Difference: JetCalibrationTTBarEvents (2 vs. 3)

Revision 32010-01-21 - AndreaMassironi

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META TOPICPARENT name="AndreaMassironi"

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

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

How

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How to prepare the environment for the analysis
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How to prepare the environment for the analysis:

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cmsrel CMSSW_3_3_4
cd CMSSW_3_3_4/src/
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 cd HiggsAnalysis/TTBarAnalysis scramv1 b
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Results

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\[ k(i\eta,ip_{T}) \]
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with $i\eta$ = $\eta$ / $\Delta\eta$ and $ip_{T}$ = $p_{T}$ / $\Delta p_{T}$
 

  • MiB : Minuit Bare minimization
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  • SFit: Squared Fit
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imge23af1bfdcb80ab7f79d0d87c20143d6.png
Occupancy plot
img9dcb746a02eee3dbd4ca34cda1242a30.png
pT Reco / pT MC before jet corrections. Gauss fit mean superimposed.
img6560dd27a3a5044ab64256650a816089.png
pT Reco / pT MC before jet corrections.
imgbb1fa00c1605a0f5f4a6c005a3bad19b.png
Reco invariant mass before jet corrections vs η.
imgf3b5cf0ec64a77d4db4448844aa3e1c7.png
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
pT Reco / pT MC vs η. Gauss fit mean superimposed.
img360aa9a99bdc005457e49fb56404258a.png
pT Reco / pT MC vs pT Reco.
imgc2e8493e3a6350a7ef4f3457e7c0b405.png
Reco invariant mass vs η.
imgca31c4360217c2f20f983265c90b7b67.png
Reco invariant mass vs pT.
img8f2af0c0330599a9b7403285d52e85a3.png
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
pT Reco / pT MC vs η. Gauss fit mean superimposed.
imgdaaccadf5aa495a8cfbbf8e2026ef01f.png
pT Reco / pT MC vs pT Reco.
imga4d0ff3627a78a9ff50e997305927cc6.png
Reco invariant mass vs pT.
img8e6e68e8b0f96e5553e6495bdea52a11.png
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
pT Reco / pT MC vs η. Gauss fit mean superimposed.
img54c973c5daafdd92ba0d0f739df0eff7.png
pT Reco / pT MC vs pT Reco.
imgfd6e1a0548f795e4c289747061e8911a.png
Reco invariant mass vs pT.
img44e18dd700c1879e65516c23f73d9c1a.png
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
pT Reco / pT MC vs η. Gauss fit mean superimposed.
img16a3b39383a720cee3a887aad429d465.png
pT Reco / pT MC vs pT Reco.
img950b2a49463c08318ce128041aa20eb2.png
Reco invariant mass vs pT.
imgfeaeb7f2d1abf69a2c5220db1ca72e53.png
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.

imgbc596787fd4a2b285b2fea1bc3cd3702.png
pT Reco / pT MC vs η. Gauss fit mean superimposed.
img54c973c5daafdd92ba0d0f739df0eff7.png
pT Reco / pT MC vs pT Reco.
imgfd6e1a0548f795e4c289747061e8911a.png
Reco invariant mass vs pT.
img44e18dd700c1879e65516c23f73d9c1a.png
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.

img9e49dba45b3e3ff5bad3154fda34dafd.png
pT Reco / pT MC vs η. Gauss fit mean superimposed.
imgfa34f5e3424d3dbed657059e8e744744.png
pT Reco / pT MC vs pT Reco.
img117e26bc3f5861a036be3f430fb2812c.png
Reco invariant mass vs pT.
imgd8b4ac03ee712330ff9a196ab7c148eb.png
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
kUpdate
RUL3
SL3
SFit

 

Jet from W identification in $t\bar{t}$ events

 
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