Binning optimisation and unfolding

The unfolding of A_Cvsm_tt¯requires optimisation of the∆|y|binning, which is performed in a similar manner as the optimisation described in Sec.7.5, using linearity test with injected asymmetry predicted by light-mass axigluon models. Four∆|y|bins are used in a similar manner as in the single-lepton channel, to map the migrations in a sufficiently-accurate manner, and the samem_t¯t bins are used as the two highest-m_tt¯bins used in the single-lepton channel. The∆|y|binning is obtained by performing the linearity test for various values of the inner∆|y|bin edge,x, in the [−5,−x,0,x,5] binning. The∆|y| inner bin edge is scanned in steps of 0.1 for bothm_t¯t bins independently, performing a two-dimensional scan. The figure of merit for the choice of∆|y|binning is theR-factor:

R=

wheres_iando_iare the slope and offset from the linearity tests, for thei^thunfoldedm_tt¯bin. The metric is designed to penalise binning choices that yield non-unity slopes and non-zero offsets.

It is observed, that no choice of binning can achieve a slope compatible with one. The problem arises from the extrapolation to full phase space in∆|y|at parton level. The event selection criteria limit the large-Rjets to satisfy|η| <2.0. This effectively means, that approximately beyond|∆|y| |>2.0, no events are reconstructed. When injecting axigluon-induced BSM asymmetries, the charge asymmetry contribution is more enhanced in the tails of the ∆|y| distribution, reaching beyond the detector acceptance. At detector level, the enhancement of asymmetry is therefore smaller than at parton level due to the insensitivity to|∆|y| |>2.0, resulting in an underestimation of the magnitude of the unfolded asymmetry.

A possible solution to the linearity non-closure is to impose fiducial cuts at the parton level on

∆|y|observable. The linearity test is repeated with|∆|y| |< 2.0 fiducial cut, yielding linearity with slope compatible with one. The best-linearity binning for fiducial and for full-phase-space unfolding is shown in Table8.13. Restricting the parton-level∆|y|using fiducial cuts yields an out-of-fiducial tt¯background, constituted by signal events which do not pass parton-level fiducial cuts, but migrate

8.5. Expected sensitivity of the all-hadronictt¯charge asymmetry

into the signal region at detector level. It is found however, that the contribution of this background is approximately 0.03 % and is therefore neglected.

The disadvantage of the fiducial unfolding is that it introduces differences in the∆|y|definition with respect to the single-lepton channelA_Cmeasurement, complicating a potential combination. If a combination of multiple channels directly at the level of unfolding is desired, similarly to how resolved and boosted regions are combined in the single-lepton channel A_Cmeasurement, it is necessary to ensure that the parton-level∆|y|binning is the same. Both full phase space and fiducial unfolding is studied further in this analysis to asses the impact of the extrapolation to full phase space on the uncertainty of the unfolded A_Cand also on the magnitude of the extracted asymmetry.

In Fig.8.22, the migration matrix for the∆|y|vsm_tt¯double-differential distribution is shown. In general, the migrations between the differential bins reach up to 15 % in the highest-m_tt¯bin. This is a significantly lower value than in case of the single-lepton channel, where the migrations between the two highest-mt¯t bins reach up to 25 % in resolved and 30 % in boosted regions, as can be seen inm_tt¯

vs∆|y|migration matrices in App.C.1. The migrations between inner and outer∆|y|bin for the same

∆|y|sign are also smaller in the all-hadronic channel than in the single-lepton channel. The resolved single-lepton channels suffer from migrations due to mis-measurement of neutrino momentum and wrong jet-to-parton assignment. In boosted single-lepton channel the latter challenge is circumvented by reconstructing the hadronic top quark as a single large-Rjet, but the neutrino reconstruction remains an under-constrained problem.

Finally, the implicitm_tt¯ > 1000 GeV restriction in the parton-level binning in the all-hadronic channel leads to a non-fiducial contribution of events below thism_tt¯threshold, which are reconstructed withmt¯t > 1000 GeV, passing the signal region selection. The contribution of this background is 6.5 % in them_tt¯ ∈[1000,1500] GeV bin, and is negligible in them_tt¯>1500 GeV bin.

Table 8.13: The∆|y|binning for inclusive and differentialA_Cunfolding. Both the slope and the offset from the linearity test are shown, along with their uncertainties from the fit.

Differential bin ∆|y|binning Linearity

slope offset

Full phase space unfolding

m_tt¯ ∈[1000,1500] GeV [-5,-0.9, 0,0.9, 5] 0.880±0.010 -0.0000±0.0003 m_tt¯ >1500 GeV [-5,-1.1, 0,1.1, 5] 0.914±0.014 -0.0007±0.0005

Fiducial unfolding (|∆|y| |< 2.0)

m_tt¯ ∈[1000,1500] GeV [-5,-0.9, 0,0.9, 5] 0.993±0.011 -0.0006±0.0003 m_tt¯ >1500 GeV [-5,-1.2, 0,1.2, 5] 0.982±0.015 -0.0004±0.0005

8. Prospect of charge asymmetry measurement in boosted all-hadronictt¯events

10 20 30 40 50 60 70 80 90 100

Migration rate [%]

5 1 15 3 2 1

1 17 2 1

17 1 1 2

15 1 4 1 2 3

12 3 2 1 15

2 10 2 15

2 10 1 15

2 12 14 2

[TeV]

t

Reco mt

[TeV] ttTruth m

72 80

80 74

68 70

70 69

[1, 1.5]

[1, 1.5]

> 1.5 > 1.5

Fig. 8.22: Migration matrix of the∆|y| vsm_tt¯ double-differential distribution in the boosted all-hadronic channel, using the binning for full-phase-space unfolding. The groups of four bins correspond to the four∆|y|bins for a givenm_t¯t bin specified by the axis labels. The precise∆|y|binning is listed in Table8.13.

8.5.4 Systematic uncertainties

The systematic uncertainties evaluated for theA_CAsimov estimate are the same as those in Sec.8.4.1, with an addition of uncertainties on the multijet background estimate, the uncertainty on the NN discriminant modelling described in Sec.8.4.3, and the uncertainties related to unfolding.

The uncertainty on the NN discriminant, derived in Sec.8.4.3, is propagated to the all-hadronict¯t events, by applying weights to the two hadronic top-quark large-Rjet candidates, where depending on whether the jet is matched to a parton-level top quark or top anti-quark, the weight is calculated from the corresponding fitted dependence of the weight on NN discriminant previously shown in Fig.8.15.

The systematic uncertainties on the MC modelling of the non-all-hadronictt¯and single top-quark backgrounds are neglected. The normalisation uncertainties previously quoted in Table 6.5 are considered.

A number of assumptions are made in the multijet background estimate. The regions used for the estimate, including the regions used to correct for correlations between large-Rjet top-quark tagging andb-tagging, include a small contamination by non-multijet processes. No systematic uncertainties are propagated on this contamination except for the statistical uncertainties of both data and the contributions of the non-multijet processes. Strictly speaking, the systematic uncertainties on the non-multijet MC-simulated contributions in the individual regions should be propagated. For this preliminary estimate, omitting this systematic uncertainties propagation is motivated by the fact that the non-multijet contamination in the individual regions is below 10 %. Because of the different shape of the multijet background∆|y|distribution compared to the signal∆|y|distribution, both normalisation and shape effects in the modelling of the multijet background can alter the unfoldedA_C. As such, a 50 % normalisation uncertainty on the multijet background is added in the unfolding but not included