# Constraints on four-fermion interactions from the \(t\bar{t}\) charge asymmetry at hadron colliders

## Abstract

The charge asymmetry in top quark production at hadron colliders is sensitive to beyond-the-Standard-Model four-fermion interactions. In this study we compare the sensitivity of \(t\bar{t}\) cross-section and charge asymmetry measurements to effective operators describing four-fermion interactions and study the limits on the validity of this approach. A fit to a combination of Tevatron and LHC measurements yields stringent limits on the linear combinations \(C_1\) and \(C_2\) of the four-fermion effective operators.

## Keywords

Effective Operator Charge Asymmetry Differential Measurement Inclusive Measurement Differential Cross Section Measurement## 1 Introduction

Since the discovery of the top quark, its properties and interactions have been characterized in some detail. Run I of the LHC, with a top quark pair production of several million events, is extending the programme initiated at the Tevatron in several ways. The larger center-of-mass energy of the LHC moreover gains access to measurements of known processes involving top quarks in an unexplored kinematic regime and to entirely new processes (i.e. associated production: \(t\bar{t}Z\), \(t\bar{t}W\), \(t\bar{t}H\)).

All measurements so far are in good agreement with the Standard Model predictions. The most notorious exception is the measurement of the forward-backward asymmetry in \(p\bar{p}\) collisions at 1.96 TeV at the Tevatron [1, 2] and its dependence on the kinematics of the \(t\bar{t}\) system [3, 4, 5, 6, 7]. Excitement has decreased considerably in recent years, as the discrepancy failed to grow as additional Tevatron data were added. Taking into account the EW correction [8] and the full next-to-next-to-leading-order (NNLO) QCD corrections [9] the remaining tension of the inclusive measurements at the Tevatron with the SM prediction is down to the 1.5 \(\sigma \) level. Measurements of a related charge asymmetry in 7 TeV [10, 11, 12, 13] and 8 TeV [14, 15, 16] *pp* collisions at the LHC by ATLAS and CMS are consistent with the SM prediction.

In this paper we derive constraints on beyond-the-Standard-Model (BSM) four-fermion operators involving top quarks from measurements at hadron colliders. In Fig. 1 the Feynman diagram for the relevant four-fermion operator is shown, as well as the Born-level Standard Model diagram for \(q \bar{q} \rightarrow t \bar{t}\) production.

We compare the sensitivity of available and future cross-section and charge asymmetry measurements, signalling the complementarity of both types of measurements. We study the limits to the validity of the effective operator approach for a number of measurements and propose a practical solution to guarantee valid results with the current data and in the foreseeable future. Finally, we derive constraints on the four-fermion operators from Tevatron and LHC data and present the prospects for an addition of future measurements.

## 2 Effective operator setup

*q*in Table 1) can be constrained by precision electroweak observables. These seven operators can be reduced to four by using a flavour-specific linear combination [20]:

*u*-type and

*d*-type quarks with the same strength. Among the models that satisfy this requirement the axigluon [21] has received most attention in the context of the \(t\bar{t}\) charge asymmetry measurements at the Tevatron and the LHC. We note that the assumption is also valid for models that are not strictly flavour-universal, such the axigluon with an opposite-sign coupling top quarks (\(g_t = - g_q\)), that can give rise to positive contributions to the asymmetry, and the Kaluza Klein gluon as realized in Randall-Sundrum warped extra-dimensions in Refs. [22, 23], the main benchmark for direct searches for resonant signals in \(t\bar{t}\) production.

Four-fermion operators involved in \(t\bar{t}\) production at hadron colliders in the notation from [20], where *q* is the left-handed quark doublet, *u* and *d* correspond to the up and down right-handed quarks of the first two families, and *t* represents the right-handed top quark

Operator | |
---|---|

\(O_{qq}^{(8,1)} = \frac{1}{4} \left( \bar{q}^i \gamma _\mu \lambda ^A q^j \right) \left( \bar{q} \gamma ^\mu \lambda ^A q \right) \) | |

\(O_{qq}^{(8,3)} = \frac{1}{4} \left( \bar{q}^i \gamma _\mu \tau ^I \lambda ^A q^j \right) \left( \bar{q} \gamma ^\mu \tau ^I \lambda ^A q \right) \) | |

\(O_{ut}^{(8)} = \frac{1}{4} \left( \bar{u}^i \gamma _\mu \lambda ^A u^j \right) \left( \bar{t} \gamma ^\mu \lambda ^A t \right) \) | |

\(O_{dt}^{(8)} = \frac{1}{4} \left( \bar{d}^i \gamma _\mu \lambda ^A d^j \right) \left( \bar{t} \gamma ^\mu \lambda ^A t \right) \) | |

\(O_{qu}^{(1)} = \left( \bar{q} u^i \right) \left( \bar{u}^j q\right) \) | |

\(O_{qd}^{(1)} = \left( \bar{q} d^i \right) \left( \bar{d}^j q\right) \) | |

\(O_{qt}^{(1)} = \left( \bar{q}^i t \right) \left( \bar{t} q^j\right) \) |

## 3 Measurements

Measurements considered in this analysis [30]

SM prediction | Measurement | |
---|---|---|

Tevatron, 1.96 TeV \(p\bar{p}\), CDF+D0, inclusive \(\sigma \) | \(7.16 \pm 0.26\) pb [24] | \(7.60 \pm 0.41\) pb [25] |

Tevatron, 1.96 TeV \(p\bar{p}\), CDF+D0, inclusive \(A_{FB}\) | \(9.5 \pm 0.7\, \%\) [9] | |

LHC, 8 TeV | \(245.80 \pm 10.56 \) pb [24] | \(241.50 \pm 8.54 \) pb [26] |

ATLAS 8 TeV | \(1.11 \pm 0.04\, \%\) [27] | \(0.9 \pm 0.5\, \%\) [16] |

CMS 8 TeV | \(1.11 \pm 0.04\, \%\) [27] | \(0.3 \pm 0.4\, \%\) [15] |

ATLAS 8 TeV | \(1.60 \pm 0.04\, \%\) [28] | \(4.2 \pm 3.2\, \%\) [29] |

The selection of Table 2 emphasizes inclusive measurements that integrate over all kinematic regimes. The use of differential measurements, especially of the production of high-mass \(t\bar{t}\) pairs, may offer greater sensitivity to high-scale physics beyond the SM [31]. We therefore include a recent ATLAS result for the charge asymmetry in events where the top quark pair is produced with a large invariant mass [29], which we take as a proxy for measurements in boosted top quark pair production that become available at the LHC.^{1}

## 4 Sensitivity to effective operators

We generate \(t\bar{t}\) samples at parton-level with the Monte Carlo generator Madgraph5_aMC@NLO [37] using the UFO [38] model TopEffTh [39] to calculate the impact of the effective operators on the cross-section and charge asymmetry.

^{2}using the linear dependence of Eq. (3):

The results for the coefficients of Eqs. (3) and (4) are presented in Table 3. The coefficients \(\alpha _u\) and \(\alpha _d\) are defined such that they are proportional to the contribution of new interactions to the cross-section divided by the SM cross section. As such the size of \(\alpha _{u/d}\) in different measurements offers a good indication of the sensitivity of the measurements (assuming the *relative* precision of all measurements is equal, condition that is approximately met for the measurements in the Table). The \(\beta _{u/d}\) coefficients indicate the strength of the constraint for charge asymmetry measurements of the same absolute precision.

For all measurements the coefficients \(\alpha _u\) and \(\beta _u\) for the u-type operators are larger than \(\alpha _d\) and \(\beta _d\), that apply to d-type operators. The ratios \(\alpha _u/\alpha _d\) and \(\beta _u/\beta _d\) are largest at the Tevatron, where a naive estimate based on the valence quark content of the proton and anti-proton would yield a factor of four. The large ratio at the Tevatron is quite powerful to derive simultaneous constraints on u-type and d-type operators. The Tevatron bands in \(C_1^u\) and \(C_1^d\) space in Fig. 2b cross at more favourable angles than the LHC bands. At the LHC (where the naive estimate would yield a ratio of two) the u-type and d-type operator coefficients are much closer.

\(\alpha _u\) \([\%]\) | \(\alpha _d\) \([\%]\) | \(\beta _u\) \([\%]\) | \(\beta _d\) \([\%]\) | |
---|---|---|---|---|

Tevatron 1.96 TeV \(p\bar{p}\) inclusive | \(5.19\pm 0.02\) | \(1.05 \pm 0.02\) | \(1.66 \pm 0.09\) | \(0.32 \pm 0.09\) |

LHC 8 TeV | \(1.02 \pm 0.02\) | \(0.71 \pm 0.02\) | \(0.37 \pm 0.09\) | \(0.24 \pm 0.09\) |

LHC 8 TeV | \(3.03 \pm 0.09\) | \(1.56 \pm 0.09\) | \(2.16 \pm 0.09\) | \(0.6 \pm 0.09\) |

LHC 13 TeV inclusive | \(0.73 \pm 0.02\) | \(0.48 \pm 0.02\) | \(0.26 \pm 0.09\) | \(0.27 \pm 0.09\) |

LHC 13 TeV (\(m_{t\bar{t}} >\) 1.2 TeV) | \(6.61 \pm 0.02\) | \(3.60 \pm 0.02 \) | \(6.09 \pm 0.09\) | \(2.78 \pm 0.09\) |

Table 3 suggests a way to restore the sensitivity of the LHC to the level of the Tevatron and beyond. The differential measurements listed in the table correspond to the cross-section and charge asymmetry for boosted top quark production. For 8 TeV operation the phase space is limited to events with an invariant mass of the \(t\bar{t}\) system \(m_{t\bar{t}} >\) 750 GeV. For 13 TeV the cut on \(m_{t\bar{t}}\) is raised to 1.2 TeV. We see that the \(\alpha \) and \(\beta \) coefficients of these differential measurements are indeed an order of magnitude larger than those of the inclusive measurements at the same center-of-mass energy. Therefore, the measurement of the charge asymmetry at high mass can provide a competitive constraint, even with an uncertainty that is an order of magnitude larger than that of the inclusive charge asymmetry measurement. The measurements of the charge asymmetry and cross section in boosted top quark production of Refs. [29] and [33], indicated as red dashed bands in Fig. 2, provide quite competitive constraints. These measurements are still statistically limited in run I, with a non-negligible contribution from modelling uncertainties in these relatively unexplored corners of phase space. With the large \(t\bar{t}\) samples that become available in run 2 of the LHC there is considerable margin for improvement of this and other differential measurements.

## 5 Validity of the effective operator approach

^{3}

The interval of validity shrinks with the increase in center-of-mass energy: at the 8 TeV LHC it is typically a factor two smaller than at the Tevatron. In combination with the reduced sensitivity to four-fermion operators of the LHC data there is a risk that adding a measurement may reduce the interval of validity more than the 95 % CL interval. The differential measurements can see a very strong reduction of the interval of validity, in particular once we enter the regime of boosted top quark pair production. However, in this case the sensitivity grows to compensate the reduced interval of validity. Therefore, a differential measurement of sufficient precision may prove to be useful in the fit.

The same trend towards smaller interval of validity for increasing center-of-mass energy is observed for the cross section and the charge asymmetry. The interval of validity of the charge asymmetry is generally somewhat smaller than that of the cross section, but the difference is small compared to that between the Tevatron and the LHC, or between inclusive and differential measurements. For the inclusive measurements at the 8 TeV LHC the tension between interval of validity and the 95 % CL interval on individual coefficients is much more pronounced for the cross-section measurement than for the charge asymmetry.

## 6 Multi-parameter fit

*i*defined in Table 2.

We minimize the \(\chi ^2\) function using the root package MINUIT [41] in order to extract the parameters \(\{C_i\}\).

The simultaneous fit of the four effective operators \(\bar{C}_1^u\), \(\bar{C}_2^u\), \(\bar{C}_1^d\) and \(\bar{C}_2^d\) using all data in Table 2 yields tight constraints on the former two, that correspond to interactions initiated by u-type quarks. The 95 % CL limits are contained within the interval of validity. As we anticipated in Sect. 4 the constraint on operators corresponding to d-type quarks is much weaker, where the marginalized 95 % CL constraints from the four-parameter fit on \(\bar{C}_1^d\) and \(\bar{C}_2^d\) are 3–5 times weaker than the limits on single operators. The marginalized 95 % CL intervals extend beyond the interval of validity. The exact level of tension between range of validity and limits depends somewhat on which measurements are included in the fit, but the qualitative conclusion remains true for all combinations of the data in Table 2: none of the combinations of the cross-section and charge asymmetry data yield meaningful marginalized limits on \(\bar{C}_1^d\) and \(\bar{C}_2^d\). A similar observation was made in Ref. [18] for \(\bar{C}_2^d\).

Much stronger constraints are obtained when we assume \(C_1^u=C_1^d=C_1\) and \(C_2^u=C_2^d=C_2\). In this case, the interval is within the tightest interval of validity of the measurements used in the fit.^{4} We therefore present the constraints obtained with the two-parameter fit as the main result of this study.

## 7 Constraints on four-fermion operators

As discussed in Sect. 4 the charge asymmetry and cross-section measurements provide complementary constraints. Indeed, the simultaneous fit of \(C_1\) and \(C_2\) yields very similar results to the limits obtained when a single operator is floated in the fit.

A fit of the two linear combinations \(\bar{C}_{+} = \bar{C}_{1} + \bar{C}_{2}\) and \(\bar{C}_{-} = \bar{C}_{1} - \bar{C}_{2}\) yields limits \(-\)0.09 \(< \bar{C}_+ <\) 0.2 and -0.07 \(< \bar{C}_- <\) 0.04. In this case the results are readily related to the measurements. We see that the \(\bar{C}_{-}\) constraint, driven by the charge asymmetry, is nearly three times stronger than the constraint on \(\bar{C}_+\), that is dominated by the cross-section measurements. The central value of \({C}_+\) is 0.06, due to the Tevatron cross-section of Refs. [4, 5] that slightly exceeds the SM prediction. The \({C}_-\) fit is pulled towards negative values by the CMS measurement in Ref. [15]. This measurement, 2\(\sigma \) below the SM value, is able to compensate the positive pull from the Tevatron experiments. We propose the constraint on \(\bar{C}_{-} = \bar{C}_{1} - \bar{C}_{2}\) as a benchmark for charge asymmetry measurements: the extent of the 95 % CL allowed region is a good figure-of-merit to relate the sensitivity to high-scale new physics of measurements with different initial states (i.e. Tevatron vs. LHC), different center-of-mass energies and in different kinematic regimes. Similarly, the constraint on \(\bar{C}_{+} = \bar{C}_{1} + \bar{C}_{2}\) is a good indicator of the sensitivity of cross section measurements to high-scale new physics in processes initiated by a quark and anti-quark.

The limits on the four-fermion operators presented in this paper are stronger than those of the global fit to the top sector presented in Refs. [17, 18]. The prize to pay for this gain in precision is a loss of generality: the limits we derive are valid only under the assumption of equal coefficients for the four-fermion operators involving u-type and d-type quarks: \(C_1 = C_1^u=C_1^d\) and \(C_2 = C_2^u=C_2^d\). We believe, however, that this may be the most practical way to guarantee the validity of the effective operator approach with the current data sets. In the long run more precise data from LHC run 2 should allow to constrain the separate four-fermion operators of up-type and down-type quarks to safe intervals.^{5}

## 8 Comparison to a concrete new physics model

The limits on \(C_-\) can be recast into limits on the mass of a flavour-universal axigluon [21] (with equal couplings to all quarks) using the relation \((C_1 - C_2)/{ \Lambda ^2} = -4 g_s^2/m_{A}^2\) from Ref. [39]. The 95 % CL lower limit on the axigluon mass is 2.0 TeV. The axigluon with opposite-sign couplings to light and top quarks (\(g_t = - g_q\)), that makes a positive contribution to the charge asymmetry, is even more strongly constrained: \( m > \) 2.8 TeV. These limits extend the exclusion of earlier studies [42] considerably.

Both limits are well in excess of the 1.5 TeV that Ref. [39] quotes as the lower limit for application of the effective-operator analysis. We stress once more that these limits are valid only under the assumption that there are no new degrees of freedom below the scale \(\Lambda \).

With LHC run I the sensitivity for observation of a narrow signal on the SM \(t\bar{t}\) background has entered the sub-pb regime for a multi-TeV resonance. The ATLAS and CMS searches [43, 44] yield a 95 % CL lower limit on the axigluon mass of order 2 TeV. Limits from di-jet resonance searches at 13 TeV provide even stronger limits on this particular model [45].

## 9 Outlook to LHC run 2

During the preparation of this paper the analysis of LHC run 2 data is in full swing. CMS has published a first \(t\bar{t}\) cross-section measurement [46], while ATLAS has produced a preliminary result [47]. It is instructive to consider the effect of the inclusion of the 13 TeV results in the fit.

In 13 TeV *pp* collisions the \(q\bar{q} \rightarrow t\bar{t}\) process is further diluted by the increase in gluon-gluon-initiated \(t\bar{t}\) production. Therefore, the sensitivity of inclusive measurements to four-fermion operators is limited. In Fig. 5 the expected uncertainty on \(\bar{C}_{-}\) from the 13 TeV inclusive charge asymmetry measurement with a precision of 0.5 % is larger than that of the current LHC8 measurements with a similar precision. With the current uncertainty of approximately 15 % (dominated by the 10 % uncertainty of the preliminary estimate of the integrated luminosity) the cross-section measurements add no value to the fit. For inclusive measurements the interval of validity at 13 TeV is reduced only slightly, to \(-\)0.22 \(< \bar{C}_X <\) 0.22, and a two-parameter fit (with the assumption \(C_u = C_d \)) on measurements of comparable precision to those at 8 TeV is expected to yield a limit that remains within the interval of validity.

We already signalled in Sect. 4 that the excellent sensitivity to four-fermion operators of differential measurements, in particular measurements in the regime of boosted \(t\bar{t}\) pair production, compensates for their (current) relatively poor precision. As an example, consider highly boosted top quark pair production with \(m_{t\bar{t}} >\) 1.2 TeV, the top entry in Fig. 5. If a charge asymmetry is performed to 0.5 % precision an extremely tight constraint on four-fermion interactions can be derived. A problem for the inclusion of such measurements is the limited range of validity of the effective operator analysis for such measurements (due to large contributions from the \(\Lambda ^{-4}\) terms that are only partially known). Requiring that the \(\Lambda ^{-2}\) term dominates over \(\Lambda ^{-4}\) term reduces the interval accessible to the effective operator analysis to \(|\bar{C}_X| < \) 0.03, well below the current limits. To constrain the measurement the measurement of both \(\bar{C}_1\) and \(\bar{C}_2\) operators to this level would require a (relative) cross section measurement in the boosted regime with a precision of 4 % and a charge asymmetry measurement with a precision of 0.5 %, which is definitely challenging, but may not be impossible.

## 10 Summary

Top quark pair production data at hadron colliders provides a constraint on four-fermion interactions. Analyzing the relative sensitivities of pair production measurements at the Tevatron and the LHC we find that the cross-section and charge asymmetry measurements provide complementary constraints, where the latter are more powerful at the LHC. The sensitivity to four-fermion operators is strongly enhanced for measurements in the boosted regime.

Several authors [17, 39, 40] have signalled the importance of higher-dimension contributions of order (\({\Lambda }^{-4}\)) to high-energy collision data. We have ensured explicitly that these contributions, whose size is estimated as the contribution of the dimension-6 operator squared, are subdominant in our fit.

We have extracted limits on the dimension-6 operators \({C}_1\) and \({C}_2\), under the assumption of that the coupling strengths to up- and down-type quarks are identical (i.e. \({C}_1 = {C}_1^u = {C}_1^d\) and \({C}_2 = {C}^u_2 = {C}^d_2\)). The allowed intervals at 95 % CL, \(-\)0.06 \( < {C}_1 \times v^2/\Lambda ^2< \) 0.10 and \(-\)0.04 \( < {C}_2 \times v^2/\Lambda ^2 < \) 0.11, are in good agreement with the SM prediction \({C}_1 = C_2 =\) 0. These form stricter limits than those obtained from a global fit that includes the same data [17] (at what we believe is an acceptable loss of generality).

For an explicit UV completion such as the axigluon model these limits correspond to a lower limit on the mass in excess of 2 TeV, which is a competitive constraint when compared to direct limits from resonance searches.

## Footnotes

- 1.
ATLAS and CMS have also published differential cross section measurements at \(\sqrt{s} =\) 7 and 8 TeV [32, 33, 34, 35, 36]. These are not included in the fit as the measurements at low mass (or top \(p_T\)) provide a weak constraint, while the measurement at very high mass strongly restricts the validity interval (as discussed in Sect. 5).

- 2.
As we use a leading order calculation for the Standard Model contribution \(\sigma ^{SM}\) in Eq. (3) corresponds to the Born-level result. The charge asymmetry appears only at next-to-leading order in the SM, so the leading-order asymmetry in Eq. (4) is vanishes, \(A_{C}^{SM,Born} = \) 0. For the comparison with data NNLO+NNLL predictions are used for the purely Standard Model contribution, while the charge asymmetry \(A_C\) at the LHC is only available to NLO precision.

- 3.
This requirement ensures that the \(\chi ^2\) evaluation on the 68 % CL interval is within the \(A/A'>\) 2 \(C_i \left( \frac{1{{\mathrm {\ TeV}}}{}}{\Lambda }\right) ^2\) interval where the \(\Lambda ^{-4}\) is of minor importance. This is therefore equivalent to the criterion of Ref. [40].

- 4.
The matching of the intervals of validity of different measurements is quite delicate in a multi-parameter fit. For instance, we do not include the last bins of the differential cross section measurement of Ref. [33] in our fit. Even if the cross section measurements provides a powerful constraint on , as shown in Fig. 2a, the current charge asymmetry measurements cannot provide an equally stringent bound and the overall validity of the fit would be compromised.

- 5.
Ideally, one would float all four degrees of freedom in the fit when extracting the coefficients of the two-fermion operators, so as to avoid an artificial reduction of the uncertainty on these parameters. Then, the four-fermion operator constraints can be obtained under the assumption \(C_1 = C_1^u=C_1^d\) and \(C_2 = C_2^u=C_2^d\).

## Notes

### Acknowledgments

The authors gratefully acknowledge the help of Juan Antonio Aguilar and German Rodrigo in the preparation of the letter, the support of Celine Degrande while setting up the TopEffTh model and helpful discussion with the members of the TopFitter collaboration.

## References

- 1.V.M. Abazov et al., D0 Collaboration, First measurement of the forward-backward charge asymmetry in top quark pair production. Phys. Rev. Lett.
**100**, 142002 (2008). arXiv:0712.0851 - 2.T. Aaltonen et al., CDF Collaboration, Forward-backward asymmetry in top quark production in \(p\bar{p}\) collisions at \(\sqrt{s}=1.96\) TeV. Phys. Rev. Lett.
**101**, 202001 (2008). arXiv:0806.2472 - 3.V.M. Abazov et al., D0 Collaboration, Simultaneous measurement of forward-backward asymmetry and top polarization in dilepton final states from \(t\bar{t}\) production at the Tevatron. Phys. Rev.
**D92**(5), 052007 (2015). arXiv:1507.05666 - 4.D0 Collaboration, V.M. Abazov et al., Measurement of the forward-backward asymmetry in top quark-antiquark production in ppbar collisions using the lepton+jets channel. Phys. Rev. D
**90**, 072011 (2014). arXiv:1405.0421 - 5.CDF Collaboration, T. Aaltonen et al., Measurement of the top quark forward-backward production asymmetry and its dependence on event kinematic properties. Phys. Rev. D
**87**(9), 092002 (2013). arXiv:1211.1003 - 6.V.M. Abazov et al., D0 Collaboration, Forward-backward asymmetry in top quark-antiquark production. Phys. Rev. D
**84**, 112005 (2011). arXiv:1107.4995 - 7.T. Aaltonen et al., CDF Collaboration, Evidence for a mass dependent forward-backward asymmetry in top quark pair production. Phys. Rev. D
**83**, 112003 (2011). arXiv:1101.0034 - 8.W. Hollik, D. Pagani, The electroweak contribution to the top quark forward-backward asymmetry at the Tevatron. Phys. Rev. D
**84**, 093003 (2011). arXiv:1107.2606 - 9.M. Czakon, P. Fiedler, A. Mitov, Resolving the Tevatron top quark forward-backward asymmetry puzzle: fully differential next-to-next-to-leading-order calculation. Phys. Rev. Lett.
**115**(5), 052001 (2015). arXiv:1411.3007 - 10.C.M.S. Collaboration, Measurements of the \(t\bar{t}\) charge asymmetry using the dilepton decay channel in pp collisions at \(\sqrt{s} =\) 7 TeV. JHEP
**1404**, 191 (2014). arXiv:1402.3803 - 11.ATLAS Collaboration, Measurement of the top quark pair production charge asymmetry in proton-proton collisions at \(\sqrt{s}\) = 7 TeV using the ATLAS detector. JHEP
**1402**, 107 (2014). arXiv:1311.6724 - 12.C.M.S. Collaboration, Inclusive and differential measurements of the \(t \bar{t}\) charge asymmetry in proton-proton collisions at 7 TeV. Phys. Lett. B
**717**, 129–150 (2012). arXiv:1207.0065 - 13.ATLAS Collaboration, Measurement of the charge asymmetry in top quark pair production in \(pp\) TeV using the ATLAS detector. Eur. Phys. J. C
**72**, 2039 (2012). arXiv:1203.4211 - 14.CMS Collaboration,
*Inclusive and Differential Measurements of the*\(t \bar{t}\) 8 TeV. arXiv:1507.03119 - 15.CMS collaboration,
*Measurement of the Charge Asymmetry in Top Quark Pair Production in pp Collisions at*\(\sqrt{s} = 8\) TeV*Using a Template Method*. arXiv:1508.03862 - 16.ATLAS Collaboration,
*Measurement of the Charge Asymmetry in Top-quark Pair Production in the Lepton-Plus-Jets Final State in*\(pp\)*TeV with the ATLAS Detector*. arXiv:1509.02358 - 17.A. Buckley, C. Englert, J. Ferrando, D. J. Miller, L. Moore, M. Russell, C.D. White,
*Constraining Top Quark Effective Theory in the LHC Run II Era*. arXiv:1512.03360 - 18.A. Buckley, C. Englert, J. Ferrando, D.J. Miller, L. Moore, M. Russell, C.D. White, Global Fit of Top Quark Effective Theory to Data. Phys. Rev. D
**92**(9), 091501 (2015). arXiv:1506.08845 - 19.B. Grzadkowski, M. Iskrzynski, M. Misiak, J. Rosiek, Dimension-six terms in the standard model Lagrangian. JHEP
**10**, 085 (2010). arXiv:1008.4884 - 20.C. Zhang, S. Willenbrock, Effective-field-theory approach to top-quark production and decay. Phys. Rev. D
**83**, 034006 (2011). arXiv:1008.3869 - 21.O. Antunano, J.H. Kuhn, G. Rodrigo, Top quarks, axigluons and charge asymmetries at hadron colliders. Phys. Rev. D
**77**, 014003 (2008). arXiv:0709.1652 - 22.K. Agashe, A. Belyaev, T. Krupovnickas, G. Perez, J. Virzi, LHC signals from warped extra dimensions. Phys. Rev. D
**77**, 015003 (2008). arXiv:hep-ph/0612015 - 23.B. Lillie, L. Randall, L.-T. Wang, The Bulk RS KK-gluon at the LHC. JHEP
**09**, 074 (2007). arXiv:hep-ph/0701166 - 24.M. Czakon, P. Fiedler, A. Mitov, Total top-quark pair-production cross section at hadron colliders through \(O( \alpha \frac{4}{S} )\). Phys. Rev. Lett.
**110**, 252004 (2013). arXiv:1303.6254 - 25.CDF, D0 Collaboration, T.A. Aaltonen et al., Combination of measurements of the top-quark pair production cross section from the Tevatron collider. Phys. Rev. D
**89**(7), 072001 (2014). arXiv:1309.7570 - 26.CMS and ATLAS collaborations,
*Combination of ATLAS and CMS Top Quark Pair Cross Section Measurements Using Proton–Proton Collisions at 8 TeV, CMS-PAS-TOP-14-016, ATLAS-CONF-2014-054*. (2014). http://cds.cern.ch/record/1951322 - 27.W. Bernreuther, Z.-G. Si, Top quark and leptonic charge asymmetries for the Tevatron and LHC. Phys. Rev. D
**86**, 034026 (2012). arXiv:1205.6580 - 28.J.H. Kuhn, G. Rodrigo, Charge asymmetries of top quarks at hadron colliders revisited. JHEP
**01**, 063 (2012). arXiv:1109.6830 - 29.ATLAS collaboration,
*Measurement of the Charge Asymmetry in Highly Boosted Top-Quark Pair Production in*\(\sqrt{s} =\)*Collision Data Collected by the ATLAS Experiment*. arXiv:1512.06092 - 30.J.A. Aguilar-Saavedra, D. Amidei, A. Juste, M. Perez-Victoria, Asymmetries in top quark pair production at hadron colliders. Rev. Mod. Phys.
**87**, 421–455 (2015). arXiv:1406.1798 - 31.J.L. Hewett, J. Shelton, M. Spannowsky, T.M.P. Tait, M. Takeuchi, \(A^t_{FB}\) Meets LHC. Phys. Rev. D
**84**, 054005 (2011). arXiv:1103.4618 - 32.ATLAS collaboration,
*Measurements of Top-Quark Pair Differential Cross-Sections in the Lepton+Jets Channel in*\(pp\)*TeV Using the ATLAS Detector*. arXiv:1511.04716 - 33.ATLAS Collaboration,
*Measurement of the Differential Cross-Section of Highly Boosted Top Quarks as a Function of their Transverse Momentum in*\(\sqrt{s}\) =*8 TeV Proton-Proton Collisions Using the ATLAS Detector*. arXiv:1510.03818 - 34.ATLAS Collaboration, Differential top-antitop cross-section measurements as a function of observables constructed from final-state particles using pp collisions at \(\sqrt{s}=7\) TeV in the ATLAS detector. JHEP
**06**, 100 (2015). arXiv:1502.05923 - 35.ATLAS Collaboration, Measurements of top quark pair relative differential cross-sections with ATLAS in \(pp\) TeV. Eur. Phys. J. C
**73**, 2261 (2013). arXiv:1207.5644 - 36.CMS Collaboration, Measurement of the differential cross section for top quark pair production in pp collisions at \(\sqrt{s} = 8\,\text{ TeV } \). Eur. Phys. J. C
**75**(11), 542 (2015). arXiv:1505.04480 - 37.J. Alwall, R. Frederix, S. Frixione, V. Hirschi, F. Maltoni, O. Mattelaer, H.S. Shao, T. Stelzer, P. Torrielli, M. Zaro, The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations. JHEP
**07**, 079 (2014). arXiv:1405.0301 - 38.C. Degrande, C. Duhr, B. Fuks, D. Grellscheid, O. Mattelaer, T. Reiter, UFO—the universal FeynRules output. Comput. Phys. Commun.
**183**, 1201–1214 (2012). arXiv:1108.2040 - 39.C. Degrande, J.-M. Gerard, C. Grojean, F. Maltoni, G. Servant, Non-resonant new physics in top pair production at Hadron colliders. JHEP
**03**, 125 (2011). arXiv:1010.6304 - 40.W. Bernreuther, D. Heisler, Z.-G. Si,
*A Set of Top Quark Spin Correlation and Polarization Observables for the LHC: Standard Model Predictions and New Physics Contributions.*arXiv:1508.05271 - 41.F. James, M. Winkler, “MINUIT User’s Guide” (2014). http://seal.web.cern.ch/seal/documents/minuit/mnusersguide.pdf
- 42.P. Ferrario, G. Rodrigo, Constraining heavy colored resonances from top-antitop quark events. Phys. Rev. D
**80**, 051701 (2009). arXiv:0906.5541 - 43.ATLAS collaboration, A search for \( {t}\overline{t} \) TeV with the ATLAS detector. JHEP
**08**, 148 (2015). arXiv:1505.07018 - 44.
- 45.CMS collaboration,
*Search for Narrow Resonances Decaying to Dijets in Proton-Proton Collisions at sqrt(s) = 13 TeV*. arXiv:1512.01224 - 46.CMS collaboration,
*Measurement of the Top Quark Pair Production Cross Section in Proton–Proton Collisions at*\(\sqrt{s}=13\)*TeV*. arXiv:1510.05302 - 47.ATLAS collaboration,
*Measurement of the*\(t\bar{t}\)*Events with b-Tagged Jets*(2014). http://cds.cern.ch/record/2038144

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