# Jets calibration using events

## What

events with semileptonic decay of Ws.

## 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 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

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

### Jet from W identification in events

### Background sample

### events identification

### Result: events and background

-- AndreaMassironi - 20-Jan-2010