4.2.2. Measurements at <sup>√</sup>*<sup>s</sup>* <sup>=</sup> 8 TeV

The measurements at <sup>√</sup>*<sup>s</sup>* <sup>=</sup> 8 TeV with the full statistics were performed by both ATLAS and CMS in both -+jets and dilepton channels.

ATLAS performed two measurements in the -+jets channel using 20.3 fb−<sup>1</sup> [109,110]. In the first analysis, the asymmetry is measured inclusively (*AC* = (0.9 ± 0.5(stat. + syst.))%) and also differentially as a function of *mt*¯*t*, *yt*¯*t*, *p*T,t¯t, and *βz*,*t*¯*t*, see Figure 32 using standard unfolding procedure [109]. The inclusive measurement is compatible with the NNLO QCD + NLO EW prediction (0.97+0.02 <sup>−</sup>0.03)%. The second measurement focused on a large *<sup>t</sup>*¯*<sup>t</sup>* invariant mass region (*mt*¯*<sup>t</sup>* <sup>&</sup>gt; 0.75 TeV, another requirement is |Δ|*y*|| < 2) using reconstruction techniques specifically designed for the decay topology of highly boosted top quarks. In such cases, hadronicaly decaying top quarks are reconstructed as single large-radius jets with a specific jet substructure. In such phase space, the asymmetry is measured to be *At*¯*<sup>t</sup>* <sup>C</sup> = (4.2 ± 3.2(stat. + syst.))%. A differential measurement as a function of *mt*¯*t*is also performed, see Figure 33.

**Figure 32.** Measured *A*<sup>C</sup> values as a function of *mt*¯*<sup>t</sup>* in (**a**), *βz*,*t*¯*<sup>t</sup>* in (**b**), and *p*T,t¯t in (**c**), compared with NLO QCD + NLO EW predictions [24] and with the right-handed color octets with masses below the *t*¯*t* threshold [109].

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

CMS also performed two measurements in the -+jets channel using 19.7 fb−<sup>1</sup> [112] and 19.6 fb−<sup>1</sup> [113], respectively. In the first measurement [112], the asymmetry is measured inclusively (*At*¯*<sup>t</sup>* <sup>C</sup> = (0.10 ± 0.68(stat.) ± 0.37(syst.))%) and also differentially as a function of *mt*¯*t*, *yt*¯*t*, and *p*T,t¯t. Moreover, CMS performed here the first LHC measurement at the particle level in the fiducial phase space mimicking the selection criteria. The inclusive fiducial (*At*¯*t*, *fid <sup>C</sup>* = (−0.35 ± 0.72 ± 0.31)%) and differential measurements as a function of *mt*¯*t*, *yt*¯*t*, and *p*T,t¯t, see Figure 34, are consistent with NLO QCD + EW prediction (inclusive prediction is (1.01 ± 0.10)%).

**Figure 34.** The charge asymmetry as a function of *yt*¯*<sup>t</sup>* in (**a**), *p*T,t¯t in (**b**), and *mt*¯*<sup>t</sup>* 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].

The second CMS measurement in the -+jets channel used a template method [113]. In this method, templates based on the SM were created for symmetric and antisymmetric components of the measured distribution (*Υt*¯*<sup>t</sup>* = tanh <sup>Δ</sup>|*y*|) for various *<sup>t</sup>*¯*<sup>t</sup>* production processes, see Figure 35. Fitting data to these templates, see Figure 36, the inclusive asymmetry was measured: *At*¯*<sup>t</sup>* <sup>C</sup> = (0.33 ± 0.26 ± 0.33)% which was the most precise measurement of *A*<sup>C</sup> at that time. However, the disadvantage of this measurement was that it was more model dependent on SM predictions compared to usual unfolding measurements.

**Figure 35.** The symmetric (**left**) and antisymmetric (**right**) components of the binned probability distributions in the observable *Υt*¯*t*, constructed using POWHEG generator for different *t*¯*t* initial processes [113].

**Figure 36.** The antisymmetric *t*¯*t* contribution is measured in the *Υrec <sup>t</sup>*¯*<sup>t</sup>* distribution. The antisymmetric component of the *Υrec <sup>t</sup>*¯*<sup>t</sup>* 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 *μ*+jets (**right**) channels [113].

In the dilepton channel using 20.3 fb−1, ATLAS measured the *t*¯*t* and dileptonic asymmetry at parton level in the full phase space and at the particle level in the fiducial phase space [111]. Both, the inclusive measurements at parton level (*At*¯*<sup>t</sup>* <sup>C</sup> = (2.1 ± 1.6(stat. + syst.))%, *A*-- <sup>C</sup> = (0.8 <sup>±</sup> 0.6(stat. <sup>+</sup> syst.))%) and particle level (*At*¯*<sup>t</sup>* <sup>C</sup> = (1.7 ± 1.8(stat. + syst.))%, *A*-- <sup>C</sup> = (0.6 ± 0.5(stat. + syst.))%) are consistent with the predictions. The differential measurements in two bins were measured as a function of *mt*¯*t*, *<sup>p</sup>*T,t¯t, and *<sup>β</sup>z*,*t*¯*<sup>t</sup>* for both *<sup>A</sup>t*¯*<sup>t</sup>* <sup>C</sup> and *<sup>A</sup>*-- <sup>C</sup> in both full and fiducial phase spaces. The summary of dileptonic asymmetry measurements in the fiducial phase space is in Figure 37. The difference between the results at the parton and particle level is small given that the *t*¯*t* modeling systematics is not a dominant uncertainty.

**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].

CMS also measured the asymmetry in the dilepton channel using 19.5 fb−<sup>1</sup> [114]. It measured the *t*¯*t* and dileptonic asymmetry inclusively (*At*¯*<sup>t</sup>* <sup>C</sup> = (1.1 <sup>±</sup> 1.1(stat.) <sup>±</sup> 0.7(syst.))%, *<sup>A</sup>*-- <sup>C</sup> = (0.3 ± 0.6(stat.) ± 0.3(syst.))%) and also differentially as a function of *mt*¯*t*, *yt*¯*t*, and *p*T,t¯t.

ATLAS and CMS combined their measurements performed at <sup>√</sup>*<sup>s</sup>* <sup>=</sup> 7 TeV and <sup>√</sup>*<sup>s</sup>* <sup>=</sup> 8 TeV [91]. Only measurements of the *t*¯*t* asymmetry in the -+jets channel are combined. The measurements in the dilepton channel were statistically limited and their inclusion would not improve the overall uncertainty. The combination of inclusive measurements at <sup>√</sup>*<sup>s</sup>* <sup>=</sup> 7 TeV and <sup>√</sup>*<sup>s</sup>* <sup>=</sup> 8 TeV yielded *At*¯*t* <sup>C</sup> = (0.5 <sup>±</sup> 0.7(stat.) <sup>±</sup> 0.6(syst.))% and *<sup>A</sup>t*¯*<sup>t</sup>* <sup>C</sup> = (0.55 ± 0.23(stat.) ± 0.25(syst.))%, respectively. The CMS template measurement at <sup>√</sup>*<sup>s</sup>* <sup>=</sup> 8 TeV [113] was used in the combination for the inclusive measurement while CMS unfolding measurement at <sup>√</sup>*<sup>s</sup>* <sup>=</sup> 8 TeV [112] was used for the combination of differential measurements as a function of *mt*¯*t*. The summary of the inclusive Tevatron forward–backward and LHC 8 TeV charge asymmetry measurements together with the predictions of various BSM models is shown in Figure 14. The combined ATLAS+CMS charge asymmetry as a function of the invariant mass of the *t*¯*t* system in comparison with theoretical predictions for the SM and two versions of a color-octet model is shown in Figure 38.

**Figure 38.** The combined ATLAS+CMS charge asymmetry as a function of *mt*¯*<sup>t</sup>* in comparison with theoretical predictions for the SM [24,32] and two versions of a color-octet model [91].

In summary, the measurements at <sup>√</sup>*<sup>s</sup>* <sup>=</sup> 8 TeV provided a significant progress compared to <sup>√</sup>*<sup>s</sup>* <sup>=</sup> 7 TeV measurements. The measurements still agree with the SM prediction. Both the statistical and systematic uncertainties decreased almost at the same rate. The most precise individual inclusive measurement had an uncertainty of about 0.42% while the combined 8 TeV measurement had a precision of 0.33%. For the first time, the statistical uncertainty was no longer dominating the uncertainty in all measurements. The systematic uncertainties were smaller or similar to the statistical ones in the CMS template measurement, most of the ATLAS dilepton measurements, the ATLAS high *mt*¯*<sup>t</sup>* measurement, and the LHC combination at <sup>√</sup>*<sup>s</sup>* <sup>=</sup> 8 TeV. The first fiducial level measurements at particle level were performed although their advantage was not yet much visible due to the fact that *t*¯*t* modeling systematics were still not dominant uncertainties. In addition, a specific measurement at high *mt*¯*<sup>t</sup>* was performed.
