8 Systematic Uncertainties
8.5 NLO and Off-Shell Effects in the Top Quark Decay
Figure 8.4:Systematic uncertainties on the decay widthΓtfor all individual nuisance parame-ters (NP) of the three compared PDF sets. The quoted PDF set uncertainty is indicated by the error bar on the right.
8.5 NLO and Off-Shell Effects in the Top Quark Decay
The nominalt¯tMC sample used to derive templates for the decay width measurement is based on a generator setup with NLO matrix elements for the production oft¯tpairs and LO matrix elements for the decay of top quarks, containing an approximate implementation of finite width and interference effects. A recently published theoretical study[291]using the dileptoneµdecay channel oft¯tpairs indicated that off-shell effects which comprise not only the t¯t contribution but alsoW t single top events (plus a negligible contribution of diboson events withW bW bin the final state), in addition to their interference, may have a large impact on mass observables likem`b. Observables which are only based on angles like∆Rmin(jb,jl)are not affected to a large extent and, thus, the discussion concentrates on m`b. This can influence precision measurements in the top quark sector as the Γt measurement significantly. Since no MC implementation of NLO decay and off-shell effects is available in the lepton+jets decay channel used in this analysis, various studies were conducted in order to investigate the consequences of disregarding NLO and off-shell effects in thet¯t decay, visible in them`bdistributions. The results of these tests are discussed in the following.
Several MC generator setups were implemented by theorists in the recent past which consider these additional NLO and off-shell effects in the t¯t decay. However, these generators are still in development and thus neither included in the ATLAS simulation framework nor tuned to data yet because of free parameters in the generator setup. The studies presented in this section are mainly based on those initial test samples.
A new generator implementation that offers NLO precision in t¯t decay but does not allow for a consistent treatment of top quark resonance effects is denoted as ttb_NLO_dec [292]. As
the nominal t¯t generators used in this analysis, the new setup is based on the PO W H E G-BO X
framework. Another, more sophisticated NLO+PS generator was implemented in the PO W H E G -BO X-RE S framework [293], referred to asbb4l[291]. It contains NLO matrix elements for the process pp→`+ν``−ν¯`b¯b, uses the resonance-aware method in PO W H E G and is interfaced with PY T H I A8[277, 294]. The resonance-aware method or resonance-aware matching refers to a gen-eral NLO+PS matching technique where resonances are treated consistently, described in Ref.[293]. The physics features of this new generator setup comprise full NLO accuracy in t¯t production and decay, the mentioned NLO+PS treatment of top quark resonances, which involves quantum cor-rections to propagators of the top quark, and off-shell top quark decay chains. The setup takes exact spin correlation at NLO and interference between NLO radiation from top quark production and decay as well as an improved modelling of bquark kinematics into account. Furthermore, a unified treatment of t¯t andW t single top processes with NLO interferences is implemented. Such an approach is completely new because previous generations of MC generators rely on simulating each process separately.
The performed studies are based on these two recently developed generators, particularly on the bb4limplementation. Although this generator setup is not included in the ATLAS framework, the performed tests are sufficient to make first estimates of the impact of missing NLO and off-shell effects on the current nominal t¯t generators.
Differences between the nominal t¯t generator with LO precision in decay with leading leg cor-rections (denoted astt) and thebb4lsetup as provided in[291]are shown in Fig. 8.5a for the parton level. Since an absolute difference between the two distributions originates from the missing W t events for the standardttsetup, the two histograms are normalised to unity to visualise shape differences between the generator approaches.
Very recently the authors of [291] simulated the missing W t contribution to allow for a more consistent comparison between the LO and NLO generator setups, shown in Fig. 8.5b.
The discrepancies between the two samples in the high mass region of m`b are very distinct in case single topW t events are not included in thettsetup. This effect seems to be compensated by theW t events to a large extent. Currently, efforts by the authors of Ref.[291]aim at a better understanding of these different shape effects, as several mass observables other thanm`bdo not show such shape modifications after adding W t events. Since severe differences in the region of large m`b values are observed in the two plots of Fig 8.5, many studies were realised also in the course of this analysis to understand the impact of the region of large m`b values on the measurement ofΓt.
The first study focussed on the question whether alternativet¯tsignal MC samples used to estimate signal model uncertainties reveal similar shape effects as observed in Fig 8.5. With respect to the nominal PO W H E G+PY T H I A6t¯t event generator, most alternative setups introduce less significant shape differences. Only the differences between a PO W H E G+PY T H I A6 sample withhdamp =∞ and a PO W H E G+HE RW I Gsample, on which the evaluation of the parton shower and hadronisation model uncertainty is based (Sec. 8.4), are relatively close to the shape effects visible in Fig. 8.5.
8 . 5 N L O A N D O F F - S H E L L E F F E C T S I N T H E T O P Q U A R K D E C AY
(a) (b)
Figure 8.5:Distributions ofm`bafter normalisation to unity for two MC generator setups offering LO precision int¯tdecay (tt) or NLO precision (bb4l). Thettsample is shown (a) without single topW tevents or (b) with theW tcontribution.
Such a comparison is illustrated in Fig. 8.6, underlining that the trend of the shape difference in the high mass region is similar betweenbb4lvs. ttand PO W H E G+PY T H I A6 vs. PO W H E G+HE RW I G. However, it cannot be concluded that the differences between the LO and the NLObb4lgenerator are covered by the parton shower and hadronisation model uncertainty because the discrepancies between the two samples seen at parton level do not translate into large differences between PO W H E G+PY T H I A6 and PO W H E G+HE RW I Gat reconstruction level. The relatively small effect at reconstruction level translates into a parton shower and fragmentation model uncertainty of less than 0.1 GeV. As mentioned above, such a reconstruction level analysis is not yet possible for the new generator implementations. Thus, other methods are necessary to estimate the missing NLO and off-shell effects although it is still noteworthy that a PO W H E G+HE RW I G generator is able to partly describe expected shape variations due to these effects.
Since the shape effects in the region of large m`b values are not very well understood yet, the effect of applying cuts on the observable m`b in order to remove the right tail was investigated.
According to Fig. 8.5a, deviations betweenbb4landttsamples increase more and more for values abovem`b=150 GeV. In the same region, adding theW t events has a large impact. Hence, a cut value of 150 GeV was chosen and most systematic uncertainties as defined for the baseline analysis were evaluated using the full∆Rmin(jb,jl)range but only using events withm`b<150 GeV. The evaluation revealed that the total systematic uncertainty increases by around 29% after removing the large mass tail. This increase is equivalent to adding a further single systematic uncertainty of around 0.6 GeV, caused by this requirement onm`b. After having obtained the final result for the fit to data, the influence of removing the largem`b tail on data could be estimated. The difference
(a) (b)
Figure 8.6: Distributions for the observable m`b at parton level in the (a) electron+jets and (b) muon+jets channel for events with at least oneb-tagged jet. Illustrated are the differences between a Powheg+Pythia6 and a Powheg+Herwig sample which are utilised to derive the parton shower and hadronisation model uncertainty as well as the differences between the two generator setups offering LO precision in decay (tt) or NLO precision (bb4l). To visualise shape effects and to allow for a better comparison, the distributions are normalised to unity. The lower panels contain the ratio between the Powheg+Pythia6 and a Powheg+Herwig histograms (dark yellow, dotted line) and between the LO and NLO generator approaches (blue, dashed line). The uncertainty bands comprise only statistical uncertainties.
in the final result amounts to 0.45 GeV, stable for cut values ofm`bbetween 140 and 160 GeV. This value is slightly smaller than the expected systematic effect of 0.6 GeV determined from pseudo-experiments but is still comparable. Assuming that NLO and off-shell effects are mainly present in the region of largem`bvalues, these studies represent a first rough approximation of those effects missing in the nominal t¯tMC samples.
Due to the fact that these cuts on m`b have to be applied to reconstruction level distributions, despite being motivated by the parton level distributions in Fig. 8.5, the correlations between the parton and reconstruction level histograms need to be investigated. Correlation plots for the two considered pseudorapidity regions and b-tag bins are given in Fig. 8.7, as an example for the muon+jets channel.
The two-dimensional distributions reveal, similar to the corresponding electron+jets channel plots, that the reconstruction level masses are slightly shifted to larger values. A cut on m`b applied on reconstruction level removes more (and other) events than such a cut applied on parton level.
Hence, cutting away events at reconstruction or parton level may lead to slightly different resulting systematic shifts, again emphasising the approximate character of the studies discussed above.
8 . 5 N L O A N D O F F - S H E L L E F F E C T S I N T H E T O P Q U A R K D E C AY
(a) (b)
(c) (d)
Figure 8.7:Correlation between parton level and reconstruction level distributions ofm`bin the muon+jets channel. Shown are two-dimensional histograms for events with (a,c) exactly one and (b,d) at least twob-tagged jets as well as events in the two pseudorapidity regions, (a,b)|η| ≤1 and (c,d)|η|>1, respectively. The correlation values range from 55% to 67%.
Nevertheless, the distributions contained in Fig. 8.7 have considerably large correlation values, and since the above tested values between 140 and 160 GeV for the cut yields similar values, a requirement ofm`b<150 GeV is justified for such an estimate.
The differences between the two distributions given in Fig. 8.5b after adding theW t contribution to the tt sample are expected to originate from NLO and off-shell effects. Consequently, the deviations visible in the ratio plot can be utilised to reweight the m`bdistribution of the nominal t¯t sample used in this measurement. The weights derived at truth level were transferred to the corresponding events at reconstruction level to obtain properly reweighted observable templates.
These reweighted distributions were treated as a systematic variation so that the standard treatment to evaluate systematic uncertainties as presented in Sec. 8.1 could be applied. 1,000 pseudo-experiments were performed. A comparison of the resulting mean values yields a shift of the measured top quark decay width of -0.42 GeV, a value close to the total signal model uncertainty obtained for this measurement. As the reweighting relies on a sample which has not been validated, the resulting difference is not included in the systematic uncertainties onΓt.
Nonetheless, both approaches to estimate the effect of missing NLO precision and further off-shell and non-resonant effects, the cut onm`band the reweighting procedure, can be regarded as first estimates of these effects. As these studies predict differences of around or less than 0.5 GeV, the influence on the final result of such a precision measurement is not negligible. The obtained numbers indicate that ignoring such effects may undersestimate the total systematic uncertainty.
Future analyses would thus benefit from MC samples providing an NLO description of the t¯t decay in different channels as well as off-shell effects to allow for well-justified quantitative statements and to verify whether uncertainties are in fact underestimated.