutdown which is planned for years 2019–2021. Given the much higher energy of interactions and much larger luminosity at the LHC compared to the Tevatron, many more top quarks have been produced which allowed for much more detailed measurements of top quark properties.

One of the top quark properties which has been studied is a charge asymmetry in the top quark pair production. This means there is a difference in the angular distribution for top and antitop quarks with respect to a given direction. It is a small effect in the SM [11–32] which could be greatly enhanced by various BSM models [33–39]. The initial measurements at the Tevatron observed larger asymmetries than predicted by the SM at that time [40–44]. A few deviations larger than two standard deviations (SD) were observed by both experiments, with the largest deviation of more than 3 SD observed by the CDF experiment at a large invariant mass of the top quark pair [42].

The unexpectedly large measured charge asymmetries started a huge interest in both theoretical and experimental communities in studying this effect in a much more detail. Theoretical physicists calculated the asymmetry more precisely within the SM [17–22,24–26,28–32] and also tried to explain it with many new BSM models, see Refs. [45,46] and references therein. A few years ago the full next-to-next-leading order (NNLO) prediction in quantum chromodynamics (QCD) for the top quark pair production [47,48] and later for the *t*¯*t* charge asymmetry became available [30–32]. The experiments studied the underlying effect at both the Tevatron and the LHC, using different channels, studying various observables, and measuring the asymmetry in more detail differentially. The experiments at the Tevatron and the LHC are complementary. They can not measure the exact same asymmetry, rather two different observables based on the same underlying cause. There are advantages and disadvantages to perform the measurements at both colliders. The advantage at the Tevatron is that the predicted asymmetry (≈10%) is about an order of magnitude larger compared to the LHC (≈1%). On the other hand, the disadvantage at the Tevatron compared to the LHC is a limited data statistics. The non-zero forward–backward asymmetry has been already observed (≥5 SD) at the Tevatron a few years ago [49], while one of the LHC experiments, A Toroidal LHC Apparatus (ATLAS), has been able to see the evidence (≥3 SD) for a non-zero charge asymmetry for the first time only the last year [50].

Given that large theoretical and experimental progress in the *t*¯*t* charge asymmetry during the past more than 10 years, the review of these studies is in order which this article tries to address. In the next section, the basic description of the top quark charge asymmetry and its various definitions are provided. Section 3 gives a brief overview of theoretical predictions for the charge asymmetry expected in the SM at various orders in the perturbative theory and also for various BSM models. In Section 4, the review of both Tevatron and LHC measurements is presented. In Section 5 follows a discussion of current results and the outlook for next measurements at the LHC and future colliders with the conclusion being in Section 6.
