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Jets calibration using $t\bar{t}$ events

Contents:

What

$t\bar{t}$ events with semileptonic decay of Ws.

$t\bar{t}$ $ \rightarrow $ $W^{+} b W^{-}\bar{b}$ $ \rightarrow $ $l \nu qq' b \bar{b}$

Why

Where

http://cmssw.cvs.cern.ch/cgi-bin/cmssw.cgi/UserCode/Bicocca/HiggsAnalysis/TTBarAnalysis/

How

How to prepare the environment for the analysis:

More  Less  

cmsrel CMSSW_3_3_4
cd CMSSW_3_3_4/src/
cmsenv
cvs co -d HiggsAnalysis/TTBarAnalysis UserCode/Bicocca/HiggsAnalysis/TTBarAnalysis
cvs co -d PhysicsTools/NtupleUtils UserCode/Bicocca/PhysicsTools/NtupleUtils


cd HiggsAnalysis/TTBarAnalysis
scramv1 b

Results

Signal sample used

Feasibility study: MC analysis

Calibration algorithms

Main idea: invariant mass of the reconstructed jets $\sim$ M$_{W}$.

Jet correction coefficients are defined by

\[ p^{true} = k(\eta,p_{T}) p^{reco} \]
where $p^{reco}$ is the reconstructed momentum of the jet, $p^{true}$ is the correct momentum of the jet and k, the correction function, may depend on $p_{T}$ and $\eta$ of the jets. The purpose is to estimate the function
\[ k(\eta,p_{T}) \]
The function k has been "binned" in $\Delta\eta$ and $\Delta p_{T}$ rectangle in the $\eta, p_{T}$ plane. The width of these bins are determined by the number of events required by calibration algorithm (and then the number of events in a given integrated luminosity) and the accuracy on k that is required. It may be useful enable a dynamic binning of the function k according to the occupancy plot in the $\eta, p_{T}$ plane.

\[ k(i\eta,ip_{T}) \]

with $i\eta$ = $\eta$ / $\Delta\eta$ and $ip_{T}$ = $p_{T}$ / $\Delta p_{T}$

  • MiB : Minuit Bare minimization
  • kUpdate
  • RUL3 : Random Update L3
  • SL3: Squared L3
  • RUFit : Random Update Fit
  • SFit: Squared Fit

imge23af1bfdcb80ab7f79d0d87c20143d6.png
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Occupancy plot
img9dcb746a02eee3dbd4ca34cda1242a30.png
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pT Reco / pT MC before jet corrections. Gauss fit mean superimposed.
img6560dd27a3a5044ab64256650a816089.png
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pT Reco / pT MC before jet corrections.
imgbb1fa00c1605a0f5f4a6c005a3bad19b.png
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Reco invariant mass before jet corrections vs η.
imgf3b5cf0ec64a77d4db4448844aa3e1c7.png
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Reco invariant mass before jet corrections vs pT.

MiB : Minuit Bare minimization
Minimization in $k(i\eta,ip_{T})$ space of the function
\[ |M_{RECO} - M_{W}|^{2} \]
assuming massless jets, using TMinuit package.

Result: still invariant mass underestimation!

imgb1fb98d09e8e6e74be1be7a24ca9e97f.png
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pT Reco / pT MC vs η. Gauss fit mean superimposed.
img360aa9a99bdc005457e49fb56404258a.png
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pT Reco / pT MC vs pT Reco.
imgc2e8493e3a6350a7ef4f3457e7c0b405.png
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Reco invariant mass vs η.
imgca31c4360217c2f20f983265c90b7b67.png
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Reco invariant mass vs pT.
img8f2af0c0330599a9b7403285d52e85a3.png
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Reco invariant mass. Red = before jet corrections, Green = after jet corrections

kUpdate
Analytic minimization of $ |M^{2}_{RECO} - M^{2}_{W}|^{2} $. Result:
\[ k' = M_{W}^{2} \frac{\sum M^{2}_{RECO} k_{l}}{\sum (M^{2}_{RECO} k_{l})^2} \]
No iterative method: just one step!

Result: invariant mass overestimation!

img780ffcf65961c9a8b9e089c4a4569efd.png
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pT Reco / pT MC vs η. Gauss fit mean superimposed.
imgdaaccadf5aa495a8cfbbf8e2026ef01f.png
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pT Reco / pT MC vs pT Reco.
imga4d0ff3627a78a9ff50e997305927cc6.png
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Reco invariant mass vs pT.
img8e6e68e8b0f96e5553e6495bdea52a11.png
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Reco invariant mass. Red = before jet corrections, Green = after jet corrections

RUL3 : Random Update L3
As L3 method
\[ k' = k \frac{\sum (\frac{M_{W}}{M_{RECO}})^2}{N} \]
but with random update that is: after analysing all the events, not every k is update but only a random sample (tipically one half of the k space). This method is intrinsically iterative, that is many k updates are required.

Why random update? L3 method works fine for "intercalbrations", that is the mean value of k is 1. For jet corrections that is not the truth, then, if for example every k should be about 2, we have $\frac{M_{W}}{M_{RECO}}$ about 4 ($M_{RECO}$ is proportional to $k_{i} * k_{j}$) and if every k is updated then the mass will be overestimated by a factor 4, and so on, jumping around the right mass but never approaching it.

imgbc596787fd4a2b285b2fea1bc3cd3702.png
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pT Reco / pT MC vs η. Gauss fit mean superimposed.
img54c973c5daafdd92ba0d0f739df0eff7.png
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pT Reco / pT MC vs pT Reco.
imgfd6e1a0548f795e4c289747061e8911a.png
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Reco invariant mass vs pT.
img44e18dd700c1879e65516c23f73d9c1a.png
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Reco invariant mass. Red = before jet corrections, Green = after jet corrections

SL3: Squared L3
As L3 method, but with the ratio of the masses instead of the squared ratio
\[ k' = k \frac{\sum \frac{M_{W}}{M_{RECO} } }{N} \]
then the "dimension" of the correction is proportional to k and convergence is reached.

img0b33f00ec4cfd6ae393f5c3cc6c41142.png
Enlarge
pT Reco / pT MC vs η. Gauss fit mean superimposed.
img16a3b39383a720cee3a887aad429d465.png
Enlarge
pT Reco / pT MC vs pT Reco.
img950b2a49463c08318ce128041aa20eb2.png
Enlarge
Reco invariant mass vs pT.
imgfeaeb7f2d1abf69a2c5220db1ca72e53.png
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Reco invariant mass. Red = before jet corrections, Green = after jet corrections

RUFit : Random Update Fit
Fitting the invariant mass spectrum for a fixed k, that if filling an invariant mass spectrum for all jet pairs where at least one of the two jet is in the selected bin in k space, and imposing the invariant mass peak to be the right one
\[ k' = k (\frac{M_{W}}{M_{RECO fit}})^2 \]
but with random update that is: after analysing all the events, not every k is update but only a random sample (tipically one half of the k space), see RUL3 for details. This method is intrinsically iterative, that is many k updates are required to k values to converge.

Result: not performing!

SFit: Squared Fit
Fitting the invariant mass spectrum for a fixed k, that if filling an invariant mass spectrum for all jet pairs where at least one of the two jet is in the selected bin in k space, and imposing the invariant mass peak to be the right one
\[ k' = k \frac{M_{W}}{M_{RECO fit}} \]
This method is iterative, that is many k updates are required to k values to converge.

img9e49dba45b3e3ff5bad3154fda34dafd.png
Enlarge
pT Reco / pT MC vs η. Gauss fit mean superimposed.
imgfa34f5e3424d3dbed657059e8e744744.png
Enlarge
pT Reco / pT MC vs pT Reco.
img117e26bc3f5861a036be3f430fb2812c.png
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Reco invariant mass vs pT.
imgd8b4ac03ee712330ff9a196ab7c148eb.png
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Reco invariant mass. Red = before jet corrections, Green = after jet corrections

Summary
Algorithm pT Reco / pT MC vs pT Reco pT Reco / pT MC vs η Invariant Mass vs pT Reco Invariant Mass
MiB
img360aa9a99bdc005457e49fb56404258a.png
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imgb1fb98d09e8e6e74be1be7a24ca9e97f.png
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imgca31c4360217c2f20f983265c90b7b67.png
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img8f2af0c0330599a9b7403285d52e85a3.png
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kUpdate
imgdaaccadf5aa495a8cfbbf8e2026ef01f.png
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img780ffcf65961c9a8b9e089c4a4569efd.png
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imga4d0ff3627a78a9ff50e997305927cc6.png
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img8e6e68e8b0f96e5553e6495bdea52a11.png
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RUL3
img54c973c5daafdd92ba0d0f739df0eff7.png
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imgbc596787fd4a2b285b2fea1bc3cd3702.png
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imgfd6e1a0548f795e4c289747061e8911a.png
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img44e18dd700c1879e65516c23f73d9c1a.png
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SL3
img16a3b39383a720cee3a887aad429d465.png
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img0b33f00ec4cfd6ae393f5c3cc6c41142.png
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img950b2a49463c08318ce128041aa20eb2.png
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imgfeaeb7f2d1abf69a2c5220db1ca72e53.png
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SFit
imgfa34f5e3424d3dbed657059e8e744744.png
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img9e49dba45b3e3ff5bad3154fda34dafd.png
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img117e26bc3f5861a036be3f430fb2812c.png
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imgd8b4ac03ee712330ff9a196ab7c148eb.png
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Jet from W identification in $t\bar{t}$ events

Identification of 4 jets based on LikelihoodRatio estimator: LR = L(signal) / L(background). Variables used:

  • ΔR bb
  • ΔR qq
  • b tag from b
  • b tag from q
  • pT from b
  • pT from q

Following images may be obtimized!

img78c5da62fbacd32652117af2e76dc0fd.png
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ΔR bb
imgec74bf0ffdd6c81d943dbed82131e40a.png
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ΔR qq
img2ebf118138fe2b77aa4ed38c91d44d2d.png
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pT of RECO b jet
imgc0e30bac7a2076781843cb19ecfb1c72.png
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trackCountingHighEffBJetTags of RECO b jet
img1d5df28b2639b8823a5063ced9d87708.png
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trackCountingHighEffBJetTags of RECO q (from W) jet

The best jet combination is defined as the one that maximizes

\[ P = \Pi LR_{i} \]

Results: After "pool" matched with ΔR<0.3 and pT RECO / pT MC between 0.1 an 2.0.

  • ~ 20% for 4 matched jets
  • ~ 40% for 3+4 matched jets

-> not very performing: distribution bad parametrized + range of distributions to be reviewed.

BDT method:

(6) bkg + sig: one combination for every event (random)

(9) bkg + sig: all combinations for every event

Results: (6) or (9) (similar results)

  • ~ 35-40% for 4 matched jets
  • ~ 70% for 3+4 matched jets

"Simple" method:

(13) Two highest b-tag values are jets from b quark, while between the remaining jets the two highest pT ones are jets from W.

Results:

  • ~ 20% for 4 matched jets
  • ~ 55% for 3+4 matched jets

do http://cmsdoc.cern.ch/~amassiro/TTBar/Code/TestBestIDAlgo.txt to test

Background sample

$t\bar{t}$ events identification

Result: $t\bar{t}$ events and background

-- AndreaMassironi - 20-Jan-2010

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Topic revision: r6 - 2010-02-03 - AndreaMassironi
 
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