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

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

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 - ……..

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

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

Detector Geometry ANTARES

Detector Geometry NEMO

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

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)

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

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

ANTARES events ANTARES

Nemo events NEMO

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

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

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 )

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)

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

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)

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

Trigger efficiency T3 efficiency N0 ANTARES

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

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

Hit selection true L0 Before After false L0 T3 ANTARES

Average number of false hits/event ANTARES

Average number of true hits/event ANTARES

Fit Use Mathematica “NMinimise” Four possible minimization methods: 1) Nelder Mead Simplex 12% fail, 5sec/event 2) Simulated Annealing 10% fail, 5 sec/event 3) Random Sampling 5% fail, 8 sec/event 4) Differential Evolution 24% fail, 20 sec/event Quite sensitive to starting values and initial steps Each method has many parameters Extensive tuning needed to optimize

September MRECO Efficiency ANTARES

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

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 - ……

Existing Code All comments and help welcome http://antares.in2p3.fr/users/carr/internal/Mathematica/ MGEN Simulation code MTRIG Code to apply trigger MRECO Reconstruction code All comments and help welcome