KM3NeT detector optimization with HOU simulation and reconstruction software

A. G. Tsirigotis

In the framework of the KM3NeT Design Study

WP2 - Paris, 10-11 December 2008

The HOU software chain

Underwater Detector

•Generation of atmospheric muons and neutrino events (F77)

•Detailed detector simulation (GEANT4-GDML) (C++)

•Optical noise and PMT response simulation (F77)

•Filtering Algorithms (F77 –C++)

•Muon reconstruction (C++)

Calibration (Sea top) Detector

•Atmospheric Shower Simulation (CORSIKA) – Unthinning Algorithm (F77)

•Detailed Scintillation Counter Simulation (GEANT4) (C++) – Fast Scintillation Counter Simulation (F77)

•Reconstruction of the shower direction (F77)

•Muon Transportation to the Underwater Detector (C++)

•Estimation of: resolution, offset (F77)

Event Generation – Flux Parameterization

•Neutrino Interaction Events

•Atmospheric Muon Generation(CORSIKA Files, Parametrized fluxes )

μ

•Atmospheric Neutrinos(Bartol Flux)

ν

ν•Cosmic Neutrinos(AGN – GRB – GZK and more) Earth

Survival probability

Shadowing of neutrinos by Earth

GEANT4 Simulation – Detector Description

• Any detector geometry can be described in a very effective way

Use of Geomery Description Markup Language (GDML-XML) software package

•All the relevant physics processes are included in the simulation• (NO SCATTERING)

Fast Simulation EM Shower Parameterization

•Number of Cherenkov Photons Emitted (~shower energy)

•Angular and Longitudal profile of emitted photons

Visualization

Detector componentsParticle Tracks and Hits

Simulation of the PMT response to optical photons

Single Photoelectron Spectrum

mV

Quantum Efficiency

Πρότυπος παλμός

Standard electrical pulse for a response to a single p.e.

Arrival Pulse Time resolution

Prefit, filtering and muon reconstruction algorithms

•Local (storey) Coincidence (Applicable only when there are more than one PMT looking towards the same hemisphere)•Global clustering (causality) filter•Local clustering (causality) filter•Prefit and Filtering based on clustering of candidate track segments (Direct Walk)

•Χ2 fit without taking into account the charge (number of photons)

•Kalman Filter (novel application in this area)

•Charge – Direction Likelihood

dm

L-dm

(Vx,Vy,Vz) pseudo-vertex

dγ

d

Track Parameters

θ : zenith angle φ: azimuth angle (Vx,Vy,Vz): pseudo-vertex coordinates

θc

(x,y,z)

State vector

1

exp

k

k

x x

tH

x

0 0,x CInitial estimation

Update Equations

Kalman Gain Matrix

Updated residual and chi-square contribution

Kalman Filter application to track reconstruction

(timing uncertainty)

Kalman Filter – Muon Track Reconstruction - Algorithm

Extrapolate the state vector

Extrapolate the covariance matrix

Calculate the residual of predictionsDecide to include or not the measurement (rough criterion)

Update the state vector

Update the covariance matrix

2Calculate the contribution of the filtered pointDecide to include or not the measurement (precise criterion)

Prediction Filtering

Initial estimates for the state vector and

covariance matrix

Charge Likelihood

hit nohit

hit nohit

N N

exp expi data ii 1 i 1

; ;

(N N )

ln P (V ) P (0 )

L

i data exp PMTresolutionexp datan 1

P (V ; ) F(n, )G n(V ;n, )

dataV Hit charge in PEs

exp Mean expected number of Pes (depends on distance form track and PMT orientation)

expF(n, ) Not a poisson distribution)

10,8,6,3m

20 floors per tower30m seperationBetween floors

30m

Tower Geometry Floor Geometry

45o 45o

Geometry: 10920 OMs in a hexagonal grid.91 Towers seperated by 130m, 20 floors each. 30m between floors

Optical Module

•10 inch PMT housed in a 17inch benthos sphere•35%Maximum Quantum Efficiency•Genova ANTARES Parametrization for angular acceptance

50KHz of K40 optical noise

Neutrino Angular resolution (no cuts applied)Results

Neutrino effective area (no cuts applied)Results

Results Efficiency of cuts

Min compatible tracks = 10

Min compatible tracks = 25

Min compatible tracks = 40

1 hour of generated atmospheric muons

Number of misreconstructed muons per day

Number of reconstructed atmospheric neutrinos per day

Ratio = (muons)/(neutrinos) (%)

Results

Effective Area and angular resolution :

Without applying any cuts

Applying the cuts that give zero misreconstructed atmospheric muons per day:Likelihod < 1.0 and Minimum number of combatible tracks 40

Results

Without applying any cuts

Applying the cuts that give zero misreconstructed atmospheric muons per day:Likelihod < 1.0 and Minimum number of combatible tracks 40

Number of reconstructed atmospheric neutrinos per day vs Neutrino Energy:

Conclusions

Kalman Filter is a promising new way for filtering and reconstruction for KM3NeT

However for the rejection of badly misreconstructed tracks additional cuts must be applied

Presented by Apostolos G. TsirigotisEmail: tsirigotis@eap.gr

Kalman Filter – Basics (Linear system)

1kk k kx F x w

Equation describing the evolution of the state vector (System Equation):

k k k km H x Measurement equation:

Definitions

kx Estimated state vector after inclusion of the kth measurement (hit) (a

posteriori estimation)

km Measurement k

x Vector of parameters describing the state of the system (State vector)

kF Track propagator

kw Process noise (e.g. multiple scattering)

k Measurement noise

kH Projection (in measurement space) matrix

kx a priori estimation of the state vector based on the previous (k-1)

measurements

cov( )k kw Q

cov( )k kV

Kalman Filter – Basics (Linear system)

Prediction (Estimation based on previous knowledge)

1kk kx F x

Extrapolation of the state vector

Extrapolation of the covariance matrix

1cov( )

k

Tk k k k kC x F C F Q

Residual of predictions

k k k kr m H x

Covariance matrix of predicted residuals

Tk k k k kR V H C H

(criterion to decide the quality of the measurement)

Kalman Filter – Basics (Linear system)

Filtering (Update equations)

( )k k k k k kx x K m H x

(1 )k k k kC K H C

where,

1( )T Tk k k k k kK C H V H C H

is the Kalman Gain Matrix

Filtered residuals:

(1 )k kk k k k kr m H x H K r cov( ) (1 )k k k k kR r K H V 2 Contribution of the filtered point:

2 1,

Tk F k k kr R r (criterion to decide the quality of the measurement)

Kalman Filter – (Non-Linear system)

( )k k k kF x f x ( )k k k kH x h x

Extended Kalman Filter (EKF)

kk

k

fF

x

k

kk

hH

x

Unscented Kalman Filter (UKF)

A new extension of the Kalman Filter to nonlinear systems, S. J. Julier and J. K. Uhlmann (1997)

Kalman Filter Extensions – Gaussian Sum Filter (GSF)

t-texpected

•Approximation of proccess or measurement noise by a sum of Gaussians

•Run several Kalman filters in parallel one for each Gaussian component

V

x

Kalman Filter – Muon Track Reconstruction

Pseudo-vertex

Zenith angle

Azimuth angle

State vector

Measurement vector t

mq

Hit Arrival time

Hit charge

1kkx x

System Equation:

Track Propagator=1 (parameter estimation)

No Process noise (multiple scattering negligible for Eμ>1TeV)

( )k k k km h x

Measurement equation:

exp

exp

( )( )

( )

t xh x

q x

2

2

0cov( )

0t

kq