Progress report of the HOU contribution to TDR (WP2)

A. G. Tsirigotis

In the framework of the KM3NeT Design Study

WP2 - Demokritos, 31 March 2009

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++)

•Effective areas, resolution and more (scripts)

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

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)

•Compination of Χ2 fit and Kalman Filter (novel application in this area) using the arrival time information of the hits•Charge – Direction Likelihood using the charge (number of photons) of the hits

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 (rejection criterion for hit)

Kalman Filter application to track reconstruction

timing uncertainty

Many (40-200) candidate tracks are estimated starting from different initial conditions The best candidate is chosen using the chi-square value and the number of hits each track has accumulated.

0 0( , ).x C

Charge Likelihood

hit nohit

hit nohit

N N

i data ii 1 i 1

;E,D, ;E,D,

(N N )

ln P (V ) P (0 )

L

i data PMTresolutiondatan 1

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

dataV Hit charge in PEs

Probability depends on muon energy, distance from track and PMT orientation

F(n;E,D, ) Not a poisson distribution, due to discrete radiation processes

Ln(F

(n))

Ln(n)

E=1TeVD=37mθ=0deg

Log(E/GeV)

hit nohitL (N N )

8m

20 floors per tower30m seperationBetween floors

30m

Tower Geometry Floor Geometry

45o 45o

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

Working Example 60 meters maximum abs. length no scattering

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

Working Example

Results

Atmospheric Muons (Corsika files - 1 hour of generated showers)

Cos(theta)

dN

dTd(Time in days)

Without any cuts (21000/day misrec. as upgoing)

With optimal cuts(0 misrec. as upgoing)#hit>=12#solutions>=20#compatible>=10#compatible / #sol >0.5

Mild likelihood cut depended on reconstructed energy

Neutrino effective area (E-2 spectrum)Results

Eff

ecti

ve a

rea

(m2 )

Neutrino Energy (log(E/GeV))

Without any cuts

With optimal cuts

Neutrino Angular resolution (median in degrees)Results

Neutrino Energy (log(E/GeV))

An

gu

lar

reso

luti

on

(m

edia

n d

egre

es)

Without any cuts

With optimal cuts

Results Atmospheric neutrinos (Bartol Flux)

Cos(theta)

dN

dTd

(Time in days)

With optimal cuts (130/day rec.)

Without any cuts (200/day rec.) 65% cut efficiency

Neutrino Energy (log(E/GeV))

dN

dTdE

(Time in days)

Results Muon energy reconstruction (at the closest approach to the detector)Simulation data from E-2 neutrino flux

Log(Etrue/GeV)

Lo

g(E

rec/

GeV

)

Results Muon energy reconstruction resolution

Log(Etrue/GeV)

RM

S(L

og

(E/G

eV))

Δ(Log(E/GeV))

Work to be done

•Calculation of point source sensitivities for varius depths (~ 2 weeks)

•Simulation of more Geometries (Benchmark – MultiPMT string detector and more) (~ 2 weeks)

•Optical photon scattering in GEANT4 simulation (~ 1 month)

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

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

Simulation of the PMT response to optical photons

Quantum Efficiency

Arrival Pulse Time resolution

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

Single Photoelectron Spectrum

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