To study the event selection we will try to approach the Monte-Carlo generator level results to the experimental measures by clustering high pT objects which will correspond to the groups of particles flowing into the detector. This can be done by using the standard clustering algorithms provided by PYTHIA. We choose the CellJet
algorithm (aka as PYCELL
in PYTHIA 6).
The CellJet
algorithm consists in dividing the phase space in equally distant cells. The flux of energy-momentum is measured in each cell. The cell with highest pT is chosen as a cluster seed and will aglutinate all the neighboring cells within a range: . If the cluster's total pT is higher than a given threshold then the cluster is considered as a jet or CellJet
. The algorithm proceeds to find other cells with high pT which can be used as seeds for clustered jets. For more details (consult PYTHIA 6 manual or the PYTHIA 8 online documentation ).
To match a jet to a primordial parton we find within a range which is the jet that minimizes . If no jet is found within or we discard the event. Some 'event displays' are shown below.
Event display (with matched leptons and b-jets) |
The following plot shows the distribution of the number of jets found in event after subtracting the jets matched to leptons. One can see that there's a non negligible number of events where 0 or 1 jets were found. Even selecting only the events in which both b-quarks are matched to a jet we count events in which only one jet was found.
Due to the fixed size of the cells used to cluster the high pT objects and to the usage of a minimum pT threshold to initiate the clustering procedure, some errors might occur when matching the generated leptons and partons to the pT clusters (CellJets
). Some examples are shown below:
Event display (with matching exceptions examples) |
To minimize the errors in the identification of the jets corresponding to the generator level particles we:
In the following plots we compare the generator level distributions (plot on the left) with the jet level distributions. Note that for the special case of the leptons we use always the generator level values because experimentally they will be, in principle, resolved by the detector.
Object separation | |||
Kinematics |
MC sample | All b | All q | Mix | ||||
---|---|---|---|---|---|---|---|
50000 | 50000 | 40000 | |||||
"reconstructed" | 50000 | 22837 | 50000 | 23252 | 40000 | 17720 | |
Selection | Generator level | Jet level | Generator level | Jet level | Generator level | Jet level | |
Event topology: | 49750 | 22043 | 49745 | 23217 | 39796 | 17671 | |
2 charged leptons: | 21306 | 9018 | 21091 | 9432 | 16832 | 7073 | |
2 jets: | 14623 | 6918 | 14437 | 7554 | 11482 | 5509 | |
MET | MET > 60 GeV | 14019 | 5282 | 13819 | 5771 | 11051 | 4171 |
Yield = (%) |
As a combined result we obtain for the yield .
The error presented in this yield is statistical (from counting). The measurement of this yield is however affected by several systematic effects, namely:
When the energy of a jet is reconstructed it depends on several factor namely the jet algorithm used, the resolution and granularity of the calorimeter, etc. At the generator level we can estimate how these errors propagate to the final yields. In our case the jet algorithm that clusters the particles collected in cells within a radius will introduce an error in the measurement of the pT and . This mainly due to the granularity of the grid used to count particles. Below we plot the error distributions for: , using a grid for the MC samples in which 100% of the cases.
From this distribution we conclude that the CellJet
tends to underestimate the pT of the original parton. This can be related to the fact that not all the hadrons are clustered in the same jet. Some of the hadrons might be left outside of the cells used to construct a jet. An improvement on this algorithm would be to re-iterate the clustering using the CellJets
and the remaining SingleCells
(not clustered yet). This second step would enable to colect the remaining energy and would also merge jets that are very close to each other.
We turn now to the effect that the calorimeter measurement of the particles might have on the event yield. In a crude approach the calorimeter will measure the pT of the particles with a resolution that can be given by if we only take into account the fluctuations from Poisson statistics (calorimeter with linear response). We can estimate how this fluctuation propagates to the expected event yields by changing the pT of the leptons and the jets by the following amount:
To discriminate the contribution from positive and negative smearings we try also the following changes:
Applying both these smearings to the sample "All b" sample with a resolution R=0.4 we get the results summarized in the table below:
Generator level | Jet level | |||||
---|---|---|---|---|---|---|
50000 | 22043 | |||||
Smear mode | 0 | 0 | ||||
Topology in range | 49601 | 49748 | 49834 | 21965 | 21983 | 22005 |
Leptons in range | 19702 | 21282 | 22862 | 8350 | 9031 | 9730 |
Jets in range | 13019 | 14571 | 16160 | 6156 | 6935 | 7717 |
MET in range | 12452 | 13984 | 15536 | 4673 | 5283 | 5926 |
Yield(R=0.4) | 0.249 | 0.280 | 0.311 | 0.212 | 0.240 | 0.269 |
Yield(R=0.4)-Yield(R=0) | -0.031 | 0.000 | +0.031 | -0.028 | 0.000 | +0.029 |
From these yield diferences we get an estimate for the systematic error due to the precision in measuring the pT.
Using the previous method we obtain the following result:
MC sample | All b | All q | Mix | |
---|---|---|---|---|
5282 | 5771 | 4171 | ||
Events counted using all jets found | ||||
N b-tags | 0 tags | 471 | 5134 | 517 |
1 tag | 2018 | 547 | 1815 | |
2 tags | 2524 | 82 | 1677 | |
2 tags | 269 | 8 | 162 | |
Events counted using jets from top decay only | ||||
N b-tags | 0 tags | 521 | 5630 | 570 |
1 tag | 2164 | 138 | 1924 | |
2 tags | 2597 | 3 | 1677 |
If we consider the All b sample and measure the efficiency on the b-tag of the jets from top decay we find . On the other and if we take the All q sample and measure the probability of identifying a jet from top decay as a b-jet we get . This are first estimates for the b-tag and mistag efficiencies. Next we try to discuss this efficiencies in more detail.
R is the the ratio of with respect to .
Using the MC samples one can attempt to reproduce the R simulated in the samples (1,0 or 0.9 for the All b, All q and Mix samples respectively). In order to do that one must account for the number of events expected with 0, 1 or 2 b-jets and for the probability to identify them correctly.
When writing down the expected rates we make use of the following variables:
Doing so we have the following expressions for the probability of measuring 0, 1 or 2 b-tags in a di-lepton decay:
To find the value of R that best fits the data we then proceed to maximize the following likelihood:
Applying this procedure for the All b and Mix samples, choosing only the jets generated from decay and using the values for and computed before, we get the following result:
The table below summarizes the results obtained using also all the jets and tags in an event.
MC sample | All b | Mix |
---|---|---|
R expected | 1.0 | 0.9 |
R measured from all jets in an event | ||
R measured jets generated from top decay only |
We see that when we take all the jets measured in an event R is not well estimated, specially in the mix sample. As so we tune in order to reproduce R=0.9 in the Mix sample when all the jets are used. This gives us . The plot below shows the result of fitting a straight line to this scan.
Using and for we make a estimate for the event rates with a luminosity of and for the statistical error associated to the measurement of R.
Event yields for | ||||
---|---|---|---|---|
Yield after kinematics' selection (%) | ||||
MC sample | All b | Mix | All q | |
1.0 | 0.9 | 0 | ||
with k b-tags | 0 | |||
1 | ||||
2 | ||||
R |
-- PedroSilva - 11 Feb 2008
Webs
Welcome Guest