Object selection
Leptons
Leptons are reconstructed in the following way:
- electrons -
pixelMatchGsfElectrons
- muons -
globalMuons
Observables for leptons
The main characteristic for leptons coming from the W decay is the fact that they should be prompt and isolated. Other variables can be used to clean the leptons of interest: electromagnetic fraction, E/p, lepton identification, etc.
Reconstructed lepton observables |
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spectrum |
distribution |
Track impact parameter |
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e |
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electromagnetic fraction |
Isolation in tracker and calorimeter |
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e |
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Single lepton selection efficiency and purity
Our lepton selection is defined below.
Lepton selection |
Selection steps |
Electrons selected |
Muons selected |
kinematics |
; |
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calorimetric cuts |
e only : ; |
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isolation |
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tau veto |
, |
id |
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After selection the lepton purity is the following:
Sample |
Leptonic purity |
e |
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Madgraph |
1.00 0.02 |
0.98 0.02 |
Alpgen |
0.96 0.01 |
0.952 0.005 |
Purity |
0.96 0.01 (stat) 0.03 (syst) |
0.952 0.005 (stat) 0.03 (syst) |
The probability of reconstructing and selecting both hard leptons is the following:
Sample |
P(select n hard leptons) |
0 |
1 |
2 |
Madgraph |
0.240 0.004 |
0.487 0.006 |
0.273 0.004 |
Alpgen |
0.227 0.001 |
0.483 0.002 |
0.290 0.002 |
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0.227 0.001 (stat) 0.013 (syst) |
0.483 0.002 (stat) 0.004 (syst) |
0.290 0.002 (stat) 0.018 (syst) |
Jets
Jets are reconstructed using the iterative cone algorithm with
from the calorimetric towers with
. A minimum
of 2
GeV and 2 towers is required as pre-selection. The tracks with at least 8 hits, a
and
are associated to the calorimetric cluster if they are matched to it within a cone of
. No jet cleaning (matching with reconstructed electrons or muons is done).
Observables for jets
Reconstructed jet observables |
spectrum |
distribution |
emf |
b-tag discriminator |
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Calorimetric constituents |
Associated tracks |
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nearest jet |
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Likelihood ratio method
In order to increase the purity of the jets selected in an event we try to characterize better some experimentally measurable distributions of the jets (e.g. jet width, number of tracks, charge, etc.). For each jet we compute a list of observables and we check if it can be matched to the quark generated by the top decay (b,s or d ). This allows us to define two distributions:
- - the "signal" distribution for the jets whose purity we want to increase.
- - the "background" distribution for the jets remaining, after the selection, which you want to remove.
The distributions
S(x) and
B(x) are defined with inclusive first and last bins. As so, the first(last) bin should be interpreted as the number of jets with an observable
x ,
(
). The probability distribution function -
gives the probability that a signal jet has an observable
x between x and x+dx.
Having defined the p.d.f.'s for signal jets one can define the combined likelihood as:
In order to reduce possible bias sources the different p.d.f.'s must:
- have low correlations ()
- not bias towards the selection of a specific jet flavor (b,s,d)
The table below summarizes the distributions for the observables chosen and the correspondent likelihood obtained when using Madgraph (
All b
and
All q
samples).
Jet properties |
x |
S(x) and B(x) |
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x |
S(x) and B(x) |
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(jet order in ) |
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(number of towers with 90% of transverse energy) |
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Legend: - red - signal jets;
- black - background jets;
- closed markers -
All b sample; - open markers -
All q sample; |
Combined Likelihood |
likelihood |
efficiency |
signal efficiency vs. background efficiency |
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Single jet selection efficiency and purity
Our jet selection is defined below
Jet selection |
Selection steps |
Jets surviving selection |
Multiplicity |
Likelihood (after pre-selection) |
kinematics |
; |
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calorimetric cuts |
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topology |
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likelihood |
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After selection the jet purity is lower than lepton purity (as expected due to the high jet multiplicity):
Sample |
Jet purity |
Madgraph |
0.726 0.007 |
Alpgen |
0.725 0.003 |
Purity |
0.725 0.003 (stat) 0.01 (syst) |
The probability of reconstructing and selecting both hard jets from the top decay is, however higher than the one obtainde for leptons:
Sample |
P(select n hard jets) |
0 |
1 |
2 |
Madgraph |
0.137 0.003 |
0.427 0.005 |
0.435 0.005 |
Alpgen |
0.124 0.001 |
0.425 0.002 |
0.451 0.002 |
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0.124 0.001 (stat) 0.013 (syst) |
0.425 0.002 (stat) 0.003 (syst) |
0.451 0.002 (stat) 0.016 (syst) |
MET
In the di-leptonic channel the missing transverse energy has two main sources:
- neutrinos emitted by the decay of the W's generated by the top decay
- neutrinos emitted in the leptonic decay of 's
The spectrum of the MET reconstructed by the
corMetType1Icone5
algorithm, after selecting at least 2 leptons and 2 jets, is shown below:
Our MET pre-selection is defined as:
MET > 50 GeV .
Event selection
Trigger
We require a
or
of HLT trigger bits for single leptons. We define the following trigger efficiencies:
- trigger efficiency for all reconstructed events:
- trigger efficiency for all events with true MC in trigger acceptance range:
- trigger efficiency for all events in with reco objects in trigger acceptance range:
The pre-selection is defined as the one for the
di-leptonic channel: "2 leptons with opposite charge: 1 with
or
and the other
in
(isolation not required); 2 jets with
and
" (see
trigger note).
The table below summarizes the results obtained from CSA07:
HLT trigger paths |
HLT1ElectronRelaxed |
HLT1Electron |
HLT1MuonIso |
HLT1MuonNonIso |
L1 requirement |
L1_SingleEG15 |
L1_SingleIsoEG_12 |
L1_SingleMu7 |
cut |
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cut |
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Trigger efficiencies for channel |
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0.497 0.003 |
0.501 0.003 |
0.593 0.003 |
0.67 0.003 |
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Selection
The table below summarizes the event selection used for the di-leptonic channel:
Selection step |
Constraints |
Event selection |
2 leptons |
; |
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e only : ; |
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tau veto: , |
id : |
2 jets |
; |
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op. sign leptons |
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The table below summarizes the events surviving each selection step (computed from the
CSA07
samples).
Total events accepted (L=100/pb) |
Selection step |
Physics process |
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other |
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triggered |
2282 11 |
20790 39 |
138520 146 |
62711 185 |
0.01017 0.00005 |
leptons |
870 7 |
33 11 |
51 2 |
161 5 |
0.78 0.01 |
jets |
642 6 |
27 9 |
11 1 |
26 2 |
0.91 0.02 |
MET |
387 5 |
9 7 |
1.2 0.3 |
8 1 |
0.96 0.02 |
opposite sign |
387 5 |
9 7 |
1.2 0.3 |
8 1 |
0.96 0.02 |
After the last selection step the acceptance for the total
cross section is the following:
Sample |
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Madgraph (all b) |
0.0035 0.0004 |
Madgraph (all q) |
0.0040 0.0005 |
Alpgen |
0.0043 0.0005 |
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4.3 0.5 (stat) 0.8 (syst) |
Control distributions
Below we show some control distributions for the selected events, that can be used for the di-leptonic channel.
Background estimation from data
Flipped (and swapped) method (summary)
Below we explore how to use a
based method to subtract background from the data. The baseline idea is to build
measure that, by a change variables, leaves the background invariant but not the signal. Having a
with such probabilities one can do the following event selection:
- normal selection: - will select signal-like events with some quality criteria and some background events
- flipped selection: - will reject signal-like events but will select combinatorial background events
The
is well constructed if both selections yields more or less the same background events leaving the distributions of interest (kinematics, b-tagging multiplicity, etc.) invariant.
By the procedure described above one obtains two distinct distributions
and
depending on the event selection used. By taking the difference of these distributions the background contributions will be eliminated effectively if the requirement for the
is met. Then
is equivalent to
obtained from a 100% pure signal sample.
Next we discuss the construction of the
having in mind these requirmentes.
Jet + lepton kinematics based
As point of departure we choose 2 distributions based on the kinematics of the jet and lepton produced at a top decay vertex: the invariant mass and the transverse mass of the pair. The distributions, for these quantities, obtained at Monte-Carlo level, are shown below:
Jet+lepton pair kinematics at Monte-Carlo level |
Invariant mass |
Transverse mass (square root) |
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For each event selected we proceed as follows:
- select the 2 highest leptons as the leptons from W decay generated after the top decay;
- if the number of selected jets is higher than 2 than we select the 3 jets with highest combined likelihood ratio value;
- try all jet+lepton combinations to build the matrix using the formulas from the table above;
- find the 2 jet+lepton pairs (excluding double-counting) that minimize the matrix;
- repeat the computation of the matrix but flipping the lepton's momentum - ;
We compute then the following quantities for the 2 pairs that minimize the
matrix:
- - sum;
- - inverting the 3-momentum of the hardest lepton;
- - swapping the leptons in each pair;
The table below shows the distributions obtained for signal and background events for these quantities:
distributions |
Event type |
==Signal== |
efficiency for signal |
==Background== |
efficiency for background |
Invariant mass |
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Transverse mass |
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Choosing a cut for
we select each event using the 3
defined above. For each selected event we compute the b-tag multiplicity for different values of the b-tagging discriminator. The distributions obtained for each selection are shown below. We also show the results obtained after subtracting the distribution obtained with the
or
selections from the one obtained with the
selection.
b-tag multiplicity distributions |
Multiplicity |
Invariant mass |
Transverse mass |
==Signal== |
==Background== |
==Signal== |
==Background== |
0 |
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1 |
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2 |
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"Loose point" |
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"Medium point" |
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