# Charge Asymmetry in Top Quark Pair Production

## Abstract

**:**

## 1. Introduction

## 2. Charge Asymmetry in $\mathit{t}\overline{\mathit{t}}$ Production

#### 2.1. Top Quark Production in the SM at Hadron Colliders

#### 2.2. Charge Asymmetry in QED and EW Theory

#### 2.3. Charge Asymmetry in QCD

#### 2.4. Top Quark Pair Charge Asymmetry

#### 2.5. Asymmetry Definitions

#### 2.5.1. Asymmetry Definitions for Tevatron

#### 2.5.2. Asymmetry Definitions for LHC

## 3. Theory Overview

#### 3.1. SM Predictions

#### Summary of SM Predictions

#### 3.2. BSM Models

- axigluons (a color octet vector ${\mathcal{G}}_{\mu}$): massive gluons with axial currents (’axigluons’). Similarly to EW theory with the axial current which has a massless photon and a massive Z boson and there is an asymmetry due to the $\gamma -Z$ interference already at LO, the interference between gluon and axigluon in the s-channel mediating $q\overline{q}\to t\overline{t}$ process produces a charge asymmetry;
- ${Z}^{\prime}$ (a neutral vector boson ${\mathcal{B}}_{\mu}$): a flavour violating Z’ exchanged in the t-channel in $u\overline{u}\to t\overline{t}$;
- ${W}^{\prime}$ (a charged boson ${\mathcal{B}}_{\mu}^{1}$): a boson with right-handed couplings exchanged in the t-channel in $d\overline{d}\to t\overline{t}$;
- ${\omega}^{4}$ (color-triplet scalar): a color triplet with right-handed flavour-violating $tu$ couplings exchanged in the u-channel in $u\overline{u}\to t\overline{t}$;
- ${\Omega}^{4}$ (color-sextet scalar): similarly as above, a color sextet with right-handed flavour-violating $t-u$ couplings exchanged in the u-channel. There may be diagonal $uu$, $tt$ couplings, in contrast with the ${\omega}^{4}$ triplet above;
- $\varphi $ (scalar isodoublet): a color-singlet Higgs-like isodoublet, which contains neutral and charged scalars, coupling the top quark to the first generation and exchanged in the t-channel.

## 4. Experimental Measurements

#### 4.1. Forward–Backward Asymmetry Measurements at the Tevatron

#### 4.1.1. Initial Measurements

#### 4.1.2. Measurements with Half of Run II Statistics

#### 4.1.3. Measurements with Full Statistics

#### 4.1.4. Full Dataset Combinations

#### 4.1.5. Summary and Discussion of Tevatron Measurements

#### 4.2. LHC Measurements

#### 4.2.1. Measurements at $\sqrt{s}=7$ TeV

#### 4.2.2. Measurements at $\sqrt{s}=8$ TeV

#### 4.2.3. Measurements at $\sqrt{s}=13$ TeV

#### 4.2.4. Summary of LHC Measurements

## 5. Discussion and Outlook

## 6. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The Feynman diagrams of leading order processes contributing to the top quark pair production at hadron colliders.

**Figure 2.**The Feynman diagrams for the single-top quark production: (

**a**) s-channel, (

**b**) t-channel, and (

**c**) Wt-channel.

**Figure 3.**Measured inclusive cross-sections at the Tevatron and at the LHC compared to NNLO + NNLL predictions [55].

**Figure 5.**Diagrams of processes contributing to the quantum electrodynamic (QED) charge asymmetry for the ${e}^{+}{e}^{-}\to {\mu}^{+}{\mu}^{-}$ production: the box diagram in (

**a**) interfering with the leading order (LO) diagram in (

**b**), and breamshtrahlung diagrams with C-odd in (

**c**) and C-even state in (

**d**) [56].

**Figure 6.**The measured angular distribution for the ${e}^{+}{e}^{-}\to {\mu}^{+}{\mu}^{-}$ production together with the QED prediction [57]. The angle $\theta $ is the angle between the incoming ${e}^{+}$ direction and the outgoing ${\mu}^{+}$ direction.

**Figure 7.**The diagrams contributing to the QCD charge asymmetry in the production of heavy quarks at hadron colliders: interference of final-state (

**a**) with initial-state (

**b**) gluon breamshtrahlung plus interference of the box (

**c**) with the Born diagram (

**d**) [13].

**Figure 9.**The differential charge asymmetry (

**left**) in the $t\overline{t}$ pair production $q\overline{q}\to t\overline{t}$ for the fixed partonic center-of-mass energy $\sqrt{\widehat{s}}=400$ GeV. The integrated charge asymmetry (

**right**) for $q\overline{q}\to t\overline{t}$ as a function of $\sqrt{\widehat{s}}$ [12].

**Figure 10.**Various levels predictions of the inclusive forward–backward asymmetry at the Tevatron compared to the CDF and D0 measurements. Capital letters (NLO, NNLO) correspond to the unexpanded definition, while small letters (nlo, nnlo) to the expanded definition [30].

**Figure 11.**Various predictions of the inclusive charge asymmetry for the LHC at $\sqrt{s}=8$ TeV compared to the A Toroidal LHC ApparatuS (ATLAS) and the Compact Muon Solenoid (CMS) experiment measurements. ${A}_{\mathrm{C}}$ corresponds to the unexpanded definition while ${A}_{\mathrm{C}}^{ex}$ corresponds to the expanded definition [32].

**Figure 12.**The NNLO predictions for the differential charge asymmetry as a function of ${m}_{t\overline{t}}$ in (

**a**), ${y}_{t\overline{t}}$ in (

**b**), ${p}_{\mathrm{T},t\overline{t}}$ in (

**c**), and ${\beta}_{z,t\overline{t}}$ in (

**d**) at the LHC at $\sqrt{s}=8$ TeV [32].

**Figure 13.**The interference of various beyond the Standard Model (BSM) particles which contribute to the charge asymmetry with the gluons [90].

**Figure 14.**The measured inclusive charge asymmetry ${A}_{\mathrm{C}}$ at the LHC at $\sqrt{s}=8$ TeV (horizontal line) plotted against the forward–backward asymmetry ${A}_{\mathrm{FB}}$ (vertical lines) at the Tevatron. The data are compared with the SM prediction at NNLO QCD + NLO electroweak (EW) and predictions incorporating various potential BSM contributions: a ${W}^{\prime}$ boson, a heavy axigluon (${G}_{\mu}$), a scalar isodoublet (f), a color triplet scalar (${\omega}^{4}$), and a color sextet scalar (${\Omega}^{4}$) [91].

**Figure 15.**The $\Delta y$ distribution at the reco level in (

**a**), at the reco level after the background subtraction in (

**b**), and at the parton level in (

**c**), compared to the prediction [97].

**Figure 16.**The production angle $\mathrm{cos}\theta $ (

**left**) and $\Delta y$ (

**right**) distribution at the reco level for the ${A}_{\mathrm{FB}}$ measurements in the $p\overline{p}$ and $t\overline{t}$ frame, respectively. The solid line is the prediction for $t\overline{t}$ with mc@nlo generator and ${\sigma}_{t\overline{t}}=8.2$ pb, plus the expected non-$t\overline{t}$ backgrounds. The dashed curve shows the prediction when $t\overline{t}$ is reweighted according to the form $1+{A}_{\mathrm{FB}}\mathrm{cos}\alpha $ using measured values of ${A}_{\mathrm{FB}}$ [41].

**Figure 17.**The $\Delta y$ (

**left**) and ${y}_{t}$ (

**right**) distribution at the reco level corresponding to the CDF measurement performed in the $\ell +$jets channel using $5.3\phantom{\rule{3.33333pt}{0ex}}{\mathrm{fb}}^{-1}$ [42].

**Figure 18.**Parton level asymmetries as a function of $\Delta y$ (

**left**) and ${m}_{t\overline{t}}$ (

**right**) compared to the SM prediction of mcfm. The negative going uncertainty for $\Delta y<1.0$ is suppressed [42].

**Figure 19.**The reconstructed $\Delta y$ (

**left**) and the charge-signed lepton rapidity (

**right**) corresponding to the D0 measurement in the $\ell +$jets channel [43].

**Figure 20.**The forward–backward asymmetry as a function of $|\Delta y|$ (

**left**) and ${m}_{t\overline{t}}$ (

**right**) with a best-fit line superimposed. The shaded region represents the theoretical uncertainty on the slope of the prediction [97].

**Figure 21.**The ${A}_{\mathrm{FB}}$ dependence on $|\Delta y|$ (

**left**) and on ${m}_{t\overline{t}}$ (

**right**). The dashed line shows the fit to the data with the dotted lines indicating the fit uncertainty. The x coordinate of each datum point is the observed average of $|\Delta y|$ in the corresponding bin [102].

**Figure 23.**The reco level distribution of $q\xb7\eta $ (

**left**) and $\Delta \eta ={\eta}_{{\ell}^{+}}-{\eta}_{{\ell}^{-}}$ (

**right**). The error bars indicate the statistical uncertainty on the data [101].

**Figure 24.**Summary of inclusive forward–backward asymmetries used in the Tevatron combination together with their combination [49].

**Figure 25.**The dependence of ${A}_{\mathrm{FB}}$ as a function of ${m}_{t\overline{t}}$ (

**left**). The individual measurements and the Tevatron combination are shown together with the NNLO QCD + NLO EW prediction. The dependence of ${A}_{\mathrm{FB}}$ as a function of $\Delta y$ (

**right**). Here, the individual measurements are shown together with the simultaneous fit and the NNLO QCD + NLO EW prediction [49].

**Figure 26.**The individual CDF and D0 measurements of ${A}_{\mathrm{FB}}^{\ell}$ as a function of $|{q}_{\ell}{\eta}_{\ell}|$ (

**left**) and of ${A}_{\mathrm{FB}}^{\ell \ell}$ as a function of $|\Delta \eta |$ (

**right**) together with the NLO QCD prediction [49].

**Figure 27.**Reconstructed $\Delta \left|\eta \right|$ (

**left**) and $\Delta {y}^{2}$ (

**right**) distributions for the $\ell +$jets channel. The outermost bins include the overflows [69].

**Figure 28.**Distributions of ${A}_{\mathrm{C}}$ as a function of ${m}_{t\overline{t}}$ in (

**a**), ${p}_{\mathrm{T},t\overline{t}}$ in (

**b**), and ${y}_{t\overline{t}}$ in (

**c**). The measured ${A}_{\mathrm{C}}$ values are compared with the NLO QCD + EW predictions (SM) [24] and the predictions for a color-octet axigluon [105].

**Figure 29.**The unfolded $\Delta \left|y\right|$ distribution in (

**a**), the charge asymmetry as a function of ${y}_{t\overline{t}}$ in (

**b**), ${p}_{\mathrm{T},t\overline{t}}$ in (

**c**), and ${m}_{t\overline{t}}$ in (

**c**). The measured values are compared to NLO QCD + EW calculations of Ref. [21], and to the predictions of a model featuring an effective axial-vector coupling of the gluon (EAG) [117]. The error bars on the differential asymmetry values indicate the statistical and total uncertainties [107].

**Figure 31.**The dependence of ${A}_{\mathrm{C}}^{\ell \ell}$ on ${m}_{t\overline{t}}$ in (

**a**), ${y}_{t\overline{t}}$ in (

**b**), and ${p}_{\mathrm{T},t\overline{t}}$ in (

**c**). The inner and outer error bars represent the statistical and total uncertainty, respectively [108].

**Figure 32.**Measured ${A}_{\mathrm{C}}$ values as a function of ${m}_{t\overline{t}}$ in (

**a**), ${\beta}_{z,t\overline{t}}$ in (

**b**), and ${p}_{\mathrm{T},t\overline{t}}$ in (

**c**), compared with NLO QCD + NLO EW predictions [24] and with the right-handed color octets with masses below the $t\overline{t}$ threshold [109].

**Figure 33.**A summary of the charge asymmetry measurements for different ranges of ${m}_{t\overline{t}}$. The error bars on the data indicate the modeling and unfolding systematic uncertainties, shown as the inner bar, and the total uncertainty [110].

**Figure 34.**The charge asymmetry as a function of ${y}_{t\overline{t}}$ in (

**a**), ${p}_{\mathrm{T},t\overline{t}}$ in (

**b**), and ${m}_{t\overline{t}}$ in (

**c**) measured at the particle level in the fiducial phase space. The inner bars indicate the statistical uncertainties, while the outer bars represent the statistical and systematic uncertainties added in quadrature [112].

**Figure 35.**The symmetric (

**left**) and antisymmetric (

**right**) components of the binned probability distributions in the observable ${{\rm Y}}_{t\overline{t}}$, constructed using powheg generator for different $t\overline{t}$ initial processes [113].

**Figure 36.**The antisymmetric $t\overline{t}$ contribution is measured in the ${{\rm Y}}_{t\overline{t}}^{rec}$ distribution. The antisymmetric component of the ${{\rm Y}}_{t\overline{t}}^{rec}$ distribution is shown here. The thick line shows the antisymmetric component of the fit model. The measurements are performed independently in the e+jets (

**left**) and $\mu $+jets (

**right**) channels [113].

**Figure 37.**Summary of the measurements for the dileptonic asymmetry in the fiducial volume. The predictions shown in blue are obtained using powheg + pythia at NLO [111].

**Figure 39.**The normalized differential $t\overline{t}$ production cross-section as a function of $\Delta \left|y\right|$ at the parton level in the full phase space (

**left**) and as a function of $\Delta \left|\eta \right|$ in the fiducial phase space at the particle level (

**right**) [116].

**Figure 40.**The results of the ${A}_{\mathrm{C}}$ extraction from integrating normalized parton level and particle level differential cross-section measurements as a function of $\Delta \left|y\right|$ and $\Delta \left|\eta \right|$ are shown [116].

**Figure 41.**The generator-level $\mathrm{cos}\theta $ (labeled here as ${c}^{*}$) in (

**a**), ${x}_{\mathrm{F}}$ in (

**b**), and ${m}_{t\overline{t}}$ normalized distributions in (

**c**) for the subprocesses $q\overline{q}$, $qg$, and $gg$. These distributions correspond to the CMS measurement in the $\ell +$jets channel performed at $\sqrt{s}=13$ TeV using $35.9\phantom{\rule{3.33333pt}{0ex}}{\mathrm{fb}}^{-1}$ [115].

**Figure 42.**Differential charge asymmetry measurements as a function of ${\beta}_{z,t\overline{t}}$ (

**left**) and ${m}_{t\overline{t}}$ (

**right**) [50].

**Figure 43.**Constraints on linear combination ${C}^{-}/{\Lambda}^{2}$ of Wilson coefficients of dimension 6 operators from inclusive and ${m}_{t\overline{t}}$ differential charge asymmetry measurements [50].

**Table 1.**The predicted next-to-next-to-leading order (NNLO) $t\overline{t}$ production cross-sections in pb for various energies at the Tevatron and at the Large Hadron Collider (LHC) and for different available calculations. The uncertainties include the factorization and renormalization scale and parton distribution function (PDF)+${\alpha}_{s}$ uncertainties. The assumed top quark mass is always ${m}_{t}=173.3$ GeV except for NNLO + next-to-next-leading-logarithm (NNLL) prediction at the LHC where it is ${m}_{t}=173.2$ GeV.

Collider | $\sqrt{\mathit{s}}$ [TeV] | NNLO + NNLL [48] | aN^{3}LO [51] | NNLO [54] |
---|---|---|---|---|

Tevatron | 1.96 | ${7.16}_{-0.23}^{+0.20}$ | $7.37\pm 0.39$ | |

LHC | 7 | ${174}_{-11}^{+10}$ | ${174}_{-12}^{+11}$ | |

LHC | 8 | ${248}_{-14}^{+13}$ | ${248}_{-15}^{+14}$ | |

LHC | 13 | ${816}_{-45}^{+39}$ | ${810}_{-36}^{+38}$ | ${794}_{-45}^{+28}$ |

**Table 2.**The summary of Standard Model (SM) predictions for $t\overline{t}$ and leptonic forward–backward asymmetries at the Tevatron at various levels of the perturbation theory. Some predictions are in the laboratory frame (lab) while some are in the $t\overline{t}$ rest frame ($t\overline{t}$). Some of the predictions are using the unexpanded definition while the others use the expanded (ex) definition.

Prediction | ${\mathit{A}}_{\mathbf{FB}}^{\mathit{t}\overline{\mathit{t}}}$ [%] | ${\mathit{A}}_{\mathbf{FB}}^{\mathbf{\ell}}$ [%] | ${\mathit{A}}_{\mathbf{FB}}^{\mathbf{\ell}\mathbf{\ell}}$ [%] |
---|---|---|---|

NLO QCD [12,13] | 4–5 (lab) | ||

NLO QCD [30] | ${5.89}_{-1.40}^{+2.70}$ ($t\overline{t}$) | ||

NLO QCD [30] | ${7.34}_{-0.58}^{+0.68}$ ($t\overline{t}$, ex) | ||

NLO QCD [23] | ${4.9}_{-0.4}^{+0.5}$ (lab, ex) | ||

NLO QCD [23] | ${7.6}_{-0.5}^{+0.8}$ ($t\overline{t}$, ex) | ||

NLOW [23] | ${5.1}_{-0.3}^{+0.5}$ (lab, ex) | ||

NLOW [23] | ${8.0}_{-0.5}^{+0.7}$ ($t\overline{t}$, ex) | ||

NLO QCD + EW [20,21,24,25] | 5–6 (lab) | ||

NLO QCD [24] | $3.1\pm 0.3$ (lab, ex) | $4.0\pm 0.4$ (ex) | |

NLO QCD + EW [24] | ${5.77}_{-0.31}^{+0.40}$ (lab, ex) | $3.8\pm 0.3$ (lab, ex) | $4.8\pm 0.4$ (ex) |

NLO QCD + EW [24] | ${8.75}_{-0.48}^{+0.58}$ ($t\overline{t}$, ex) | ||

NLO QCD + NNLL [30] | ${7.24}_{-0.67}^{+1.04}$ ($t\overline{t}$, ex) | ||

NNLO [30] | ${7.49}_{-0.86}^{+0.49}$ ($t\overline{t}$) | ||

NNLO(matrix) | ${7.4}_{-0.8}^{+0.3}$ ($t\overline{t}$) | ||

NNLO [30] | ${8.28}_{-0.26}^{+0.27}$ ($t\overline{t}$, ex) | ||

aN${}^{3}$LO QCD [29] | $8.7\pm 0.2$ ($t\overline{t}$, ex) | ||

NNLO QCD + EW [30] | $9.5\pm 0.7$ ($t\overline{t}$, ex) | ||

aN${}^{3}$LO QCD + EW [29] | $10.0\pm 0.6$ ($t\overline{t}$, ex) | ||

PMC [28] | $12.5$ ($t\overline{t}$, ex) |

**Table 3.**The summary of SM predictions for charge asymmetry at various levels of perturbation theory at the LHC for different center-of-mass energies. All of these predictions are in the laboratory frame. Some of the predictions are using the unexpanded definition while the others use the expanded (ex) definition.

Prediction | $\sqrt{\mathit{s}}$ [TeV] | ${\mathit{A}}_{\mathbf{C}}^{\mathit{t}\overline{\mathit{t}}}$ [%] | ${\mathit{A}}_{\mathbf{C}}^{\mathbf{\ell}\mathbf{\ell}}$ [%] |
---|---|---|---|

NLO [24] | 7 | $1.07\pm 0.04$ (ex) | $0.61\pm 0.03$ |

NLO+EW [24] | 7 | $1.23\pm 0.05$ (ex) | $0.70\pm 0.03$ |

NLO+EW [21] | 7 | $1.15\pm 0.06$ (ex) | |

NLO+EW ($\Delta \left|\eta \right|$) [21] | 7 | $1.36\pm 0.08$ (ex) | |

NNLO (MATRIX) | 7 | $0.95\pm 0.08$ | |

PMC [27] | 7 | ${1.15}_{-0.03}^{+0.01}$ (ex) | |

NLO [24] | 8 | $0.96\pm 0.04$ (ex) | $0.55\pm 0.03$ |

NLO+EW [24] | 8 | $1.11\pm 0.04$ (ex) | $0.64\pm 0.03$ |

NLO [32] | 8 | ${0.73}_{-0.13}^{+0.23}$ | |

NLO [32] | 8 | ${0.96}_{-0.09}^{+0.11}$ (ex) | |

NLO+EW [32] | 8 | ${0.86}_{-0.14}^{+0.25}$ | |

NLO+EW [32] | 8 | ${1.13}_{-0.08}^{+0.10}$ (ex) | |

NNLO [32] | 8 | ${0.83}_{-0.06}^{+0.03}$ | |

NNLO [32] | 8 | ${0.85}_{-0.04}^{+0.02}$ (ex) | |

NNLO+EW [32] | 8 | ${0.95}_{-0.07}^{+0.05}$ | |

NNLO+EW [32] | 8 | ${0.97}_{-0.03}^{+0.02}$ (ex) | |

PMC [27] | 8 | ${1.03}_{-0.00}^{+0.01}$ (ex) | |

NLO+EW [25] | 13 | ${0.75}_{-0.05}^{+0.04}$ (ex) | $0.55\pm 0.03$ (ex) |

NNLO+EW [88] | 13 | ${0.64}_{-0.05}^{+0.06}$ | |

NLO [24] | 14 | $0.58\pm 0.03$ (ex) | $0.36\pm 0.02$ (ex) |

NLO+EW [24,25] | 14 | ${0.66}_{-0.04}^{+0.05}$ (ex) | $0.43\pm 0.02$ (ex) |

PMC [27] | 14 | ${0.62}_{-0.02}^{+0.00}$(ex) |

**Table 4.**The mc@nlo predictions and measured forward–backward asymmetries at reco level as a function of the number of jets in the D0 measurement using $0.9\phantom{\rule{0.166667em}{0ex}}{\mathrm{fb}}^{-1}$ [40].

Number of Jets | ${\mathit{A}}_{\mathbf{FB}}^{\mathit{t}\overline{\mathit{t}}}$(mc@nlo) [%] | ${\mathit{A}}_{\mathbf{FB}}^{\mathit{t}\overline{\mathit{t}}}$(data) [%] |
---|---|---|

≥4 | $0.8\pm 1.0$ | $\phantom{\rule{4pt}{0ex}}12\pm 8(\mathrm{stat}.)\pm 1(\mathrm{syst}.)$ |

4 | $2.3\pm 1.0$ | $\phantom{\rule{4pt}{0ex}}19\pm 9(\mathrm{stat}.)\pm 2(\mathrm{syst}.)$ |

≥5 | $-4.9\pm 1.1$ | $-{16}_{-17}^{+15}(\mathrm{stat}.)\pm 3(\mathrm{syst}.)$ |

**Table 5.**The summary of inclusive asymmetries in $t\overline{t}$ and $p\overline{p}$ rest frames at the reco level with and without including the background, and at the parton level corresponding to the CDF measurement using $5.3\phantom{\rule{0.166667em}{0ex}}{\mathrm{fb}}^{-1}$. Uncertainties include statistical, systematic, and theoretical uncertainties [42].

Sample | Level | ${\mathit{A}}_{\mathbf{FB}}^{\mathit{t}\overline{\mathit{t}}}$ [%] | ${\mathit{A}}_{\mathbf{FB}}^{\mathit{p}\overline{\mathit{p}}}$ [%] |
---|---|---|---|

data | reco (with background) | $5.7\pm 2.8$ | $7.3\pm 2.8$ |

mc@nlo | reco (with background) | $1.7\pm 0.4$ | $0.1\pm 0.3$ |

data | reco (without background) | $7.5\pm 3.7$ | $11.0\pm 3.9$ |

mc@nlo | reco (without background) | $2.4\pm 0.5$ | $1.8\pm 0.5$ |

data | parton | $15.8\pm 7.4$ | $15.0\pm 5.5$ |

mcfm | parton | $5.8\pm 0.9$ | $3.8\pm 0.6$ |

**Table 6.**The reco level ${A}_{\mathrm{FB}}^{t\overline{t}}$ by subsample in the D0 $\ell +$jets measurement using $5.4\phantom{\rule{0.166667em}{0ex}}{\mathrm{fb}}^{-1}$ [43].

Subsample | ${\mathit{A}}_{\mathbf{FB}}^{\mathit{t}\overline{\mathit{t}}}$ (Data) [%] | ${\mathit{A}}_{\mathbf{FB}}^{\mathit{t}\overline{\mathit{t}}}$ (mc@nlo) [%] |
---|---|---|

${m}_{t\overline{t}}<450\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{4pt}{0ex}}\mathrm{Ge}\phantom{\rule{-1.00006pt}{0ex}}\mathrm{V}$ | $7.8\pm 4.8$ | $1.3\pm 0.6$ |

${m}_{t\overline{t}}>450\phantom{\rule{3.33333pt}{0ex}}\phantom{\rule{4pt}{0ex}}\mathrm{Ge}\phantom{\rule{-1.00006pt}{0ex}}\mathrm{V}$ | $11.5\pm 6.0$ | $4.3\pm 1.3$ |

$|\Delta y|<1.0$ | $6.1\pm 4.1$ | $1.4\pm 0.6$ |

$|\Delta y|>1.0$ | $21.3\pm 9.7$ | $6.3\pm 1.6$ |

**Table 7.**Summary of Tevatron measurements of inclusive forward–backward asymmetries. For a given measurement, if there is just one uncertainty, it is combined statistical and systematic uncertainty. If there are two uncertainties, the first one is always statistical and the second one is systematic uncertainty.

Experiment, Channel | $\mathcal{L}$[${\mathbf{fb}}^{-1}$] | ${\mathit{A}}_{\mathbf{FB}}^{\mathit{t}\overline{\mathit{t}}}$ [%] | ${\mathit{A}}_{\mathbf{FB}}^{\mathbf{\ell}}$ [%] | ${\mathit{A}}_{\mathbf{FB}}^{\mathbf{\ell}\mathbf{\ell}}$ [%] |
---|---|---|---|---|

CDF, $\ell +$jets | 1.9 | $24\pm 13\pm 4$ | ||

CDF, $\ell +$jets | 5.3 | $15.8\pm 7.4$ | ||

D0, $\ell +$jets | 5.4 | $19.6\pm 6.5$ | $15.2\pm 4.0$ | |

D0, dilepton | 5.4 | $5.8\pm 5.1\pm 1.3$ | $5.3\pm 7.9\pm 2.9$ | |

D0, combination | 5.4 | $11.8\pm 3.2$ | ||

CDF, $\ell +$jets | 9.4 | $16.4\pm 3.9\pm 2.6$ | ${10.5}_{-2.9}^{+3.2}$ | |

CDF, dil | 9.1 | $12\pm 11\pm 7$ | $7.2\pm 5.2\pm 3.0$ | $7.6\pm 7.2\pm 3.9$ |

D0, $\ell +$jets | 9.7 | $10.6\pm 3.0$ | ${5.0}_{-3.7}^{+3.4}$ | |

D0, dil | 9.7 | $17.5\pm 5.6\pm 3.1$ | $4.4\pm 3.7\pm 1.1$ | $12.3\pm 5.4\pm 1.5$ |

CDF, combination | 9.7 | $16.0\pm 4.5$ | ${9.0}_{-2.6}^{+2.8}$ | |

D0, combination | 9.7 | $11.8\pm 2.5\pm 1.3$ | ||

Tevatron, combination | 9.7 | $12.8\pm 2.1\pm 1.4$ | $7.3\pm 1.6\pm 1.2$ | $10.8\pm 4.3\pm 1.6$ |

**Table 8.**Summary of inclusive $t\overline{t}$ and leptonic charge asymmetry measurements performed at the LHC. For a given measurement, if there is just one uncertainty, it is combined statistical and systematical uncertainty. If there are two uncertainties, the first one is statistical and the second one is systematic uncertainty. All measurements used $\Delta \left|y\right|$ variable except for the measurement with * which used $\Delta \left|\eta \right|$. All measurements were performed at the parton level except for the measurement with ** which was performed at particle level.

Experiment, Channel | $\sqrt{\mathit{s}}$ [TeV] | L [${\mathbf{fb}}^{-1}$] | ${\mathit{A}}_{\mathbf{C}}^{\mathit{t}\overline{\mathit{t}}}$ [%] | ${\mathit{A}}_{\mathbf{C}}^{\mathbf{\ell}\mathbf{\ell}}$ [%] |
---|---|---|---|---|

CMS, $\ell +$jets | 7 | 1.1 | $-1.7\pm {3.2}_{-3.6}^{+2.5}$ * | |

ATLAS, $\ell +$jets | 7 | 1.1 | $-1.9\pm 2.8\pm 2.4$ | |

CMS, $\ell +$jets | 7 | 5.0 | $0.4\pm 1.0\pm 1.1$ | |

CMS, dil | 7 | 5.0 | $-1.0\pm 1.7\pm 0.8$ | $0.9\pm 1.0\pm 0.6$ |

ATLAS, $\ell +$jets | 7 | 4.7 | $0.6\pm 1.0$ | |

ATLAS, dil | 7 | 4.6 | $2.1\pm 2.5\pm 1.7$ | $2.4\pm 1.5\pm 0.9$ |

LHC, combination | 7 | 5.0 | $0.5\pm 0.7\pm 0.6$ | |

CMS, $\ell +$jets | 8 | 19.7 | $0.10\pm 0.68\pm 0.37$ | |

CMS, $\ell +$jets(template) | 8 | 19.6 | $0.33\pm 0.26\pm 0.33$ | |

CMS, dil | 8 | 19.5 | $1.1\pm 1.1\pm 0.7$ | $0.3\pm 0.6\pm 0.3$ |

ATLAS, $\ell +$jets | 8 | 20.3 | $0.9\pm 0.5$ | |

ATLAS, dil | 8 | 20.3 | $2.1\pm 1.6$ | $0.8\pm 0.6$ |

LHC, combination | 8 | 20.3 | $0.55\pm 0.23\pm 0.25$ | |

CMS, dilepton | 13 | 35.9 | $1.0\pm 0.9$ | $-0.5\pm 0.4$ ** |

ATLAS,$\ell +$jets | 13 | 139 | $0.60\pm 0.15$ |

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**MDPI and ACS Style**

Lysák, R.
Charge Asymmetry in Top Quark Pair Production. *Symmetry* **2020**, *12*, 1278.
https://doi.org/10.3390/sym12081278

**AMA Style**

Lysák R.
Charge Asymmetry in Top Quark Pair Production. *Symmetry*. 2020; 12(8):1278.
https://doi.org/10.3390/sym12081278

**Chicago/Turabian Style**

Lysák, Roman.
2020. "Charge Asymmetry in Top Quark Pair Production" *Symmetry* 12, no. 8: 1278.
https://doi.org/10.3390/sym12081278