Drell-Yan analysis Procedure (8 TeV)

Drell-Yan analysis Procedure

This twiki documents the most important steps of the Drell-Yan cross section measurement. It is intended to familiarize you with the technical aspects of the analysis procedure. 

The pdf file of the AN-13-420 attached here contains the notes with the macro name used to produce each plot. In addition, there is  a table which contains the same information.

Step 1: Producing ntuples

• Samples
• The CMSSW_53X MC samples are used for 8 TeV analysis. Below is the list of starting GEN-SIM-RECO samples used in the muon and electro analyses:

• DATA:

• We use SingleMu and DoubleMu Primary Datasets (PD), January2013 ReReco version

  /DoubleMu/Run2012A-22Jan2013-v1/AOD : 190645-193621

  /DoubleElectron/Run2012A-22Jan2013-v1/AOD

  /DoubleMuParked/Run2012B-22Jan2013-v1/AOD : 193834-196531

  /DoubleElectron/Run2012B-22Jan2013-v1/AOD

  /DoubleMuParked/Run2012C-22Jan2013-v1/AOD : 198049-203742

  /DoubleElectron/Run2012C-22Jan2013-v1/AOD

  /DoubleMuParked/Run2012D-22Jan2013-v1/AOD : 203777-208686

  /DoubleElectron/Run2012D-22Jan2013-v1/AOD

  /SingleMu/Run2012A-22Jan2013-v1/AOD : 190645-193621

  /SingleMu/Run2012B-22Jan2013-v1/AOD : 193834-196531

  /SingleMu/Run2012C-22Jan2013-v1/AOD : 198049-203742

  /SingleMu/Run2012D-22Jan2013-v1/AOD : 203777-208686

  /MuEG/Run2012A-22Jan2013-v1/AOD

  /MuEG/Run2012B-22Jan2013-v1/AOD

  /MuEG/Run2012C-22Jan2013-v1/AOD

  /MuEG/Run2012D-22Jan2013-v1/AOD

  /Photon/Run2012A-22Jan2013-v1/AOD

  /SinglePhoton/Run2012B-22Jan2013-v1/AOD

  /SinglePhoton/Run2012C-22Jan2013-v1/AOD

  /SinglePhotonParked/Run2012D-22Jan2013-v1/AOD

• JSONs: Cert190456-2086868TeV22Jan2013ReRecoCollisions12JSON.txt, Jan22Jan2013
• Double muon and double electron samples are used for the main analysis, single muon samples are used for the efficiency correction estimation steps. Other samples are used for the backgrounds estimation purposes.

• Relevant software: CMSSW_5_3_3_patch2
  • Use latest global tags for MC data for a given release as documented here
  • DY analysis package (Purdue), DY analysis package (MIT) are used 

cmsrel CMSSW_5_3_4
cd CMSSW_5_3_4/src
cmsenv
git cms-addpkg DataFormats/PatCandidates
git cms-addpkg PhysicsTools/PatAlgos
git cms-addpkg PhysicsTools/PatUtils
git clone git@github.com:ASvyatkovskiy/DYAnalysis DimuonAnalysis/DYPackage
cp -r DimuonAnalysis/DYPackage/CMSSW_5_3_11/src/DataFormats/ .
cp -r DimuonAnalysis/DYPackage/CMSSW_5_3_11/src/DimuonAnalysis/DYPackage/BuildFile.xml DimuonAnalysis/DYPackage/
cp -r DimuonAnalysis/DYPackage/CMSSW_5_3_11/src/DimuonAnalysis/DYPackage/ntuples/* DimuonAnalysis/DYPackage/ntuples/
rm -rf DimuonAnalysis/DYPackage/CMSSW_5_3_11/
rm -rf DimuonAnalysis/DYPackage/DimuonAnalysis/ 
scram b -j8
export DYWorkDir=$PWD/DimuonAnalysis/DYPackage
cd $DYWorkDir/ntuples

Note: that for proper compilation slc5 machine is necessary, and the code might not compile out of the box on slc6 or later CMSSW release versions (it would need to be ported first).

To simply perform a local test of the ntuple-maker run:

cmsRun ntuple_cfg.py

to produce the ntuples over full dataset use CRAB:

crab -create -submit -cfg crab.cfg
crab -get all -c <crab_0_datetime>

Various ntuples are used for the final result. XXX

Step 2: Event Selection

First, you will have to get a custom rootlogon file. Note: some of the libraries loaded in this rootlogon might interfere with the Proof environment in your machine.

cp rootlogon.C ~/.rootlogon.C

Once the ntuples are ready, one can proceed to the actual physics analysis. The first step of the analysis is the event selection. Currently, we use the so-called cut-based approach to discriminate between signal and background. For more on event selection read chapter 5 in the analysis note CMS-AN-13-420. Before starting to run a macro, set up the working area. Find all the necessary scripts in:

cd $DYWorkDir/test/ControlPlots

The code for event selection consists of 3 main files (and a few auxiliary). First of all the TSelector class which is customized for event selection used in a given analysis, necessary weights (pileup, FEWZ and momentum scale correction) are applied in the macro. The Monte-Carlo weights are also hardcoded inside the macro for each MC sample used. Next, is the wrapper ROOT macro which calls the TSelector to run on a given dataset. This wrapper is shown below, and explained step-by-step:

//macro takes 3 arguments, which are passed from the python script. These are: the histogram name (invariant mass, or for instance rapidity), ntuple weight or/custom (this option is deprecated - we always use custom weight), and the type of momentum scale correction (also deprecated - the correction does not depend on the run range in 8 TeV analysis)
void analyseYield(const char* WHICHHIST, const char* NTUPLEWEIGHT, const char* MOMCORRTYPE) {

  // Depending on the directory with data, the protocol used to access data will be different: "file" or "xrootd" are the most commonly used.
  TString protocol = "file://";
  //TString protocol = "root://xrootd.rcac.purdue.edu/";


  //Pointer to the location of the data used. Can be on /mnt/hadoop or on the scratch
  TString dirname = "/mnt/hadoop/store/group/ewk/DY2013/";

  // Next, the TFileCollection is created. This section is specific for each dataset: data or MC, so we prepare this wrapper macro for each sample
  TFileCollection* c1 = new TFileCollection("data","data");
  //Splitting criteria by runs/eras is happening here switch to RunAB, RunC, RunD. This is handy for studies of run dependencies 
  if (MOMCORRTYPE == "RunAB") c1->Add(protocol+dirname+"Data_RunAJan2013_Oct"+"/*.root");
  if (MOMCORRTYPE == "RunAB") c1->Add(protocol+dirname+"Data_RunBJan2013_Oct_p1"+"/*.root");
  if (MOMCORRTYPE == "RunAB") c1->Add(protocol+dirname+"Data_RunBJan2013_Oct_p2"+"/*.root");
  if (MOMCORRTYPE == "RunC1") c1->Add(protocol+dirname+"Data_RunCJan2013_Oct_p1"+"/*.root");
  if (MOMCORRTYPE == "RunC2") c1->Add(protocol+dirname+"Data_RunCJan2013_Oct_p2"+"/*.root");
  if (MOMCORRTYPE == "RunD1") c1->Add(protocol+dirname+"Data_RunDJan2013_Oct_p1"+"/*.root");
  if (MOMCORRTYPE == "RunD2") c1->Add(protocol+dirname+"Data_RunDJan2013_Oct_p2"+"/*.root");

  //Set the location of ProofLite Sandbox. It is more convenient to use the custom path rather than $HOME/.proof
  gEnv->SetValue("ProofLite.Sandbox", "<path to your working dir>/test/ControlPlots/proofbox/");
  
  //splitting criteria: how many worker nodes to use for the run: using more than 10-15 nodes usually will cause instability and lead to a crash subsequently
  TProof* p = TProof::Open("workers=20"); 
  p->RegisterDataSet("DATA", c1,"OV");
  p->ShowDataSets();
 
  //Deprecated - just leave as is, always
  TObjString* useNtupleWeightFlag = new TObjString(NTUPLEWEIGHT);
  p->AddInput(new TNamed("useNtupleWeightFlag",NTUPLEWEIGHT));

  //The histogram should always be "imvm" - it will give both 1D and 2D histograms. But if one needs to study N-1 selection, then the string should be the name of the cut to exclude
  TObjString* histogramThis = new TObjString(WHICHHIST);
  p->AddInput(new TNamed("histogramThis",WHICHHIST));
  //This is now useless, but for later studies it might become useful again, if there is a run dependency for the momentum scale correction
  TObjString* momCorrType = new TObjString(MOMCORRTYPE);
  p->AddInput(new TNamed("momCorrType",MOMCORRTYPE));

  gROOT->Time();
  p->SetParameter("PROOF_LookupOpt", "all");
  //This invokes the TSelector: "recoTree/DiMuonTree" is the name of the ROOT tree inside the file, "EventSelector_CP.C" is the name os the TSelector
  p->Process("DATA#/recoTree/DiMuonTree","EventSelector_CP.C+");
}

• There is one extra level here -  the python script. It calls the above ROOT wrapper macro and typically looks like this:

#!/usr/bin/env python
from subprocess import Popen

#This normally is just "imvm", but for N-1 control plots like 18-25 in the AN-13-420 one needs to set to a custom cut name, for instance: 'relPFisoNoEGamma','chi2dof','trackerHits','pixelHits','CosAngle','muonHits','nMatches','dxyBS','relPFisoNoEGamma','vtxTrkProb','trigMatches','pT','eta']
histos = ['invm'] 
 
#normally one needs to run over all of them. Splitting to a set of runs is useful because loading very large number of files into one session can cause instability
eras = ['RunAB','RunC1','RunC2','RunD1','RunD2'] 
#Simply invoke ROOT wrapper macro using Popen
for run in eras:
    for hist in histos:
        Popen('root -b -l -q \'analyseYield.C(\"'+hist+'\",\"False\",\"'+run+'\")\'',shell=True).wait()

Once this is understood, one can run the macro. To produce plots like 35-37 use the analyse.py macro, which calls the wrapper for TSelector for the DY analysis (as described above):

mkdir runfolder
python analyseYield_mc.py
python analyseYield_data.py

Important information about the reweightings. Pileup reweighing is accessed from the ntuple, directly from the branch on a per event basis. The FEWZ weights are extracted from theoretical calculation, and are provided as arrays inside the efficiencyWeightToBin2012.C file located in the same directory (or any other directory, as long as there is an appropriate include in the header of the TSelector). The FEWZ weights are looked up based on the GEN mass as follows inside the code, only for signal MC:

To Finally, the Rochester momentum scale correction recipe is described here: http://www-cdf.fnal.gov/~jyhan/cms_momscl/cms_rochcor_manual.html

Few words about the normalization. The data events are not renormalized. The MC weights are weighted according to the probability of each event to be observed in a real collision event and according to the number of events generated in the sample. Therefore  

Event_weight ~ (Cross section x filter efficiency)/(Number of generated events)

For better accuracy we use the number of events actually ran on, rather than the number generated. We calculate it in the event loop, and apply it in the EventSelector::Terminate() method. In both the 7 and 8 TeV analysis, we normalized the MC tack (signal and backgrounds) to the number of events in data in the Z peak region (before the efficiency corrections). A special post-processing macro takes care of this:

python postprocessor.py
cp runfolder/stack* ../Inputs/rawYield

This python script adds up individual ROOT files with hadd and invokes ROOT macros parser.C and parser_2D.C which has a method for normalization of MC stack to data in the Z peak region.

After that, switch to the Dielectron working directory and produce necessary yield histograms before continuing with the style plotting 

cd ../FullChain

Inspect the wrapper_EE.sh file inside and set the do_selection flag to 1 (true), and check the input files to run on are properly specified in the conf_file 

//top of the file
filename_data="../config_files/test.conf"
//scroll down a little
do_selection=1
do_prepareYields=1

Then run in two steps: (1) produce reduced ntuples, (2) prepare binned yields for analysis

./wrapper_EE.sh

To switch between 1D and 2D cases open the ../Include/DYTools.hh file and change the flag to const int study2D=1;.

After that, the style macro is used to plot the publication quality plots.

cd ../style/DY
root -l plot.C

the style macro is used This would plot the 1D yields distribution (the switch between the electrons and muons is done manually inside the macro by adjusting the paths).

To plot the 2D distributions do:

root -l ControlPlots_2D.C

Step 3: Acceptance and Efficiency estimation

Another constituent of the cross-section measurement is the acceptance-efficiency.

• Acceptance is determined using GEN level information

To be able to produce the acceptance and efficiency one needs to change to a different folder, and run a different TSelector. But the general flow TSelector->ROOT wrapper->python wrapper is almost the same:

cd $DYWorkDir/AccEffMCtruth
python analyseMCtruth.py

The script will produce the root file with histograms corresponding to the mass and rapidity spectra after the acceptance cuts, selection cuts or both which are then used to calculate the acceptances, efficiencies and acceptance-efficiency products with and without pileup and FEWZ reweighing by executing:

root -l plotMCtruth.C
root -l plotMCtruth_2D.C

To get the corresponding distributions in the electron channel change to FullChain folder:

cd ../FullChain
//doAcceptance = 1
//doEfficiency = 1 
./wrapper_EE.sh

The macro output a root file starting with out1* or out2* containing the histograms corresponding to the acceptance, efficiency and their product. To produce the publication level plots, the style macro described in the previous section needs to be used again

cd ../style/DY
root -l plot.C

To get the 2D plots do:

root -l plot_acc_2D.C

Step 4: Data-driven efficiency correction

Only in the muon channel, the electron efficiency scale factors are obtained from the EGamma group, and not re-measured independently.

Next, the data-driven efficiency corrections are applied. This is done using the standard CMSSW recipe, so a lot of additional packages needs to be checked out. Follow this twiki: https://twiki.cern.ch/twiki/bin/viewauth/CMS/MuonTagAndProbe to set up your working area for the ntuple production (alternatively, one can use the trees already produced!)

• The procedure goes in two steps: T&P tree production -> rerun seldom (ideally once), it depends only on the definitions of the tag and probe

cd ../ntuples
cmsRun tpTree_Producer_Data.py

cmsRun tpTree_Producer_MC.py

• If you haven't produced TP trees you can always use the official ntuples located as described in MuonTagAndProbe twiki:

• Second step of the procedure is fitting: separate job for trigger and all the muonID related efficiencies -> reran frequently and usually interactively (change binning, definitions)

cd ../test/TagAndProbe
cmsRun fitMuonID_data_all_2012_1_53X.py

cmsRun fitMuonID_mc_all_2012_1_53X.py

After familiarizing yourself with the TagAndProbe package, you need to produce the muon efficiencies as a function of pT and eta. You can use the wrapper.py script specifying which variables to bin the efficiency in and what runs/MC samples to process.

Finally, produce the plots with

 python auxPlotProducer.py

Step 5: Background estimation

QCD data driven background estimation

In 8 TeV analysis, the main method to estimate the QCD background in the dimuon channel is the ABCD method (the fake-rate method is used in the electron channel). Before starting, let me summarize the ABCD method in a nutshell:

ABCD method

1) choose 2 variables: assume two variables are independent 

2) assume the fraction should be same if there is no correlation: N_A / N_B = N_C / N_D

3) In our study, use two variables: sign of muon pair, muon isolation

4) QCD fraction in each region has a dependence. We produce the correction factor for each region: B, C, D

5) Produce N_B, N_C, N_D from data sample, and estimate N_A from them at the end (applying the correction factors)

Now, let's go step by step.

First, change to the ABCD folder:

cd $DYWorkDir/ABCDmethod

The procedure consists of few steps and is guided by the wrapper.py script located inside the folder:

Popen("python QCDFrac_p1.py",shell=True).wait()
Popen("python qcdFracHadder.py rootfiles",shell=True).wait()
Popen("python ABCD2vari_init.py",shell=True).wait()
Popen("python ABCD2vari_p1.py",shell=True).wait()

Thus, for each of the MC samples and for the real data a set of sequences is ran. First the QCDFrac_*.py, which invoke the EventSelector_Bkg.C TSelector class for various values of charge and isolation (the variables defining the signal and background regions), based on the histograms filled, the coefficients are calculated. Second, the qcdFracHadder.py scripts is ran on the on the output of the first step. It is a utility script which repacks the histograms in an appropriate format. Third, the ABCD2vari_init.py script which actually performs the etiolation of ABCD coefficients in each region. Finally, the ABCD2vari_*.py scripts invoke the EventSelector_Bkg2.C TSelector class, passing the ABCD coefficients as TObjString objects inside the macro.

The post-processing and the output harvesting step is performed by the following python script: 

python abcdPostprocessor.py

It uses the output of the second TSelector as an inout, hadds it and produces a root file with th histogram which is then used in the analysis.

E-mu data-driven background estimation method

To estimate all the non-QCD backgrounds we employ the so-called e-mu data driven background estimation method. The same method is applied in the muon and electron channels. The code used for that purpose was originally adapted from Manny and it uses the so-called Bambu workflow. First, let's change into the e-mu working directory:

cd $DYWorkDir/EmuBackground

First, reduced ntuples are generated from the original Bambu ntuples:

root -l (shared libraries should compile if they have not already done so)
root [0] .L selectEmuEvents.C+
root [1] selectEmuEvents("../config_files/data_emu.conf")
root [2].q

The above script needs to be ran twice in 2 modes: SS (same-sign pairs) and OS (opposite-sign pairs). The switch is don win the selectEmuEvents.C script by switching:

if (!isOppositeSign) continue; //if (isOppositeSign) continue;

And also changing the ntupDir name. One will have to edit the data_emu.conf to point to the local ntuples before running.

After running this step, the reduced ntuples should be output to a directory (../root_files/selected_events/DY/ntuples/EMU/). One would also need to run selectEvents.C to generate reduced electron ntuples.These ntuples must contain two branches, mass (dilepton invariant mass) and weight. After this is done, the e-mu macro can be ran:

#compile code
> gmake eMuBkgExe
#This should produce the binary eMuBkgExe. There are many options to run it. See the the possible options below
./eMuBkgExe #run emu method for 1D analysis and produce plots
./eMuBkgExe --doDMDY #run 2D analysis and produce plots
./eMuBkgExe --doDMDY --saveRootFile #same as above but output ROOT file with yield, statistical and systematic info as true2eBkgDataPoints.root

This macro is also ran in two regimes: using SS and OS ntuples as an input, and the proper true2eBackground file are produced and saved. The reason why we need to rerun SS and OS cases is because we rely on this for estimation of missing QCD contribution in the e-mu spectrum. These true2eBackground files and the dilepton yields serve as an input to the final step of e-mu background estimation, the production of a final root file with histograms:

root -l calculateEMu.C
root -l calculateEMu_2D.C
root -l calculateEMu_EE.C
root -l calculateEMu_2D_EE.C

As you can see, 4 different macros are re-ran for electrons, muons, 1D and 2D.

One other source of background considered in this analysis is the photon induced background. This background is irreducible and is not estimated based on MC. The bulk of the calculations of this background is done in FEWZ3, by switching the photon induced components on and off. Once the output files are ready, one can simply parse them, get the bin-by-bin correction:

python dimitriExtracter.py
python dimitriParser.py

Following scripts can be used to visualize and compare the PI background yields: 

root -l PIvalidation.C

Once the correction is prepared in a root file, it is simply loaded in the shapeR plotting macro as discussed in the sections below.

Step 6: Unfolding

Unfolding is applied to correct for migration of entries between bins caused by mass resolution effects (FSR correction is taken into account as a separate step, although it also uses the unfolding technique).  In 8 TeV analysis, we use the iterative Bayesian unfolding technique. Provides a common interface between channels for symmetry and ease in combination and systematic studies. Both the iterative Bayesian and matrix inversion technique (used in 7 TeV) are implemented and described below.

To do any unfolding with MC, this requires 3 things:

• Producing the response matrix
• Making the histogram of measured events
• Making the true histogram & closure test

First, change to the unfolding working directory (common for electron and muons).

cd ../Unfold

The main steps for unfolding procedure go as follows:

1. Produce the response matrix.

2. To produce the unfolded yield

3. Visualize the yields and ratios of yields

The first step is rather time consuming, and is done by:

python ResMatrix.py

which takes care of the response matrix production for both the 1D and 2D cases. Inputs for these macros are ntuples, and the output is the ROOT file with the true and measured MC yields as well as the response matrix. To visualize the resulting response matrices do:

root -l Matrix.C

The above matrix access the ROOT file which we produced on the previous step and simply does drawing. There is a switch inside this macro allows to change 1D and 2D plots, written with a comment inline.

Once this is done, one can continue to apply the unfolding technique. Open the unfold.C file and familiarize yourself with various flags (pre-processor pragmas to be more precise), namely:

#define USE_OVERFLOWS true
#define DATA_DRIVEN_BKG true
#define DO_ROO true
#define DO_BAYES true
#define FEWZ_CORRECTED true

The input to this file is the true, measured MC yields and the response matrix as well as the observed, reconstructed signal and background MC yields. A possibility to read the data-driven backgrounds is also implemented and controlled by the DATA_DRIVEN_BKG flag.

The Bayesian unfolding is performed using the RooUnfold package which is described here: http://hepunx.rl.ac.uk/~adye/software/unfold/RooUnfold.html, and it relies on the code committed here https://github.com/ASvyatkovskiy/DrellYanAnalysis/tree/master/DimuonAnalysis/DYPackage/test/Unfold/RooUnfold-1.1.1. Alternative would be the response matrix inversion (which uses this implementation: https://github.com/ASvyatkovskiy/DrellYanAnalysis/tree/master/DimuonAnalysis/DYPackage/test/Unfold/include) or singular value decomposition (SVD). For convenience, the latter two options are available for the user, but they are not enabled by default. To enable the SVD one can set:

#define DO_ROO true
#define DO_BAYES false

To enable matrix inversion:

#define DO_ROO false
#define DO_BAYES false

Above is the default setting, as we use iterative Bayesian method as default for 8 TeV in both channels. First run in the closure test mode by setting the run to 'POWHEG' inside the wrapper unfold.py, then switch to '' flag which will do the actually unfolding – we do not make any distinction between the run ranges in 8 TeV as the scale corrections are run independent

python unfold.py

It outputs 1 ROOT file with the yields before and after unfolding.

Repeat all for 2D:

python unfold_2D.py

Similarly to 1D, it calls the unfold_2D.C macro which takes the true, measured MC yields and the response matrix as well as the observed, reconstructed signal and background MC yields as inputs. A possibility to read the data-driven backgrounds is also implemented and controlled by the DATA_DRIVEN_BKG flag. It outputs 1 ROOT file with the yields before and after unfolding.

Then to repeat for electrons change to the FullChain folder and set the appropriate  flags for runnings the response matrix production step

cd ../FullChain
vim wrapper_EE.sh
do_unfolding=1

That summarizes the unfolding step, and the output of this step will be used on the following analysis steps.

Step 7: FSR correction

 The effect of FSR is manifested by photon emission off the final state lepton. It leads to a change of the dimuon invariant mass and as a result a dilepton has invariant mass distinct from the propagator (or Z/gamma*) mass.

For our analysis we estimate the effect of FSR and the corresponding correction by estimating the unfolding correction in invariant mass and rapidity bins. This is done by applying an exact same unfolding procedure as for the mass resolution effects described above. A minor difference is that we also apply bin-by-bin corrections for event classes that do not enter the response matrix.

Change to the FSRunfold directory

cd ../FSRunfold

And run the similar steps as above:

python FSRResMatrix.py

This script will give you the response matrix in 1D and 2D and also additional bin-by-bin corrections for events not entering the response matrix. In addition, there is an option to run fully bin-by-bin as a cross check. If you inspect the contents of this python script, you will be able too understand what actually is done. After the jobs are complete, you need to merge the individual root files using hadd, and then run the fracEff.C script to extract the additional corrections:

root -l fracEff.C

Similarly to the detector resolution unfolding step, you can inspect the response matrix:

root -l Matrix.C

To get these all quantities in the electron channel, similarly to the detector resolution unfolding case you just need to:

cd ../FullChain
vim wrapper_EE.py
doUnfoldingFsr=1
python wrapper_EE.py

Step 8: Cross section calculation

Once all the constituents of the cross section are in place, one can continue with the cross section calculation results. First, the results are calculated in each individual channel and then they are combined using the BLUE method (as described in the Step 10 section). To calculate the 1D cross section in muon channel change to:

cd ../ShapeR
python shapeDY.py

this will produce an output root file in the ../Outputs directory. All the necessary input files are expected to be available in the ../Inputs directory. To get the 2D cross section change to

cd ../shapeR2D
python shapeR2D.py

The output file is also going to be created in the ../Outputs directory. To get the electron cross section do as usually:

cd ../FullChain
//set do_crossSectionFsr=1
./wrapper_EE.sh

One would have to rerun this step twice switching the flag between 1D and 2D.

This produces the necessary root files with the histograms of the cross section and uncertainties

Step 9: Electron-muon combination with the BLUE method

Having the root files for individual cross section measurements i the dielectron and dimuon channels, we need to combine them for a higher precision. The combination is performed with the BLUE method, which takes 2 vectors of measured values of the cross section and the covariance matrices.

First of all, switch the rootlogon for this task:

cp ../../rootlogon_defaultgluon.C ~/.rootlogon.C

Next, we need to make sure that the inputs are in the form the BLUE macro expects it (i.e. ASCII, not root):

cd ../BLUE
python bluePrinter.py
python bluePrinter_2D.py

This macro takes a ROOT file as an input and outputs the ASCII file as an output. The input ROOT files are produced using macros in the ShapeR and shapeR2D folders and supposed to be in the ../Outputs directory.

We can use the txt2Plot.py macro to validate the txt input by visualizing it.

After we have the inputs in proper format, we just need to run the resultCombiner.C macro. To pass all the inputs properly (which should be in the current folder), we specify them in the wrapper.py script and run it as

python wrapper.py
python wrapper_2D.py

The output will be the ASCII format again, but we normally need it in root. So we have to run another converter file after we finished:

python outToPeople.py
python outToPeople_2D.py

After that, we have the root file with the cross section histogram of the same format as we have for the individual cross sections, and we can visualize it (produce a plot for the publication) on the same step as we did for other cross sections in the previous section

cd ../ShapeR
root -l plot_Comb.C //for 1D
root -l plotter.C   //for 2D, make sure that the input file is pointing at the combination

Step 10: Double ratio calculations

Once the cross actions have been obtained, the double ratios – ratios of the normalized differential and double-differential cross sections – can be calculated. Most of the macros for the double ratio calculation is located in the ../ShapeR folder, so first change to that folder:

cd ../ShapeR

Produce the double ratios and uncertainties:

python doubleratio_1Dee.py

python doubleratio_1Dmu.py
python doubleratio_1Dcomb.py
python doubleratio_2Dmu.py
python doubleratio_2Dcomb.py
python uncertEE.py
python uncert_2D.py
python uncertEE_2D.py 

Step 11: Plotting the final results

The final results are the absolute cross sections in bins of mass and rapidity in dielectron, dimuon channels and combination. As well as the double ratios. To plot the 1D differential cross sections do:

To plot the 1D double ratios (switch between the lepton channels is inside):

root -l plot_dratio.C

To plot the 2D cross sections and double ratios do:

root -l plotter.C
root -l plot_dratio2D.C

Appendix: List of macros used and paths