CMS Data Analysis School Pre-Exercises - Fourth Set

Overview

Teaching: 0 min
Exercises: 60 min

Questions

How do we analyze an EDM ROOT file using an EDAnalyzer?

How do we analyze an EDM ROOT file using an FWLite executable?

How do we use ROOT/RooFit to fit a function to a histogram?

Objectives

Learn how to use an EDAnalyzer

Learn how to use FWLite

Understand a variety of methods for performing a fit to a histogram

Introduction

In this set of exercises, we will analyze the MiniAOD file that was made in the third set of exercise. You must have this skimmed MiniAOD stored locally (in your eos user space) in order to access them. We will use several different workflows for analyzing the MiniAOD, namely an EDAnalyzer, a FWLite executable, a FWLite Macro, and a FWLite PyROOT script. We will basically re-make the Z peak and few other histograms and store them in an output root file. In the exercise in the end we will try to fit with a Gaussian, Breit-Wigner function, etc.

Warning

To perform this set of exercises, a CERN computing account, Grid Certificate, and CMS VO membership are required. You should already have these things, but if not, follow these instructions from the setup instructions.

Objective

Please post your answers to the questions in the Google form fourth set.

Exercise 15 - Analyzing MiniAOD with an EDAnalyzer

In this exercise we will analyze the skimmed MiniAODs created in the third set of exercises using an EDAnalyzer. In these skimmed MiniAODs, if you recall, we saved only the muons and electrons. So do not look for jets, photons, or other objects as they were simply not saved. We will use a python config file and an EDAnalyzer ( a .cc file) to make a Z mass peak. You can find an example list of files below, but please first try using the files you created.

Example file list

root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_1.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_10.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_11.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_12.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_13.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_14.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_15.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_16.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_17.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_18.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_19.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_2.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_20.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_21.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_22.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_23.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_24.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_25.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_26.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_27.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_28.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_29.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_3.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_30.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_31.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_4.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_5.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_6.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_7.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_8.root
root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/slimMiniAOD_data_MuEle_9.root

First we will add the PhysicsTools/PatExamples package as follows to <YOURWORKINGAREA>/CMSSW_10_6_18/src. The PatExamples package has lot of examples for a user to try. However, we will add our own code and config file to it and then compile. To add this package, do this:

cd $CMSSW_BASE/src/
git cms-addpkg PhysicsTools/PatExamples

Note

We are assuming that you’ve already checked out a CMSSW_10_6_18 release and have performed the cmsenv setup command.

In this package, you will find the python configuration file $CMSSW_BASE/src/PhysicsTools/PatExamples/test/analyzePatBasics_cfg.py. You will also see the EDAnalyzer in $CMSSW_BASE/src/PhysicsTools/PatExamples/plugins/PatBasicAnalyzer.cc.

Next, create the following two files (download/save): $CMSSW_BASE/src/PhysicsTools/PatExamples/src/MyZPeakAnalyzer.cc and $CMSSW_BASE/src/MyZPeak_cfg.py.

Hint

A quick way to do this on Linux, or any machine with wget, is by using the following commands:

wget https://cern-cms-das-2023.github.io/cms-das-pre-exercises/code/MyZPeakAnalyzer-CMSSW_10_6_18.cc -O $CMSSW_BASE/src/PhysicsTools/PatExamples/src/MyZPeakAnalyzer.cc
wget https://cern-cms-das-2023.github.io/cms-das-pre-exercises/code/MyZPeak_cfg.py -O $CMSSW_BASE/src/MyZPeak_cfg.py

Then we will compile the code that you just saved by doing:

cd $CMSSW_BASE/src/
scram b

The compilation should print many lines of text to your terminal. Among those lines you should see a line like the one below. If you can’t find a similar line, then the code you just added is not compiled.

>> Compiling  <$CMSSW_BASE>/src/PhysicsTools/PatExamples/src/MyZPeakAnalyzer.cc

After successful compilation, you must run the config file as follows:

cmsRun MyZPeak_cfg.py

Successful running of the above config file will produce an output file myZPeakCRAB.root. The output file myZPeakCRAB.root has several histograms, besides the Z peak, called mumuMass, like muonMult, muonEta, muonPhi, muonPt and similarly for electrons.

Note

In the case above, the file MyZPeak_cfg.py will read from area root://cmseos.fnal.gov//store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/. You should have a similar location from where you can read your CRAB output ROOT files. You can edit the MyZPeak_cfg.py file to use the MiniAOD files you made in Exercise 13 by replacing the location of the input files to the path of file you generated. From my side, the files are stored in:
'/eos/user/v/vmilosev/DoubleMuon/crab_CMSDAS_Data_analysis_test0/230421_160319/0000/slimMiniAOD_data_MuEle_1.root'

Question 15

What is the number of entries in the mumuMass plot if you just used the first input file, probably named slimMiniAOD_data_MuEle_1.root?

Exercise 16 - Analyzing MiniAOD with an FWLite executable

In this exercise we will make the same ROOT file, myZPeakCRAB.root, as in Exercise 15, but we call it myZPeakCRAB_fwlite.root so that you do not end up overwriting the file previously made in Exercise 15.

First, check out the following two packages by doing:

cd $CMSSW_BASE/src/
git cms-addpkg PhysicsTools/FWLite
git cms-addpkg PhysicsTools/UtilAlgos

Next, replace the existing $CMSSW_BASE/src/PhysicsTools/FWLite/bin/FWLiteWithPythonConfig.cc with this FWLiteWithPythonConfig.cc. You are simply updating an existing analyzer. Then, create the file $CMSSW_BASE/src/parameters.py.

Hint

You can easily download the needed files by running the following commands:

wget https://cern-cms-das-2023.github.io/cms-das-pre-exercises/code/FWLiteWithPythonConfig.cc -O $CMSSW_BASE/src/PhysicsTools/FWLite/bin/FWLiteWithPythonConfig.cc
wget https://cern-cms-das-2023.github.io/cms-das-pre-exercises/code/parameters.py -O $CMSSW_BASE/src/parameters.py

Note

In case you have completed Exercise Set 3 successfully, put the names and path of the ROOT files that you made yourself via submitting CRAB job, instead of those currently in parameters.py.

parameters.py will read from area root://cmseos.fnal.gov//store/user/cmsdas/2023/pre_exercises/Set4/Input/DoubleMuon/. You should have a similar location from where you can read your CRAB output ROOT files. You can edit the parameters.py file to use the MiniAOD files you made in Exercise 13 by replacing the location of the input files. From my side, the files are stored in:
 '/eos/user/v/vmilosev/DoubleMuon/crab_CMSDAS_Data_analysis_test0/230421_160319/0000/slimMiniAOD_data_MuEle_1.root'

Then we will compile the code that you just saved by doing:

cd $CMSSW_BASE/src/
scram b -j 4

You should see among the output a line like the one below. If not, it is probable that you haven’t compiled the code on which we are working.

>> Compiling  /your_path/YOURWORKINGAREA/CMSSW_10_6_18/src/PhysicsTools/FWLite/bin/FWLiteWithPythonConfig.cc

After successful compilation, you must run the config file as follows:

cd $CMSSW_BASE/src/
cmsenv
FWLiteWithPythonConfig parameters.py

Note

Take note of the extra cmsenv is to ensure the changes to files in the bin subdirectory are picked up in your path.

Warning

You might get a segfault when running this exercise. Just ignore it; the output ROOT file will still be created and be readable.

Note

Take a look at how the parameters defined in parameters.py get input to the executable code FWLiteWithPythonConfig.cc.

A successful running of the FWLite executable, FWLiteWithPythonConfig, results in an output file called myZPeakCRAB_fwlite.root.

The output ROOT file myZPeakCRAB_fwlite.root is a bit different from myZPeakCRAB.root made in Exercise 15 since we did not make any of the electron histograms. The histograms do have the mumuMass, besides, muonEta, muonPhi, and muonPt.

Question 16

What is the number in entries in the mumuMass obtained in Exercise 16, again using only the first input file.?

Exercise 17 - Fitting the Z mass peak

The main intention of fitting the Z mass peak is to show how to fit a distribution. To do this exercise, you will need the ROOT files that you made in Exercise 15 and Exercise 16. Make sure you have the ROOT file $CMSSW_BASE/src/myZPeakCRAB.root ( Exercise 15) or myZPeakCRAB_fwlite.root (Exercise 16). If you have not managed to create at least one of these ROOT files, you can get them from the following locations:

File list

/afs/cern.ch/cms/Tutorials/TWIKI_DATA/CMSDataAnaSch/myZPeakCRAB.root # lxplus or Bari
root://cmseos.fnal.gov//store/user/cmsdas/2023/pre_exercises/Set4/Output/myZPeakCRAB.root # cmslpc
root://cmseos.fnal.gov//store/user/cmsdas/2023/pre_exercises/Set4/Output/myZPeakCRAB_fwlite.root # cmslpc

This will allow you to continue with Exercise 17. For this exercise, we will use the ROOT file myZPeakCRAB.root. Alternatively, you can use the file myZPeakCRAB_fwlite.root, but just make sure to have the right name of the ROOT file. The most important factor is that both of these files have the histogram mumuMass.

We also ask that you create a rootlogon.C file in the $CMSSW_BASE/src/ directory. We will reference this version as opposed to anyone’s personalized rootlogon file. This sets up the libraries needed to complete this exercise.

The different distribution that we would fit to the Z mass peak are:

Gaussian

$http://latex.codecogs.com/svg.latex? \begin{displaymath} G(x; \mu, \sigma) = \frac{1}{\sqrt{2\pi}\sigma}\exp\left[-\frac{(x-\mu)^2}{2\sigma^2}\right] \end{displaymath}$

Relativistic Breit-Wigner

$http://latex.codecogs.com/svg.latex? \begin{displaymath} B(m; M, \Gamma) = N \cdot \frac{2}{\pi} \cdot \frac{\Gamma^{2}M^{2}}{(m^{2}-M^{2})^{2}+m^{4}(\Gamma^{2}/M^{2})} \end{displaymath}$

Convolution of relativistic Breit-Wigner plus interference term with a Gaussian

$http://latex.codecogs.com/svg.latex? \begin{displaymath} P(m) = \int B(m'; M, \Gamma)\cdot G(m-m'; \mu, \sigma) dm' \end{displaymath}$

Some general remarks about fitting a Z peak

To fit a generator-level Z peak, a Breit-Wigner fit makes sense. However, reconstructed-level Z peaks have many detector resolutions that smear the Z mass peak. If the detector resolution is relatively poor, then it is usually good enough to fit a Gaussian (since the gaussian detector resolution will overwhelm the inherent Briet-Wigner shape of the peak). If the detector resolution is fairly good, then another option is to fit a Breit-Wigner (for the inherent shape) convolved with a Gaussian (to describe the detector effects). This is in the “no-background” case. If you have backgrounds in your sample (Drell-Yan, cosmics, etc…), and you want to do the fit over a large mass range, then another function needs to be included to take care of this; an exponential is commonly used.

Fitting a Gaussian

There are several options to fit a Gaussian

Using the inbuilt Gaussian in ROOT

Open ROOT as follows:

root -l

Then execute the following commands:

TFile f("myZPeakCRAB.root");
f.cd("analyzeBasicPat");
gStyle->SetOptFit(111111);   
mumuMass->Fit("gaus");

This will pop up the following histogram. Save this histogram as pdf, ps, or eps file using the menu of the histogram window. As you can see we should fit a sub-range as this fit is not a good fit. In the next part of this exercise, we will fit a sub-range of the mumuMass distribution, but for this we will use a ROOT macro as using inbuilt ROOT functions have very minimal usage. For more complex or useful fitting functions, one has to use a macro.

For now, we can improve the fit description of the Z resonance by limiting our fit range:

TFile f("myZPeakCRAB.root");
f.cd("analyzeBasicPat");
gStyle->SetOptFit(111111);   
g1 = new TF1("m1","gaus",85,95);
mumuMass->Fit(g1,"R");

One should obtain a similar histogram as:

GaussFitZmm

Reminder

You can quit ROOT using the .q command.

The line gStyle->SetOptFit(111111);` enables all the histogram statistics to be displayed. For more options and other information please refer to ROOT documentation.

Question 17.1a

What is the value of the mean Z Mass that you get?

Question 17.1b

What is the value of the chisquare/ndf that you get?

Using a macro of your own in ROOT

As you have seen above, we should fit a sub-range of the Z mass distribution because the fit in the full range is not all that great. In this exercise, we will fit a sub-range of the mumuMass distribution but for this we will use a ROOT macro. For more complex or useful fitting functions, one has to use a macro. The macro to run is FitZPeak.C. This macro calls another macro, BW.C. Please download/save them with the corresponding names in $CMSSW_BASE/src. Note that now the myZPeakCRAB.root file is opened by executing the macro itself, in addition to fitting the Z mass peak.

To run this macro execute the following command from the $CMSSW_BASE/src directory:

root -l FitZPeak.C

This should pop up a histogram (shown below) and you will find yourself in a ROOT session.

FitZPeak

Reminder

You can save this plot from the menu on top of the histogram and then quit ROOT using the .q command.

Hint

You can also save the plot to an encapsulated postscript file by running the macro as:
root -l FitZPeak.C$true$

Here is some explanation of the macro. We have defined the Gaussian distribution that we want to fit in the macro BW.C (shown below). Note that in the same macro we have also is defined a Breit-Wigner function that you can try yourself. However, in the later part of the exercise, we will use RooFit to fit the distribution using a Breit-Wigner function.

Double_t mygauss(Double_t * x, Double_t * par)
{
  Double_t arg = 0;
  if (par[2]<0) par[2]=-par[2];  // par[2]: sigma
  if (par[2] != 0) arg = (x[0] - par[1])/par[2];  // par[1]: mean
 
 //return par[0]*BIN_SIZE*TMath::Exp(-0.5*arg*arg)/
  //   (TMath::Sqrt(2*TMath::Pi())*par[2]); 
   return par[0]*TMath::Exp(-0.5*arg*arg)/
     (TMath::Sqrt(2*TMath::Pi())*par[2]); // par[0] is constant
 
}

par[0], par[1], and par[2] are the constant, mean, and sigma parameters, respectively. Also x[0] mean the x-axis variable. BW.C is called by FitZPeak.C in the line gROOT->LoadMacro("BW.C");. The initial values of the three fitted parameters are defined in FitZPeak.C as follows:

func->SetParameter(0,1.0);   func->SetParName(0,"const");  
func->SetParameter(2,5.0);   func->SetParName(2,"sigma");  
func->SetParameter(1,95.0);     func->SetParName(1,"mean");

Also note that in the macro FitZPeak.C, we have commented the following lines and used the two lines below it. The reason being that we want to fit a sub-range. If you would want to fit the entire range of the histogram, get the minimum and maximum value of the range by instead using the lines that have been commented.

//float massMIN = Z_mass->GetBinLowEdge(1);
//float massMAX = Z_mass->GetBinLowEdge(Z_mass->GetNbinsX()+1);

float massMIN = 85.0;
float massMAX = 96.0;

Question 17.2

What mean value of the Z mass do you get in the fitted sub-range?

Using a macro in RooFit

Before we start, have a look at the RooFit twiki to get a feeling for it. Then save the macro RooFitMacro.C in the $CMSSW_BASE/src/ directory. This macro will fit the Z mass peak using RooFit.

Take a look at the code and then execute the following:

root -l RooFitMacro.C

You may need to add the following line to your rootlogon.C file to get this interpreted code to work:

gROOT->ProcessLine(".include $ROOFITSYS/include/");

This should pop a histogram (shown below) and you will find yourself in a ROOT session.

Reminder

You can save this plot from the menu on top of the histogram and then quit ROOT using the .q command.

We fit the distribution with a Gaussian by default. However, we can fit a Breit-Wigner or Voigtian (convolution of Breit-Wigner and Gaussian) by uncommenting the appropriate lines.

ZmmGaussROOTFit

Question 17.3a

What is the mean for the gaussian fit in RooFit?

Question 17.3b

What is the sigma for the gaussian fit in RooFit?

Fitting a Breit-Wigner

Using a macro in ROOT

To fit the Z mass peak using a Breit-Wigner distribution, we first uncomment the Breit-Wigner part of FitZPeak.C and comment out the Gaussian part as follows (using /* and */):

////////////////
//For Gaussian//
///////////////
/*
TF1 *func = new TF1("mygauss",mygauss,massMIN, massMAX,3); 
func->SetParameter(0,1.0);   func->SetParName(0,"const");  
func->SetParameter(2,5.0);   func->SetParName(2,"sigma");  
func->SetParameter(1,95.0);     func->SetParName(1,"mean");

Z_mass->Fit("mygauss","QR");
TF1 *fit = Z_mass->GetFunction("mygauss");
*/
/////////////////////
// For Breit-Wigner//
////////////////////
TF1 *func = new TF1("mybw",mybw,massMIN, massMAX,3);
func->SetParameter(0,1.0);   func->SetParName(0,"const");
func->SetParameter(2,5.0);     func->SetParName(1,"sigma");
func->SetParameter(1,95.0);    func->SetParName(2,"mean");

Z_mass->Fit("mybw","QR");
TF1 *fit = Z_mass->GetFunction("mybw");

Then execute the following:

root -l FitZPeak.C

This should pop a histogram (shown below) and you will find yourself in ROOT seession.

BWFitZmm

Reminder

You can save this plot from the menu on top of the histogram and then quit ROOT using the .q command.

Question 17.4a

What is the mean for the Breit-Wigner fit using the macro?

Question 17.4b

What is the sigma for Breit-Wigner fit using the macro?

Using a macro in RooFit

Before we proceed we need to uncomment and comment out few lines in RooFitMacro.C to have them look as follows:

//RooGaussian gauss("gauss","gauss",x,mean,sigma);
RooBreitWigner gauss("gauss","gauss",x,mean,sigma);
// RooVoigtian gauss("gauss","gauss",x,mean,width,sigma);

Then execute:

root -l RooFitMacro.C

This should pop a histogram (shown below) as follows and you will find yourself in ROOT session.

myZmmBWROOTFit

Reminder

You can save this plot from the menu on top of the histogram and then quit ROOT using the .q command.

Question 17.5a

What is the mean for the Breit-Wigner fit using RooFit tool?

Question 17.5b

What is the sigma for the Breit-Wigner fit using RooFit tool?

Fitting a Convolution of Gaussian and Breit-Wigner

Using a macro in RooFit

Before we proceed we need to uncomment and comment out few lines in RooFitMacro.C to have them look as follows:

//RooGaussian gauss("gauss","gauss",x,mean,sigma);
// RooBreitWigner gauss("gauss","gauss",x,mean,sigma);
RooVoigtian gauss("gauss","gauss",x,mean,width,sigma);

Then execute:

root -l RooFitMacro.C

This should pop a histogram (shown below) as follows and you will find yourself in ROOT seession.

myZmmVoigtianROOTFit

Reminder

You can save this plot from the menu on top of the histogram and then quit ROOT using the .q command.

Question 17.6a

What is the mean for the convolved fit using RooFit tool?

Question 17.6b

What is the sigma for the convolved fit using RooFit tool?

Key Points

You can use both an EDAnalyzer or FWLite to analyze MiniAOD files

Various methods exist for performing fits. You can use inbuilt functions or user defined functions. You can use plain ROOT or the RooFit package.

previous episode

CMS DAS Pre-Exercises

next episode

CMS Data Analysis School Pre-Exercises - Fourth Set

Overview

Introduction

Warning

Objective

Exercise 15 - Analyzing MiniAOD with an EDAnalyzer

Example file list

Note

Hint

Note

Question 15

Exercise 16 - Analyzing MiniAOD with an FWLite executable

Hint

Note

Note

Warning

Note

Question 16

Exercise 17 - Fitting the Z mass peak

File list

Some general remarks about fitting a Z peak

Fitting a Gaussian

Using the inbuilt Gaussian in ROOT

Reminder

Question 17.1a

Question 17.1b

Using a macro of your own in ROOT

Reminder

Hint

Question 17.2

Using a macro in RooFit

Reminder

Question 17.3a

Question 17.3b

Fitting a Breit-Wigner

Using a macro in ROOT

Reminder

Question 17.4a

Question 17.4b

Using a macro in RooFit

Reminder

Question 17.5a

Question 17.5b

Fitting a Convolution of Gaussian and Breit-Wigner

Using a macro in RooFit

Reminder

Question 17.6a

Question 17.6b

Key Points

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