1. CMS-Bijing weekly meeting
Unconverted Gamma/Pi0 discrimination in ECAL Barrel with CMSSW_3_1_2
J.Tao
IHEP-Beijing
CMS-Bijing weekly meeting
Oct. 15, 2009

2. Introduction N = MC samples: Single , π0 → plsames in CMSSW_3_1_2
6 PT bins: 15-25GeV;25-35GeV; 35-45GeV; 45-55GeV;55-65GeV;65-75GeV
η (geometry) range: -3.0~3.0 and  range: - π~ π
10k events for each PT bin
Unconverted Gamma/Pi0 discrimination in ECAL Barrel
Unconverted photon selection
6 PT bins of Rec. photon: GeV GeV GeV
45-55GeV GeV GeV
ROOT version : 5.24/00
TMVA analysis: BDT & MLP
Method:
NN 12 variables (previous presentation)
Moments variables from CMS AN-2008/075: 3 variables
Parametric EM shower fitting variables: 6 variables
Combination: NN+Moments+Parametric =
ConvID
track N

3. Moments variable 1 – second-order moments
Distribution of energy deposit for π0 with = 6 cm, overlaid with the major (solid line) and minor(dotted line) axes.
Definition of monents of order n:
where dMAJi (dMINi ) is the distance between the center of the i-th crystal and the major (minor) axis, expressed in terms of η,  indices.
Major & minor axes, dened as the eigenvectors of the covariance matrix
where N is the number of crystals in the cluster, i and i are the η,  indices that identify the i-th crystal of the cluster and The weight I
(The eigenvalues are 1 and 2 in NN variables)
Moments with n > 2 are strongly correlated with second-order moments and therefore they are useless.
So MMAJ2 & MMIN2. In fact only MMAJ2 is powerful for the discrimination of /π0.
Distribution of the average value of MMAJ2 for  and π0, as a function of EST
Distribution of the average value of MMin2 for  and π0, as a function of EST

4. Moments variable 2 – Lateral moment LAT
Definition of LAT:
where E1 and E2 are the energies of the two most energetic crystals of the cluster.
Expression of r2:
where ~ri is the radius vector of the i-th crystal, ~r is the radius vector of the cluster centroid and rM is the Moliere radius of the electromagnetic calorimeter (2.2 cm for PbWO4). Note that the two most energetic crystals are left out of the sum in this Eq.
Distribution of LAT

5. Moments variable 3 – Pseudo-zernike moment
The pseudo-Zernike moments Anm are dened as
where n and m are two integers.
The complex polynomials Vnm* (i,i), expressed in polar coordinates, are dened as
The cluster shape viable PZM used in the analysis is computed as
i. e. the norm of the A20 moment.
Distribution of PZM

6. TMVA analysis with Moments variables
PT20-25GeV
PT20-25GeV
PT25-35GeV
--- TFHandler_Factory : Ranking input variables...
--- IdTransformation : Ranking result (top variable is best ranked)
--- IdTransformation :
--- IdTransformation : Rank : Variable : Separation
--- IdTransformation : 1 : NN_UncEB_Mmaj2 : 2.592e-01
--- IdTransformation : 2 : NN_UncEB_LAT : 8.184e-02
--- IdTransformation : 3 : NN_UncEB_PZM : 6.097e-02
--- IdTransformation : 4 : NN_UncEB_Mmin2 : 1.055e-02

7. Results with Moments variables
Results from CMS AN-2008/075
samples: 150K single and 150K single π0 with energy uniformly distributed between 30 GeV and 70 GeV, within the barrel region
For my analysis results with moments variables for diferent PT bins, please see the next several slides after the introduction of parametric EM shower fitting method. At that time, I can compare the dicrimination results with diffirent variables.
Efciency of photon identication vs π0 rejection for MMAJ2, LAT and PZM.
Efciency of photon identication vs π0 rejection for Fisher discriminants containing MMAJ2.

8. 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).

9. TMVA analysis : BDT
PT20-25
PT25-30
PT20-25

10. Analysis with different variables
6 PT bins for the events with EM Fit ok: Fit status=3 && Not at the limits.
3 seperated group variavles: NN (N12), Moments (M3), EM Fit (F6).
4 combined group variavles: M3+F6 (9), N12+M3 (15), N12+F6 (18), N12+M3+F6(21)
Events for each PT bin - one half for training and the rest for test
Fit Ok / Used (efficiency)
PT bins (GeV)  π0
20-25
13426 / (86.0%)
9295 / (73.3%)
25-35
26871 / (87.0%)
18707 / (80.1%)
35-45
26796 / (88.1%)
18833 / (83.1%)
45-55
23324 / (88.7%)
16521 / (85.0%)
55-65
23294 / (90.1%)
15831 / (86.6%)
65-75
18632 / (91.6%)
14871 / (89.1%)

11. TMVA analysis results: BDT & MLP
Table list of the analysis results for the events with EM Fit ok
PT bins (GeV)
π0 rejection efficiency for keeping 90% photon efficincy M3 F6
M3+F6
N12
N12+M3
N12+F6
N12+M3+F6
20-25
BDT
58.7%
62.3%
70.2%
68.4%
72.0%
71.4%
73.4%
MLP
59.6%
63.3%
69.5%
71.0%
72.7%
73.3%
74.7%
25-35
44.4%
62.2%
64.8%
66.1%
66.2%
71.2%
59.0%
65.0%
69.2%
69.6%
35-45
38.8%
50.2%
59.2%
52.1%
62.0%
59.8%
66.0%
39.3%
48.0%
57.7%
51.8%
60.0%
59.5%
45-55
26.7%
40.7%
41.8%
44.3%
47.9%
26.2%
38.2%
41.2%
41.0%
42.9%
48.3%
50.5%
55-65
32.5%
34.0%
33.7%
45.9%
40.0%
49.1%
32.0%
33.3%
43.3%
33.1%
44.8%
40.4%
49.8%
65-75
17.0%
30.2%
29.7%
30.1%
34.5%
17.6%
30.7%
30.0%
30.4%
35.6%
35.7%

12. Signal eff. vs Bkg rejection: BDT & MLP (I)
PT20-25
PT20-25
PT25-35
PT25-35

13. Signal eff. vs Bkg rejection: BDT & MLP (II)
PT35-45
PT35-45
PT45-55
PT45-55

14. Signal eff. vs Bkg rejection: BDT & MLP (III)
PT55-65
PT55-65
PT65-75
PT65-75

15. Correlation of the inputs
PT25-35
PT25-35
PT55-65
PT55-65

16. Response of the analysis: PT25-35 (I)
PT25-35: M3
PT25-35: M3
PT25-35: F6
PT25-35: F6
K-S test tries to determine if two datasets differ significant. Reject the null hypothesis if P is “small”.

17. Response of the analysis: PT25-35 (II)
PT25-35: N12
PT25-35: N12
PT25-35: M3+F6+N12
PT25-35: M3+F6+N12

18. Response of the analysis: PT55-65
PT55-65: F6
PT55-65: F6
PT55-65: M3+F6+N12
PT55-65: M3+F6+N12

19. Before the application of the “Spliting method”, firstly have a look at the bias of the calculation, using parameterized values instead the wide distributions of each parameters.
PT20-75GeV Photon samples

20. (Fitted E0 – Edeposit) / Edeposit
PT20-75GeV Photon samples

21. PT20-75GeV Photon samples

22. Calculation with parametric EM shower
Seed crystal:
Calculated E1
Deposit E1
Calculated E5x5
Deposit E5x5
Photon PT35to45 sample
The energy difference of crystals was taken as the first step of “spliting method”.
Bias of the energy from the parametric EM shower calculation, will affect the method a lot.

23. Summary and plan
With the single , π0 samples, the unconverted/Converted /π0 discrimination was studied with the TMVA method, using different categories of variables.
N12+M3+F6 is the best one
First look at the bias of the Calculation with parametric EM shower. The results of the calculation using the parameterized valus instead of the distributions of each parameters show that bias exist for some events.
Ongoing: trying with the “Spliting method”

24. Backup slides