-- CristinaAnaMantillaSuarez - 2015-02-23

Projects



Summer Student Project: Measurement of mt using leptonic observables

We are interested on how is the top quark mass mt related to the kinematics of the leptons in the final state. The idea is that is this analysis the measurement won't be affected by the jet energy scale JES uncertainty.

This is the theory article from which the idea is based on: http://inspirehep.net/record/1305642

Slides: https://indico.cern.ch/event/301787/session/3/contribution/17/material/slides/0.pdf

  • It presents a procedure for determination of mt based on leptonic observables in dilepton tt events.
    • Construct the distributions from leptons only and require b-jets [anti-kT, R=0.5] within the detector (i.e. integrate over) - Minimal sensitivity to the modeling of both perturbative and non-perturbative QCD effects.
    • We shall be working with the top quark pole mass (defined as the real part of the pole in the top-quark propagator)
  • Employs kinematic distributions of leptons - we are interested in their shapes.
Label Observable
1 $p_T (l^{+})$
2 $p_T (l^{+}l^{-})$
3 $M_T (l^{+}l^{-})$
4 $E(l^{+})+E(l^{-})$
5 $p_T(l^{+})+p_T(l^{-})$
    • Working with distributions is cumbersome, but the information on the top mass that such shapes encode can be effectively provided by Mellin moments of the corresponding distributions.

ABOUT UNFOLDING

Unfolding can be defined as correcting data for detector effects. Due to the finite resolution of real world particle detectors, any measurement conducted in experimental high energy physics is contaminated by stochastic smearing. The observations recorded with any real world particle detector are always subject to undesired experimental effects, such as limited detector resolution and detection inefficiencies. The observation of such distorted collision events instead of the desired true events is called smearing or folding of the data and often results in broadening of the physical spectra measured by the LHC experiments.

Unfolding then refers to using the smeared observations to infer the true physical distribution of the events. It refers to the problem of estimating the particle level distribution of some physical quantity of interest on the basis of observations smeared by an imperfect measurement device.

There are three main reasons when unfolding is desirable:

  • To publish an estimate of the true physical distribution of events.
  • To compare measurements of 2 different experiments with different experimental resolutions
  • To compare unfolded histograms with theoretical predictions

In our case, we apply an unfolding technique because we want to compare our results with the theoretical predictions from our theory paper of reference. The measured distributions are distorted from the true underlying distributions by the limited acceptance of our detector and by bin-to-bin smearing due to a finite resolution of the variables. We perform our unfolding using TUnfold package, which consists on a matrix inversion based on a least square fit with Tikhonov regularisation. Similar (but not identical) to the SVD method. Some documentation can be found here:

http://www.desy.de/~sschmitt/tunfoldv16docu.html http://www.desy.de/~sschmitt/TUnfold/tunfold_manual_v17.3.pdf

Also we will try to follow TOP group general recomendations related to unfolding for top signatures.

https://twiki.cern.ch/twiki/bin/viewauth/CMS/TopUnfolding

Actually, the unfolding code we use is based in the code spinnet in this page:

https://twiki.cern.ch/twiki/bin/view/CMS/TopUnfoldingExampleCodes

For more information about TUnfold algorithm, have a look at:

The class TUnfold can be used to unfold measured data spectra and obtain the underlying "true" distribution. The unfolding method is summarized here: *The measured spectrum $\vec{y}$ can be expressed by the true spectrum $\vec{x}$ multiplied by a smearing matrix S, that accounts for migration of an event from one bin into another bin due to resolution effects as well as for different acceptances for the different bins:

$\vec{y}$ = S$\cdot$$\vec{x}$

By performing a regularized inversion of the matrix S, TUnfold gives an estimate for the true spectrum $\vec{x}$ and accounts for the above mentioned effects. In addition TUnfold can also take care of the proper subtraction of background contributions with a proper handling of the uncertainties on the background estimation. We use TUnfoldSys which provides methods to do systematic error propagation and to do unfolding with background subtraction.

TUnfoldSys uses a regularization parameter %\tau%, giving the strength of regularization. Will be roughly on the order of 1e-4. We use this value suggested but in principle you can determine this value by performing unfolding with many different values, maybe between 1e-3 and 1e-7 or such, and choosing the value of tau that minimizes tunfold.GetRhoAvg().

UPDATES:

  • NEW WORKING DIRECTORY: /afs/cern.ch/work/c/cmantill/public/CMSSW_5_3_22/src/UserCode/TopMassSecVtx/

22 July, 2015: Unfolding

I obtained the stability, purity and efficiency of the binning as a closure test.

Now I am having problems to define a correct binning to unfold, since the last bin and the first bin contain also the overflow and underflow bins respectively. So I am doing several tests with the binning, and using just one of the variables to test: $p_T (l^{+})$

At the end I compare the unfolded distributions obtained for each of the cases. And I compare the purity, stability and efficiency and also the

Here I describe how do I choose the bins:

The purpose of using quantiles is to choose these bins in such a way that all bins in the histograms contain the same numbers of events. This will increase the stability of the method. Depending on the case, flattening the truth spectrum after selection might be better than before selection.

  • First, I obtained the quantiles for generated and reconstructed distributions (19 and 38 respectively) and I defined the binning with those: e.g.
bins_gen = [22.72,25.45,28.18,30.92,33.67,36.42,39.17,42.01,44.89,47.77,50.94,55.06,59.19,63.63,68.15,74.76,83.59,95,115.65]

len (bins_gen) = 19

bins_rec = [21.36,22.73,24.09,25.45,26.82,28.18,29.55,30.92,32.29,33.67,35.04,36.41,37.79,39.17,40.57,42.01,43.45,44.89,46.33,47.77,49.21,50.93,53,55.06,57.12,59.18,61.37,63.63,65.89,68.15,70.73,74.76,78.74,83.59,88.75,95,102.85,115.65,138.46]

len (bins_rec) = 39

The bold bins are the extra bins in the reconstructed level.

Choosing the binning like this without any modification may lead to fill the first bin with underflow bin and last bin with overflow.

- Now: bins_gen = [22.72,25.45,28.18,30.92,33.67,36.42,39.17,42.01,44.89,47.77,50.94,55.06,59.19,63.63,68.15,74.76,83.59,95,115.65]

bins_rec = [20,21.36,22.73,24.09,25.45,26.82,28.18,29.55,30.92,32.29,33.67,35.04,36.41,37.79,39.17,40.57,42.01,43.45,44.89,46.33,47.77,49.21,50.93,53,55.06,57.12,59.18,61.37,63.63,65.89,68.15,70.73,74.76,78.74,83.59,88.75,95,102.85,115.65,138.46,250]

For ptpos :

  • 166.5 mass sample:

Generated level Reconstructed level Reconstructed level Bin-corrected Unfolded Efficiency, Purity and Stability

For all the mass samples:

Distribution comparison First Mellin Moment Unfolded vs Generated Second Mellin Moment Unfolded vs Generated u1 Unfolded vs Top Mass u2 Unfolded vs Top Mass

16 July, 2015: Calculating Mellin moments for each of the mass samples

The Mellin moments

13 July, 2015: Working with mass samples

We will start to work with mass samples from here, corresponding to mt = [166.5,169.5,171.5,173.5,175.5,178.5] GeV.

The mass samples are located in

 
/store/cmst3/group/top/summer2015/treedir_bbbcb36/ttbar/mass_scan/

for ttbar they are named as MC8TeV_TTJets_MSDecays_*.root where * is the mass. In addition, given tW/tbarW is the main background I will also use:

 
/store/cmst3/group/top/summer2015/bbbcb36/mass_scan/MC8TeV_SingleTbar_tW_*.root 
/store/cmst3/group/top/summer2015/bbbcb36/mass_scan/MC8TeV_SingleT_tW_*.root 

09 July, 2015: Rebinning distributions according to quantiles

To check the binning array I was using, I got the quantiles separately and then round those numbers a bit so I have the same bin size for a long range and then a bit bigger bins towards the end.Then I just hardcode them by adding that array into my code. At the end I got this:

Generated level Reconstructed level Reconstructed level Bin-corrected

In some cases there are events in the 0 pt bin. Could be that there are some events with only one lepton.

I checked the event selection, and there is indeed a cut on abs(EvCat) to be either 11*11, 11*13, or 13*13. But there are some events in the MC samples which have events in the 0 pt bin, we impose the condition:

 
 if not isData: 
           if tree.GenLpPt == 0 or tree.GenLmPt == 0: continue

Now the plots look like this:

Generated level Reconstructed level Reconstructed level Bin-corrected

08 July, 2015: Rebinning distributions according to quantiles

I found a bug in the way that I was calculating the quantiles, so now the distributions look like this for ptpos:

Generated level Reconstructed level Reconstructed level Bin-corrected

It looks like all the bins except the first and last are ok (they have more or less the same number of entries), but those two are wrong. I added one more quantil, by adding the 1.0 into my array

Generated level Reconstructed level Reconstructed level Bin-corrected

07 July, 2015: Rebinning distributions according to quantiles

We have started to study the unfolding procedure.

We are going to define the binning scheme for our histograms, such that we get flat distributions to unfold.

This is the idea: GetQuantiles ROOT Function gets you the values of x which divide the distribution in the quantiles you define.

You can use it to re-define the binning of the distribution, such that now you now that the statistics will be distributed according to your pre-defined quantiles.

i.e.

  • Run once with the histograms defined with a big range and equal binning and get the quantiles for |0.1, 0.2, 0.3, ...,0.9,1 ]
  • Run again with the histograms (and error matrix) defined according to the quantiles found i.e. [0, x_{0.1}, x_{0.2},...,x_{0.9},x_{1}, max]
  • Unfold using the new binning definition

  • At first I made a code which got the quantiles from each of the MC and data samples and rebinned the corresponding histograms according to each of the obtained quantiles.
  • But what they wanted me to do was to get the quantiles from one of the DataMUEG files and fix the binning for all for the plots using them. I did this but then I got too many events in the last bin.

Generated level Reconstructed level Reconstructed level Bin-corrected

I extended the bin range, but I am just increasing the range to 200 without changing the binning, so I just make one big bin from 100 to 200, which will contain all the events there.

Generated level Reconstructed level Reconstructed level Bin-corrected

Note: Github useful tips

 wget -q -O - --no-check-certificate https://raw.github.com/stiegerb/TopMassSecVtx/master/TAGS.txt | sh
 git clone git@github.com:stiegerb/TopMassSecVtx.git UserCode/TopMassSecVtx
 git status
 cp ~/.gitconfig ~/.gitconfig.orig
 cp /afs/cern.ch/user/s/stiegerb/public/forCarlotta/.gitconfig ~/
 git df
 git br
 git remote -v
 git remote add cmantill git@github.com:cmantill/TopMassSecVtx.git
 git remote -v
 git checkout -b mtdilepton
 git add scripts/runDileptonUnfolding.py
 git add scripts/utils.py
 git commit -m'Cristinas first commit'
 git l
 git push cmantill mtdilepton

history | grep git > githistory

Note:

Getting CERN Kerberos ticket in my laptop I connected my computer with lxplus using OpenAFS. In order to access your CERN AFS account you'll need to obtain an AFS token from the CERN server. I had already installed Kerberos packages but I followed instructions from this sites:

http://linux.web.cern.ch/linux/docs/kerberos-access.shtml

https://gist.github.com/KFubuki/10728230 - Also here I found some CERN very useful hacks

https://wiki.chipp.ch/twiki/bin/view/CmsTier3/HowToWorkInCmsEnv

After installing and setting it up, you should create a ticket and log on:

kinit username@CERN.CH
aklog
  

You can also test your access with:

klist
ls /afs/cern.ch/
ls /afs/cern.ch/user/c/cmantill/
  

Now you can work directly from your computer.

Note:

Request Workspace at Lxplus Locally at CERN, the personal working area on CERN's LXPLUS cluster isn't big enough to handle the output files, you'll need to write them to a larger-capacity area.

To ask for "AFS workspace" (up to 100 GB, backed up), login to the Cern account web page and go to "List Services", take the "AFS Workspaces" and then "Settings".

There you can ask for "workspace" in AFS, as well as extend the quota for your backed-up home (up to 10 GB). Please note the different AFS path to your workspace: /afs/cern.ch/work/initial/username where initial is the first letter of your username, i.e. the workspace is not hanging from your home.

Workspace path: /afs/cern.ch/work/c/cmantill

30 June, 2015: Generating first plots

Turns out I was submitting 0 jobs before because the input directory should be this one:

 
input directory with the files: /store/cmst3/group/top/summer2015/treedir_bbbcb36/ttbar
 

I got the plots for the other four distributions. I modified scripts/runDileptonUnfolding.py and got a new version. Here I attach some plots:

The notation I use in my code is the following:

  • $p_T (l^{+})$ - ptpos - Pt of the positive lepton

  • $p_T (l^{+}l^{-})$ - ptll - Pt of the charged lepton pair

Generated level Reconstructed level Reconstructed level Bin-corrected

Observed normalization PDF

  • $M (l^{+}l^{-})$ - mll - Invariant mass of the charged lepton pair

Generated level Reconstructed level Reconstructed level Bin-corrected

Observed normalization PDF

  • $E (l^{+})+E(l^{-})$-EposEm- Energy sum of the 2 leptons

Generated level Reconstructed level Reconstructed level Bin-corrected

Observed normalization PDF

  • $Pt (l^{+})+Pt(l^{-})$-ptposptm- Pt sum of the 2 leptons

Generated level Reconstructed level Reconstructed level Bin-corrected

Observed normalization PDF

29 June, 2015: Reading the twiki page and starting to work

The twiki page: https://twiki.cern.ch/twiki/bin/viewauth/CMS/CMGTopStudents2015

Working directory: /afs/cern.ch/user/c/cmantill/private/top/CMSSW_5_3_22/src/UserCode/TopMassSecVtx

  • Storing locally the normalization to be applied to the MC.
     
       ./scripts/runPlotter.py --rereadXsecWeights /store/cmst3/group/top/summer2015/bbbcb36/ -j test/topss2014/samples.json
       

  ...Processing all MC8TeV and Data8TeV
   ...
   >>> Produced xsec weights and wrote to cache (.xsecweights.pck)
   

The normalization is computed as a weight $\sigma/N_{\rm orig~events}$ where $\sigma$ is the theoretical cross section of a process and $N_{\rm orig~events}$ is the number of generated events. The luminosity $\mathcal{L}$ is the ratio of the number of events detected $\mathcal{N}$ in a certain time interval to the interaction cross-section $\sigma$. With this definition, the number of expected events after acquiring a given integrated luminosity $\mathcal{L}$, is given by $N=N_{\rm sel}\cdot\mathcal{L}\cdot\sigma/N_{\rm orig~events}$ where $N_{\rm sel}$ is the number of selected events in the analysis.

  • $p_T (l^{+})$ distributions
    • Creating the reconstructed and generator level distributions

 
python scripts/runDileptonUnfolding.py -i /store/cmst3/group/top/summer2015/treedir_bbbcb36/ -o unfoldResults/ --jobs 8

input directory with the files: /store/cmst3/group/top/summer2015/treedir_bbbcb36/

--------------------------------------------------------------------------------
Creating ROOT file with migration matrices, data and background distributions from /store/cmst3/group/top/summer2015/treedir_bbbcb36/singlet/
Discarded 0 files duplicated in cmsLs output
 Submitting jobs in 8 threads
Histograms saved in unfoldResults/Data8TeV_SingleElectron2012C.root
...
 --------------------------------------------------------------------------------

I obtained the distributions at generated and reconstructed level for %$p_T (l^{+})$ (ptpos).

Simple counting Bin-corrected

I can subtract the background from the data, and unfold the result by running

python scripts/runDileptonUnfolding.py -r unfoldResults/plots/plotter.root -v ptpos -o unfoldResults

Observed normalization PDF

Note: Eos useful commads:

eoscms ls -l /eos/cms/store/cmst3/group/top/summer2015

TFile::Open("root://eoscms.cern.ch//eos/cms/store/cmst3/group/top/summer2015/ttbar/treedir_bbbcb36/ttbar/MC8TeV_ZZ.root")

Topic attachments
I Attachment History Action Size DateSorted descending Who Comment
PNGpng bin1166_ptpos_gen.png r1 manage 19.0 K 2015-07-23 - 14:35 CristinaAnaMantillaSuarez  
PNGpng bin1166_pur_stab_eff.png r1 manage 10.4 K 2015-07-23 - 14:35 CristinaAnaMantillaSuarez  
PNGpng bin1166ptpos_rec.png r1 manage 19.0 K 2015-07-23 - 14:35 CristinaAnaMantillaSuarez  
PDFpdf bin1166ptpos_rec_wgt.pdf r1 manage 14.9 K 2015-07-23 - 14:35 CristinaAnaMantillaSuarez  
PNGpng bin1166ptpos_unfolded.png r1 manage 23.0 K 2015-07-23 - 14:35 CristinaAnaMantillaSuarez  
PNGpng bin1ptpos_gen_comparisonNorm.png r1 manage 22.6 K 2015-07-23 - 14:51 CristinaAnaMantillaSuarez  
PNGpng bin1u1_ptpos.png r1 manage 13.6 K 2015-07-23 - 14:51 CristinaAnaMantillaSuarez  
PNGpng bin1u1_ptpos_unf.png r1 manage 13.9 K 2015-07-23 - 14:51 CristinaAnaMantillaSuarez  
PNGpng bin1u2_ptpos.png r1 manage 16.2 K 2015-07-23 - 14:51 CristinaAnaMantillaSuarez  
PNGpng bin1u2_ptpos_unf.png r1 manage 15.4 K 2015-07-23 - 14:51 CristinaAnaMantillaSuarez  
PNGpng ptposPDF_unfolded.png r1 manage 24.0 K 2015-07-23 - 09:57 CristinaAnaMantillaSuarez Ptpos first distributions at reconstructed level and the unfolded distributions
PNGpng ptpos_rec.png r1 manage 23.3 K 2015-07-23 - 09:57 CristinaAnaMantillaSuarez Ptpos first distributions at reconstructed level and the unfolded distributions
PNGpng ptpos_rec_wgt.png r1 manage 23.1 K 2015-07-23 - 09:57 CristinaAnaMantillaSuarez Ptpos first distributions at reconstructed level and the unfolded distributions
PNGpng ptpos_unfolded.png r1 manage 22.6 K 2015-07-23 - 09:57 CristinaAnaMantillaSuarez Ptpos first distributions at reconstructed level and the unfolded distributions
PDFpdf u1_ptpos.pdf r1 manage 15.4 K 2015-07-17 - 16:11 CristinaAnaMantillaSuarez  
PDFpdf u1_ptpos_gen.pdf r1 manage 14.6 K 2015-07-17 - 16:11 CristinaAnaMantillaSuarez  
PDFpdf u1_ptpos_rec.pdf r1 manage 14.6 K 2015-07-17 - 16:11 CristinaAnaMantillaSuarez  
PNGpng u2_ptpos.png r1 manage 18.7 K 2015-07-17 - 16:11 CristinaAnaMantillaSuarez  
PDFpdf u2_ptpos_gen.pdf r1 manage 14.7 K 2015-07-17 - 16:11 CristinaAnaMantillaSuarez  
PDFpdf u2_ptpos_rec.pdf r1 manage 14.7 K 2015-07-17 - 16:11 CristinaAnaMantillaSuarez  
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