1. Song LIANG Email: liangs @ ihep.ac.cn CMS-IHEP, China 2009.11.27
Hadron Shower Shape
Song LIANG
ihep.ac.cn
CMS-IHEP, China

2. Outline
1. Motivation
2. Process
3. Problem
4. Conclusion

3. 1. Motivation
Test if the shower shape formula is fitting for the hadron shower shape in ECAL.
Lateral formula:
R1=6.21
Longitudinal formula:
PS: I just get the primary result, there must be some errors. Hope that you can find the problems and help me to make it better. Any of your suggestion, please tell me.
dE/dt =E0b(bt)a-1e-bt/Γ(a)

4. 2. Process 1). Data sample: pi Eta : -1.479~1.479 Phi : -3.14~3.14
E : 20GeV~100GeV
Events:800000

5. 2). Track extrapolation Devide the ECAL into 100 layers,
Find the 100 points on the track through track extrapolation

6. 3). iEta and iPhi of ECAL crystals:
iEta and iPhi are two signs of ECAL crystals
iEta: -85~ 1, 1~85; iPhi: 1~360
Calculate the iEta and iPhi of the 100 track points
Trough the value of iEta and iPhi to calculate the crystal ID.
From the crystal ID, I calculate the number of crystals which the hadron track pass through.

7. The number of crystals which the pion track pass through

8. 4). 9x9 crystals:
9x9 crystals around the crystal which the hadron hit the ECAL.
Calculate the iEta and iPhi of the crystal which the hadron hit ECAL.
Get the iEta and iPhi value of 9x9 crystals around that crystal

9. 5). Cut condition: Event: 800000 Events only have one track: 637089
Remove ionization events(Esum9x9<1.2, CMS CR-2008/040):

10. The distribution of the 9x9 crystals deposit energy

11. (1)nCrystal=1: 2D fitting
6). Fitting method:
(1)nCrystal=1: 2D fitting
Only using the lateral formula to fit the shower shape.
Lateral formula:
R1=6.21
(2)nCrystal>2: very few events, I want to fit it when the other two switchs get better results.
nCrystal: the number of crystals which the hadron pass through

12. (3)nCrystal=2: 3D fitting Lateral formula: R1=6.21
Longitudinal formula:
a=0.67*log(E/Ec)-0.29=2.024
tmax=l.04*log(E/Ec)-0.16=3.432
b=(a-1)/tmax=0.298
Ec=
E=24.83, It is the average of the deposit energy (Etot).
dE/dt =E0b(bt)a-1e-bt/Γ(a)

13. Fit the start point:
(1) Suppose one of the 100 track points is the start point
(2) Calculate the deposit energy of the 9x9 crystal through the formula.
(3) Calculate the chisquare of the deposit energy in the two crystals.
(4) Use the point which have the minimum chisquare as the start point.

14. The distribution of the minimum chisquare

15. The distribution of the start point
t_start: The distance from the start point to
the point which the hadron hits ECAL.

16. 7)Result The shower shape in 9x9 crystals around the crystal
which has the highest deposit energy.
From the fitting of the shower formula
From the reconstruction hit

17. 3. Problem 1) minimum chisquare:
Trough it has a peak near zero, but it has a very long tail. The value of many of them is too large.

18. Longitudinal formula:
2)nCrystal=2: 3D fitting
Longitudinal formula:
a=0.67*log(E/Ec)-0.29, tmax=l.04*log(E/Ec)-0.16=3.432,
b=(a-1)/tmax=0.298, Ec=
E, It is the average of the deposit energy (Etot).
From EM shower, parameter a and b are depended on parameter E. Could the formulas above be fitted to hadron Shower?
E: the average of all the deposit energy OR the average of deposit energy of 9x9 crystal?
dE/dt =E0b(bt)a-1e-bt/Γ(a)

19. 3)The distribution of the R1 with the deposited energy is as the following plots (left).
Etot is the deposited Energy.
Profile
R1= *Etot
From the plots above we can see that parameter R1 distributes a large range. If I use the average value, the shower shape may not be fit well. 19

20. 4. Conclusion
From the shower shape, we can see that the shape calculated by the formula is not fit for that by the hitting very well.
There must be something wrong in my work. And many details should be corrected.
This is a long and hard work, any small mistake may make a large error. Hope that you can help me to correct it.

21. The End!
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