1. Simulation and Reconstruction code using Mathematica
J. Carr
(with D. Dornic and S. Escoffier)
WP2 Workshop, Oct 2006

2. Spirit of this presentation
Work in progress
Will check and compare with standard code
Some results presented to illustrate intentions
No conclusions yet

3. Mathematica Complete software environment
Full incorporated online documentation
Hardcopy books available
Web site with extensive examples
Powerful programming language
- easy to start, longer to master..
- extensive graphics
- ~2000 built in functions
- ……..

4. Simulation: “MGEN”+”MTRIG”
Outline of code
Simulation: “MGEN”+”MTRIG”
“MGEN”
- tracks: all minimum ionizing, all traverse can 500m
(ie. 200 GeV and no shower generation)
- Cherenkov light travels in straight line (ie. no scattering)
- Gaussian time resolution
“MTRIG”
- white random noise for K40 and bioluminescence
- apply trigger condition
- select hits causally connected to trigger hits
Future additions planned
- simulation of charge measurement
- high energy tracks/ electromagnetic showers
- light scatting in water

5. Reconstruction : “MRECO”
Outline of code
Reconstruction : “MRECO”
Initial hit selection
based on clusters of minimum of 3 hits in adjacent storeys
causality (again) relative to barycentre of all selected hits
Prefit
only space in transverse plane, time along track
using all selected hits
reject up to 3 hits if large residual
repeat prefit
Main fit
use prefit as parameter as first starting values
then iterate with other starting values
repeat fit

6. Detector Geometry
ANTARES

7. Detector Geometry
NEMO

8. Track Generation ANTARES
All tracks minimum ionising, no showers so 200 GeV
Tracks for events >5 L0
Generate tracks isotropic in direction
Uniform entering and leaving can
ANTARES

9. Generation of Cherenkov photons
Minimum ionizing particle N0=345 photons/cm
Ch
L=R/sin(Ch) R N0
N = R
eL/
, = 55m
APMT = 440 cm2
PMT = 0.2
Without absorption
N (1m) =50 photons
Nphotons
Nphotons
With
absorption
R= distance from track OM (m)
R= distance from track OM (m)

10. Angular acceptance of OM
OM() = a ( 1 + Cos() )2 / 4  Cos() , a =0.667 
Distribution of recorded hits
Cos(zenith )
Relative acceptance
Cos()
Cos()
ANTARES

11. Generated Event ANTARES Trajectory of light from track to OM 1 hit
in storey
2 hits in storey
in 2 different OM
track
3 hits in storey
in 2 different OM
2 hits in storey
in 1 same OM
3 hits
in storey
lines
ANTARES

12. ANTARES events
ANTARES

13. Nemo events
NEMO

14. Number of single hits vs cos 
Select event with > 5 hits in total in detector
ANTARES
Total hits in detector
track cos( zenith)

15. Number of single hits vs cos 
Select event with > 5 hits in total in detector
NEMO
Total hits in detector
track cos( zenith)

16. Cluster Trigger definition
L1 = 2 L0 in a storey in 10 ns
T2 trigger
2 L1 in adjacent 2 storeys
( in 100ns gate)
T3 trigger
2 L1 in 2/3 adjacent storeys
(in 200ns gate)
( Same definition for NEMO, floor=storey )

17. Trigger efficiency ANTARES Efficiency normalized to event > 5 hits
track cos( zenith)
efficiency
ANTARES
1 T3 (4 hits)
1 T2 (4 hits)
2 T3 (8 hits)
5 L1 (10 hits)
2 T2 (8 hits)

18. Trigger efficiency NEMO Efficiency normalized to event > 5 hits
5 L1 (10 hits)
track cos( zenith)

19. Trigger efficiency with different normalization
ANTARES
Normalized to events with > 5 hits & dmin< 30m
Normalized to events with > 9 hits & dmin< 30m
efficiency
efficiency
1 T3 (4 hits)
1 T2 (4 hits)
2 T3 (8 hits)
5 L1 (10 hits)
2 T2 (8 hits)
track cos( zenith)
track cos( zenith)

20. Effect of PM size ANTARES N0=26 photons at 1 m N0=104 photons at 1 m
(~14”)
(~7”)

21. Trigger efficiency
T3 efficiency N0
ANTARES

22. Effect of Absorption length
Upward events
events/generated
>9 single hits
 55m 75m
 31%34%
T3 trigger
absorption
Downward events
events/generated
 55m 75m
 6% 8%
>9 single hits
T3 trigger
absorption
ANTARES

23. Causality relative to T3 trigger
ANTARES
R (m)
Cut around all
edges, 4 parameters
t (ns)

24. Hit selection
true L0
Before
After
false L0 T3
ANTARES

25. Average number of false hits/event
ANTARES

26. Average number of true hits/event
ANTARES

27. Fit Use Mathematica “NMinimise” Four possible minimization methods:
1) Nelder Mead Simplex 12% fail, 5sec/event
2) Simulated Annealing % fail, 5 sec/event
3) Random Sampling % fail, 8 sec/event
4) Differential Evolution % fail, 20 sec/event
Quite sensitive to starting values and initial steps
Each method has many parameters
Extensive tuning needed to optimize

28. September MRECO Efficiency
ANTARES

29. Latest MRECO Efficiency
Big improvement with a few weeks work, will keep improving
ANTARES

30. Summary and next steps Code works
Enables optimization easily changing parameters
Check results with standard ANTARE MC
- interface Mathematica code with standard ASCI output
Further developments
- make fit work better
- add scattering and showers with parameterization
- ……

31. Existing Code All comments and help welcome
MGEN Simulation code
MTRIG Code to apply trigger
MRECO Reconstruction code
All comments and help welcome