# Jets calibration using events

## What

events with semileptonic decay of Ws.

## Where

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

## How

How to prepare the environment for the analysis:

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

### Feasibility study: MC analysis

#### Calibration algorithms

Main idea: invariant mass of the reconstructed jets M.

Jet correction coefficients are defined by

where is the reconstructed momentum of the jet, is the correct momentum of the jet and k, the correction function, may depend on and of the jets. The purpose is to estimate the function
The function k has been "binned" in and rectangle in the 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 plane.

with = / and = /

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

Occupancy plot
pT Reco / pT MC before jet corrections. Gauss fit mean superimposed.
pT Reco / pT MC before jet corrections.
Reco invariant mass before jet corrections vs η.
Reco invariant mass before jet corrections vs pT.

##### MiB : Minuit Bare minimization
Minimization in space of the function
assuming massless jets, using TMinuit package.

Result: still invariant mass underestimation!

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

##### kUpdate
Analytic minimization of . Result:
No iterative method: just one step!

Result: invariant mass overestimation!

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

##### RUL3 : Random Update L3
As L3 method
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 about 4 ( is proportional to ) 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.

pT Reco / pT MC vs η. Gauss fit mean superimposed.
pT Reco / pT MC vs pT Reco.
Reco invariant mass vs pT.
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
then the "dimension" of the correction is proportional to k and convergence is reached.

pT Reco / pT MC vs η. Gauss fit mean superimposed.
pT Reco / pT MC vs pT Reco.
Reco invariant mass vs pT.
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
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
This method is iterative, that is many k updates are required to k values to converge.

pT Reco / pT MC vs η. Gauss fit mean superimposed.
pT Reco / pT MC vs pT Reco.
Reco invariant mass vs pT.
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 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!

ΔR bb
ΔR qq
pT of RECO b jet
trackCountingHighEffBJetTags of RECO b jet
trackCountingHighEffBJetTags of RECO q (from W) jet

The best jet combination is defined as the one that maximizes

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

### Result: events and background

-- AndreaMassironi - 20-Jan-2010

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

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