1. CMS-Bijing weekly meeting
Unconverted Gamma/Pi0 discrimination in ECAL Endcap with CMSSW_3_1_2
J.Tao
IHEP-Beijing
CMS-Bijing weekly meeting
Nov. 20, 2009

2. Outline Uncoverted EE case:
Analysis with variables from CMS AN-2008/063 :
25 variables
Trying the discrimination in CMSSW_3_1_2
Analysis with EM shower formulae fitting:
Formulae validation for the EE case
TMA analysis with the EM fitting results

3. Preview the 25 variables from CMS AN-2008/063

4. TMVA training results for Unconv EE: BDT & MLP with PT 15-25GeV
the first datasets of Gamma&Pi0
VtxSmearedEarly10TeVCollision
the second datasets of Gamma&Pi0
VtxSmearedGauss
~30%
<20%
NN results with CSA07 H2GaGa and Gam+jets samples

5. Vertex Smear of the First datasets
First datasets of single particles (Gamma&Pi0) in SW_3_1_2 :
Configuration/StandardSequences/VtxSmearedEarly10TeVCollision_cff
(as the default one used in SW31X, using cmsDriver.py to produce the cfg file)
Sigma(x/y)~46um
Early10TeVCollisionVtxSmearingParameters = cms.PSet(
Phi = cms.double(0.0),
BetaStar = cms.double(300.0),
Emittance = cms.double(7.03e-08),
Alpha = cms.double(0.0),
SigmaZ = cms.double(3.8),
TimeOffset = cms.double(0.0),
Y0 = cms.double(0.0),
X0 = cms.double(0.0322),
Z0 = cms.double(0.0) )
"BetafuncEvtVtxGenerator"
sqrt(femittance*(fbetastar+(((z-z0)*(z-z0))/fbetastar)));

6. Vertex Smear of the Second datasets
Reproduce the datasets of single particles again in SW_3_1_2:
Configuration/StandardSequences/VtxSmearedGauss_cff
GaussVtxSmearingParameters = cms.PSet(
MeanX = cms.double(0.0),
MeanY = cms.double(0.0),
MeanZ = cms.double(0.0),
SigmaY = cms.double(0.0015),
SigmaX = cms.double(0.0015),
SigmaZ = cms.double(5.3),
TimeOffset = cms.double(0.0) )
For 14TeV, also SCA07 samples

7. 25 variables’ distributions from the first datasets: ET=20GeV (I)

8. 25 variables’ distributions from the first datasets: ET=20GeV (II)

9. 25 variables’ distributions from the second datasets: ET=20GeV (I)

10. 25 variables’ distributions from the second datasets: ET=20GeV (II)

11. 25 variables’ distributions from CMS AN-2008/063: ET=20GeV (I)

12. 25 variables’ distributions from CMS AN-2008/063: ET=20GeV (II)

13. EM shower Formulae validation for the EE case
Different geometry with EB case
Different paramters in COG calculation using the log weighting technique.
25 layers along the particle direction; Same logitudinal paramters in the Gamma-functon, started from the front face of EE.
Same as the EB B-on case, 5 parameters were used in Minuit minimization procedure: A、 ΔE/Edep5x5 where ΔE=E0-Edep5x5、、1、2
5x5 crystal array was used for the validation
Front face: ×28.62 mm2
Rear face: 30×30 mm2
Length: 220mm ~ 24.7 X0
Supercrystal:
5×5 crystals
Dee (½ endcap):
3662 crystals
Each silicon divided into 32 strips with a pitch of 1.9 mm.
Each plane is preceded by a thin absorber of 1.9 X0 and 0.9 X0 respectively.
A total of 4304 detectors are needed, leading to channels.
Single Gamma Samples with E=50GeV, Eta=2.0, Phi=1.5
0.1%

14. EM shower Formulae Fitting in EE
Single Gamma Samples with E=50GeV, Eta=2.0, Phi=1.5
2000 gamma evetns,
1135 unconverted gamma evetns,
1006 FitOk events: FitStatus==3 && parameters not at it’s limit
FitStatus η φ 1 2 5 6 10 25 4 3 11 16 21 9 7 8 12 22 19 18 17 14 15 13 20 24 23
Crystal (or cell) number

15. Fit parameters

16. Fit parameters for unconverted case in EB with SW1_6_7

17. Fit Ok / Unconverted (efficiency)
TMVA analysis with 6 fitting variables
MC samples:
Single , π0 → samples in EE in CMSSW_3_1_2 with VtxSmearedGauss
6 PT Gen.bins: 15-25GeV;25-35GeV; 35-45GeV; 45-55GeV;55-65GeV;65-75GeV
6 PT bins of Rec. photon: GeV GeV GeV
45-55GeV GeV GeV
Method:
Parametric EM shower fitting variables: 6 variables
A、 ΔE/Edep5x5 where ΔE=E0-Edep5x5、、1、2、 2/Edep5x5
Analysis FitOk events
Fit Ok / Unconverted (efficiency)
PT bins (GeV)  π0
20-25
22507 / (76.7%)
8591 / (66.1%)
25-35
37133 / (76.8%)
17210 / (68.3%)
35-45
43523 / (79.5%)
17261 / (71.65%)
45-55
38744 / (81.3%)
17402 / (75.0%)
55-65
37927 / (83.7%)
16683 / (78.3%)
65-75
32182 / (87.3%)
13525 / (83.2%)

18. Preliminary results of TMVA analysis with 6 fitting variables
20-25GeV GeV GeV
45-55GeV GeV GeV
~30% π0 rejection efficiency for keeping 90% photon efficincy

19. 6 inputs variables: PT25-35GeV
Need to check

20. Summary
For Unconverted /π0 discrimination in the ECAL endcap, the onl variables with the information in ES, nos so powerful .
EM shower formulae was valided in EE case, the results are not so bad or not so good.
For the Unconverted /π0 discrimination in ECAL EE, the parametric shower shape fitting method was tried in CMSSW_3_1_2, ~30% π0 rejection efficiency for keeping 90% photon efficincy can be obtained for the preliminary analysis.
The fitting ok efficiency is lower than ~90%, that’s a problem.
The analysis codes maybe need further check.

21. Backup slides

22. Position measurement of cluster using log weighting technique @CMS
Earlier method need correction:
Position of cluster can be calculated with
where xi the position of crystal i, and Wi is the log weight of the crystal— the log of the fraction of the cluster energy contained in the crystal, calculated with the formula:
where the weight is constrained to be positive, or is otherwise set to zero. W0 then controls the smallest fractional energy that a crystal can have and still contribute to the position measurement. Its default value, obtained after optimization studies, is 4.2 — so that crystals in the cluster containing more than 1.5% of the cluster energy contribute to the position measurement.
CMS Note 2001/034

23. Calculate Method in CMSSW
Firstly , get the depth from A[B+log(E)] .
Max. energy deposit crystal: (θ,φ) & (x,y,z) getPosition(depth)
For each crystal,
Then using the log weighting technique:
Then

24. Parameters in CMSSW Depth A[B+log(E)] : A=0.89cm Weight W0=4.2 Refs.:
For electron B= For photon B=
Weight
W0=4.2
Refs.:
7.4 Barrel
3.1 Endcap_no_Preshower
1.2 Endcap_with_Preshowe
7.7 Barrel
6.3 Endcap_no_Preshower
3.6 Endcap_with_Preshowe

25. Empirical formula to parameterize
EM shower shape
We combine the longitudinal profile and lateral profile of EM shower to get the empirical 3-dimentional formula.
The longitudinal profile of EM shower can be well described by a Gamma-function:
where t is the shower depth. E0 is the Energy. a and b are parameters
The following formula is used to describe the lateral profile:
where r is the distance of a crystal to the COG (centre of gravity), and R is a parameter.
The longitudinal profile is validated from the CMS Geant4 simulation.
For the whole empirical formula (Longitudinal + Lateral), we use the data of ECAL test beam 2006 for validation.

26. EM Showers -- Longitudinal profile
Determine longitudinal profile from CMS Geant4 Simulation
Simulation sample in SW167
Using “EcalSimHitsValidProducer” in the CMSSW/Validation package
2000 events/sample to see the average distribution
20GeV Electron longitudinal profile
fitted by the Gamma-function
20GeV Gamma longitudinal profile
fiteed by the Gamma-function
Eta=0.1 & Phi=0.1

28. Parametric EM shower fitting method
Same as the analysis in CMSSW_1_6_7
Formulea: longitudinal profile + lateral profile
Determine longitudinal profile from CMS Geant4 Simulation: parameters a & b
For the Gamma EM shower with B-on, the energy spreading is, to good approximation, only in the -direction. Non isotropy at the same r of the lateral formula in a layer now.
Correction: The original COG obtained by the energy Log-weighted method is split into 2 new COG points; 2 interaction points with a layer are obtained; In a layer, the energy in a crystal is obtained from the average effect of the lateral formula originated at the 2 interaction points.
For the EM shower fitting method , 6 variables were used in TMVA analysis: A、 ΔE/Edep5x5 where ΔE=E0-Edep5x5、、1、2、 2/Edep5x5 instead of 2 (in SW167).