For estimating the background from Multijet events at the LHC, conventional MC predictions are only applicable in a limited number of cases.
With the given event selection, the Multijet background is a pure fake contribution. As already men- tioned in section 4.2.1, fake light leptons originating from jets are not very likely. Only the huge cross- section of QCD processes at the LHC causes contributions by a large extent to the total background after baseline event selection and in the control regions.
Due to the rareness of these Multijet fakes, an unfeasible amount of MC would be needed to generate enough statistics and therefore, alternative approaches are commonly used in many analyses. These utilize
4.4 Data-driven Estimate for the Multijets Background
Tau matched truth particle
d u s c b e μ τ gγ Z W Events 0 1000 2000 3000 4000 5000 6000 -1 = 8 TeV, 20.3 fb s
τ Standard Model W+jets Z+jets Top Quarks Dibosons
t channel μ +
(a) Z+jets CR in the τ+µ channel.
bt
Tau matched truth particle
d u s c b t e μ τ gγ Z W Events 0 2000 4000 6000 8000 10000 12000 -1 = 8 TeV, 20.3 fb s +e channel
τ Standard Model W+jets Z+jets Top Quarks Dibosons
(b) Z+jets CR in the τ+e channel.
Figure 4.13: Truth origin of the tau candidate in the Z+jets control region.
observations from the 2012 data to estimate the Multijet contribution. Depending on the selection of physics objects, various methods have been developed. The technique which is used in this analysis is based on a data-driven approach with a matrix method [204].
This procedure exploits the fact that falsely reconstructed leptons from Multijet events tend to have a weaker isolation than real leptons. For the same reason, the isolation of leptons was also used as an identification criterion in the physics object definition (compare section 4.1.1).
loose selection tight selection fake leptons real leptons εfake εreal
Figure 4.14: Illustration of the matrix method.
The method is illustrated in figure 4.14: The normal selection of signal leptons, as defined in section 4.1.1, shall be denoted as the tight selection. It is indicated by the hatched area in the illustration. The tight selection leads to a distinct number of events NTobswhich is the sum of the number of events with real leptons NTrealand the number of events where the lepton was a Multijet fake NTfake:
NTobs= NTreal+ NTfake. (4.11)
The latter is the needed background estimate. In figure 4.14 events with fake leptons are represented by the blue area, while events with real leptons are shown in red.
By loosening the selection criteria for leptons, a larger number of events NLobsis considered. For this, the baseline selection as defined in section 4.1.1 is used. For this loose selection, which is illustrated by the full colored area in figure 4.14, in particular the isolation criterion is dropped. As a result, more fake than real leptons enter the loose selection.
The ratio of the selection efficiency from loose to tight for purely fake lepton events is denoted by εfake
and the one for real leptons events by εreal. The number of observed events in the tight selection can then
be written as
NobsL = NLreal+ NLfake= εrealNTreal+ εfakeNTfake. (4.12)
If the ratios εfakeand εrealare known, equations 4.11 and 4.12 are solvable for NTfake, while depending only
on the total observed number of events for the tight and loose selection NTobsand NLobs: NTfake= N
obs
L − NTobsεreal
εfake− εreal
(4.13) To obtain the ratio εreal, a tag-and-probe method in a Z→ ℓ+ℓ−control region is used. εfakeis measured
in a Multijet-enriched control region where residual contributions from other background types are subtracted according to their MC predictions [204].
The measurements are binned in pTand η which allows for obtaining not only the prediction of the
total number of fake events with a particular selection, but also information about the correct shape of observables.
As described in section 4.1.4, prescaled triggers are used to account for the fact that the isolation criterion on the light lepton needs to be dropped completely in the loose selection. A possible influence of pile-up effects due to different prescale conditions can be ruled out by comparing the distributions of
the average number of interactions per bunch-crossing in both trigger selections. For the τ+e channel,
which has larger contributions from Multijet fakes, these distributions are displayed for the three control regions W+jets, Top Truth and Top Fake in figure 4.15. No significant difference is observed with using the prescaled trigger.
mean int. per bunch-crossing
0 5 10 15 20 25 30 35 40 0 2000 4000 6000 8000 10000 12000 14000 Prescaled Unprescaled Events
(a) W control region
mean int. per bunch-crossing
0 5 10 15 20 25 30 35 40 Events Prescaled Unprescaled 0 20 40 60 80 100 120 140 160 180 200
(b) top truth control region
Unprescaled Prescaled
mean int. per bunch-crossing
0 5 10 15 20 25 30 35 40 0 Events 100 200 300 400 500 600 700 800
(c) top fake control region
Figure 4.15: Distributions of the average number of interactions per bunch-crossing for prescaled and unprescaled triggers in the τ+e analysis.
Control distributions to validate the predictions of the matrix method are displayed in figure 4.16. These distributions are observed after the baseline selection without any further kinematic cuts, because here most of the Multijet background is still passing the selection. Figures 4.16a and 4.16b display the transverse mass distribution which was already used as an example before applying the scale factors in figure 4.5, where most of the Multijet background is found at small masses below the Jacobian peak of the W+jets background. Figures 4.16c and 4.16d show the ratio of ETmissand meff, which are both quantities used
for the design of signal regions. The transverse momenta of the muon and the electron are shown in figures 4.16e and 4.16f. Fake leptons from Multijet events are found in the lower part of the pTspectrum.