1. Hellenic Open University
Physics Laboratory
School of Science and Technology
Hellenic Open University
Antonis Leisos
KM3NeT Collaboration Meeting
Calibration of km3 with EAS
G. Bourlis, E. P. Christopoulou, N. Fragoulis, N. Gizani, A. Leisos, S. E. Tzamarias, A. Tsirigotis, B. Verganelakis
the calibration principle using atmospheric showers
Monte Carlo Studies
Lab Measurements
I am going to present you the work of our group concerning the calibration methods we propose for the Kilometer cube Neutrino Telescope which is going to be deployed in the Mediterranean Sea. The system is based on the sea level detection of low energy atmospheric showers that also trigger the v-Telescope at a depth of about 4000 meters.
This is the Outline of this talk:
First I will describe the calibration principle using atmospheric showers,
then I will show you Monte Carlo studies and experimental data from our lab in order show what we can expect to achieve with this calibration system
Pylos Greece April 2007

2. 3 stations with at 16 m2 scintillator detectors each
The Concept
Floating stations
reweighting
Blind fit
Okada model
3 stations with at 16 m2 scintillator detectors each
NESTOR: muon 4000m
The idea is actually stolen from the SPASE-AMANDA project at the Antarctic sea.
The Spase scintillation array consists of 120 scintillator counters positioned at the surface. It detects cosmic air showers in order to study the shower properties like energy, primary mass, age etc) but it also serves as a calibration module for the AMANDA detector.
The concept is that some of the reconstructed showers will also trigger the AMANDA array and a direct comparison can be made. This way SPASE measured the AMANDA B10 reconstruction accuracy and also indicated a zenith angle offset of the neutrino detector of about 1.5 degrees.
So the concept of our proposal is that we could use floating stations above the detector for small periods of time.
The general idea of such a calibration module is that a significant percentage of the reconstructed atmospheric showers contain very energetic muons that can penetrate to the detector depth and thus they can be reconstructed by the neutrino telescope.
By comparing the reconstructed muon track with the reconstructed shower direction one can estimate in principle:
The possible angular offset of the telescope
The efficiency of the telescope
The angular resolution and
The absolute position of the telescope.
That is what actually ICETOP will do, the surface partner of the ICECUBE in the Antarctic sea.
Unfortunately this can not be done for a deep sea ν-Telescope which will probably be deployed at a depth of about 4000 meters at a distance of about 20 kilometers from the shore.
The reason is that despite that the primary cosmic ray flux is isotropic at the top of the atmosphere, due to the slant depth the zenith angle distribution is modulated according to this law with a of about 10 which means that inclined showers are very rare. For the muon flux at 4000 meter deep measured by the NESTOR collaboration demonstrates that muon tracks above 60 degrees are very rare.
So such an array at the shore is practically useless for calibration purposes
We propose a minimum of 3 stations each one with at least 16 square meters of scintillator counters to operate for at least 10 days continuously.
Angular offset
Efficiency
Resolution
Position

3. Shower Detection Principle
Minimum Station Set-Up
GPS
Scintillator-PMT
Scintillator-PMT
1 m2
Scintillator-PMT
~20 m
Scintillator-PMT
Triangulation
Shower Direction
The counters of the station are the ones currently used by the HELYCON detector array. The HELYCON array is a research and education purpose detector which is planned to be operated in the area of Patras city
It consists of stations positioned at the roof of high schools or public buildings each one with 4 scintillator counters and a GPS for absolute synchronisation.
The counters are positioned at a typical distance with each other of about 20 meters and are controlled by a central DAQ hosted in a Personal Computer.
The detection principle is based on the almost true fact that the shower front of particles is a plane perpendicular to the shower axis moving with the speed of light. Then by triangulation the azimuth and the zenith shower angle can be reconstructed with at least 3 active counters.
Station Server
DAQ
4·(1W/counter)+30W(PC+electronics)

4. The Scintillator Module
trigger arrival time
The HELYCON detector module consists of 160 scintillating tiles covering an area of about 1 m2. The light produced by the scintillator is guided to a single PMT with 96 Wavelength shifting fibers. The electronic pulses are acquired from the DAQ board which also timestamps the event using a Motorrola timing module.
Scintillator 2
Scintillator 3
Scintillator 3

5. Number of particles to the ground
Simulation Tools
CORSIKA
(Extensive Air Shower
Simulation)
GEANT4
(Scintillation, WLS
& PMT response)
Fast Simulation
also available
Energy: 105 GeV – GeV
A lot of work has been carried out in order to develop accurate and efficient simulation tools for the analysis.
For the generation of the Atmospheric air showers we use the well known Corsika generation code. For demonstration in this plot you can see the number of particles that reach the ground for low energy showers.
Then for the particles that hit the detector modules, we simulate the production of scintillation the role of the WLS fibers and the PMT response using the the Geant4 simulation Package.
Due to the large number of particles we have also developed a fast simulation version with the appropiate parameterizations.
Number of particles to the ground

6. Track Reconstruction)
Simulation Tools
DAQSIM
(DAQ Simulation)
HOUANA
(Analysis &
Track Reconstruction)
Height (mV)
The next step is to simulate the Data Acquisition system, the trigger formation and the digitization. For example here you can see the generated waveform due to some particle hits.
Finally the determination of the shower parameters is performed with the Analysis and Reconstruction program which produces plots histograms etc.
Time (ns)
Zentih (degrees)

7. Muon track (s) reconstruction
Simulation Tools
GEANT4
Muon Propagation to KM3
HOU-KM3
Muon track (s) reconstruction 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)
For the need of the calibration system the simulation code includes also the propagation of the muons to the sea depth of 4000 meters taking into account all the possible muon interactions and especially the production of the Cherenkov light that is collected from the PMTs.
Finally we use the muon reconstruction code in order to reconstruct the muon track parameters namely the zenith and azimuth angle ans the psuedovertex position odf the track.

8. 4m2 Scintillator Detector
Atmospheric shower simulation by CORSIKA - muon transportation to the detector DEPTH by GEANT4 - Sea-Top Detector detailed simulation GEANT4_HOU
Angular Resolution in
Single Shower Reconstruction
Typical Values
No cut: σ= 4.5ο
Total Collected Charge > 10 mips: σ=2.22ο
Total Collected Charge > 25 mips: σ=1.33ο
Total Collected Charge > 30 mips: σ=1.2ο
PRELIMINARY
For demonstration in this slide you can see the resolution of such a station for 4 different cuts to the total collected charge.
Starting from 4.5 degrees you can go down to 1.2 degrees if you demand total collected charge grater than 30 mips.
You should have in mind that when you apply hard cuts you improve the resoluion but you loose in statistics, so in this plot you can see the zenith angle resolution offset as a function with the minimum total collected charge concluding that the resolution can be up to 0.15 degrrees.
I remind you that these results concern 3 station HELYCON detectors, that is 4 counters per station at a distance od 20 meters between them.
zenith angle resolution [degs]
Θrec-Θtrue
Minimum of total collected charge [mip equivalent]
Single Station: 4 detectors (1m2 plastic scintillator), 20 m distance between the detectors, three out of four selection trigger

9. 16m2 Scintillator Station
1 m2 Scintillation Counter
19m
dt=0
dt1
The accuracy can be better if you increase the number of counters and decrease the spacing between them.
In the rest of this talk I will refer to this station of 16 nodes with 5 meter spacing. The reconstruction procedure is simple.
Assuming that these bullets here are the detectors you measure the time difference of these hits with respect to the hit of a specific detector and minimise the corresponding chi square function.
The reconstruction procedure assumes that the shower particle front is a plane moving with the speed of light but in real life this is not true…
dt2
dt3
19m

10. Multi-Station Operation Monte Carlo Studies in Progress
First coming particles
curvature
thickness
As you can see in this picture the shower front is not a plane but it is curved so particles far from the shower core are delayed.
In addition away from the shower core as the particle density drops the time spread of the particles is bigger giving rise to the possiblity that the first particle is not close to the curved shower front. That is called thickness and it is demonstrated in this plot. The lower the collected charge the bigger the time spread.
Time Spread (ns)
Total collected charge [pe]

11. Timing vs Pulse Hight Slewing Resolution Input A Input B Trigger
Discriminator
(1.5 MIP)
Trigger
Slewing
Resolution
This facts must be taken into account in order to apply the needed corrections.
As far as the detector concerns the timing is disturbed due to slewing. The variation of the arrival time with respect to the pulse height.
We have studied slewing and found that for particle densities above 4 mips per square meter the resolution reaches a plato of about 1.3 ns.

12. Time corrections
Finally we have parameterized the delay and the delay spread due to the thickness with respect to the collected charge.
As you can see as the deposited charge is increased, the delay spread reaches a constant value which is actually the spread due to sllweing.
If we apply all these corrections and take into account the corresponding errors we cheked the procedure by calculating the time residuals of the detector hits.
As you can see they are distributed according to a normal distibution with mean zero and sigma unity.

13. Consistent Estimations
We have also checked the consistency of the fitting procedure by calculating the Xchi square probability of 2 statistics R and lamda.
R is the difference of the chi square function calculated for the true and the estimated parameter values whilst Lamda is mahalanobis distance of the generated and the estimated parameter values.
In both case the chi square probability with 2 dgrees of freddom is constant prooving that the method is unbiased an the error estimation correct.
Minuit Minimization

14. A hit is considered when there is more than 4 mips deposited charge
Detection Efficiency
Efficiency
Events
In this plot you can see the distribution of the active counters per shower and next
The efficiency of the reconstruction with respect to the distance from the shower core.
The detector can reconstruct showers which can be up to 60 meters far away
A hit is considered when there is more than 4 mips deposited charge

15. Muon Propagation Accepted if muon with E>2TeV goes through km3
Geant Simulation
(propagation & Energy Loss)
Coming back to the calibration, only a portion of the reconstructed showers are usefull.
Specifically we accept showers wich contain a muon with energy grater than 2 TeV with a direction towards the km3 detector.
The most efficient position of the platform is found to be just above the v-telescope restricting us to showers with zenith angle less than 13 degrees.
μ track
Zenith angle < 13 deg
Muon Track Reconstruction
(A. Tsirigotis talk)
km3

16. Muon Propagation
For these showers we have calculated the muon shower space angle and the zenith angle difference and we found to be 1.5 and 1.2 degrees respectively

17. Primary Zenith Angle Resolution
Deposited Charge per counter > 4 mips
Number of Hits > 10
As I have already mentiond the accuracy of determining the shower zenith angle depends on the selection cuts we apply.
In this analysis we asked for more than 4 mips per counter and more than 10 hits resulting in an accuracy of 1.2 degrees.

18. Primary Azimuth and Space angle Resolution
The azimuth angle resolution is limited to 14 degrees but remember we speak for almost vertical showers so we expect that the phi resolution is poor.
Concering the space angle between true and estimated shower direction, the mean value is 1.5 degrees.
Deposited Charge per counter > 4 mips Number of Hits > 10

19. Effective Area
Finally we have calculated the effective area with respect to the energy of the primary particle and convoluted with the defferential flux of the cosmic rays, we end up with about 30 showers per day reconstructed at he surface and in the deep sea.
So..
~ 30 showers per day reconstructed at the surface and in the deep sea
Deposited Charge per counter > 4 mips Number of Hits > 10

20. Performance Plots
The previous analysis can be repeated for different selection cuts. In this analysis we retain the demand of 4 mips per counter and we calculate the performance with respect to the minimum active counters.
As you can see when we ask for more active counters per event the effective area of the detector decreases but on the other hand the resolution increases. The resolution can go up to 1 degree and is limited by the detector effects and the electronic limitations.
In this plot you can see the expected resolution of the possible zenith offset of the telescope. It is obvious that the optimum solution is to collect as much as many events with poorer resolution in order to increase the sample. The accuracy for such detector is 0.05 deg.

21. Deposited Charge per counter > 4 mips 6 Active counters
Lab Measurements (a)
MC -Data
μ=-0.1±0.3
σ=7.6 ± 0.2
 Data
___ M.C. Prediction
Discriminator
(1.5 MIP)
Input C Trigger A1 A2 A3 B1 B2 B3
θΑ-θΒ
μ=-0.06±0.05
σ=1.02 ± 0.03
Deposited Charge per counter > 4 mips 6 Active counters
Pull

22. Deposited Charge per counter > 4 mips 6 Active counters
Lab Measurements (b)
MC Prediction
GROUP A
μ=0.1±0.6
σ=4.5 ± 0.5
DATA
δθ=4.6
Discriminator
(1.5 MIP)
Input C Trigger A1 A2 A3 B1 B2 B3
θm-θtr
μ=0.01±0.1
σ=0.9 ± 0.1
Pull
GROUP B
μ=0.3±0.8
σ=5.2 ± 0.8
DATA
δθ=5.6
Finally we have calculated the effective area with respect to the energy of the primary particle and convoluted with the defferential flux of the cosmic rays, we end up with about 30 showers per day reconstructed at he surface and in the deep sea.
So..
θm-θtr
μ=0.02±0.1
σ=0.9 ± 0.1
Deposited Charge per counter > 4 mips 6 Active counters
Pull

23. Charge Inputs Trigger At the Detector Center Data
Scintillator A
Scintillator B
Lead
discriminators
Inputs
Trigger
 Data
___ M.C. Prediction
Charge (in units of mean p.e. charge)
At the Detector Center
Data
- Monte Carlo Prediction
Time (ns)
One step further in the reconstruction analysis includes the deterimnation of the shower impact point.
The impact point can be estimated by measuring the particle density distribution wit respect to the perpendicular core distance. This distribution can be parametrised according to the AGASA formula
Where the parameters depend on the zenith angle the primary mass and the energy of the shower.
However the mean lateral distribution for all energies and zenith angles can be parameterized with respect to the perpendicular distance from the shower core
As you can see in these plots the mean particle density registered by an active counter as well as the rms value can be fitted very well.

24. Charge parameterization
AGASA parameterization (S. Yoshida et al., J Phys. G: Nucl. Part. Phys. 20,651 (1994)
Parameters depend on
(θ, Ε, primary)
“Mean particle density registered by an active counter”
One step further in the reconstruction analysis includes the deterimnation of the shower impact point.
The impact point can be estimated by measuring the particle density distribution wit respect to the perpendicular core distance. This distribution can be parametrised according to the AGASA formula
Where the parameters depend on the zenith angle the primary mass and the energy of the shower.
However the mean lateral distribution for all energies and zenith angles can be parameterized with respect to the perpendicular distance from the shower core
As you can see in these plots the mean particle density registered by an active counter as well as the rms value can be fitted very well.

25. Primary Impact determination
Consequently the impact point can be estimated with an accuracy of about 10 meters for the standard selecion cuts we apply.
Of course the resolution can be incresed as it is demonstarted in this plot by asking more collected charge.
Absolute Position resolution ~ 0.5 m

26. Telescope Resolution Telescope resolution ~ 0.1 deg
Surface Area resolution ~ 1 deg
Telescope’s resolution measurement Impossible
σ=0.014
σ=0.062
σ=0.094
Consequently the impact point can be estimated with an accuracy of about 10 meters for the standard selecion cuts we apply.
Of course the resolution can be incresed as it is demonstarted in this plot by asking more collected charge.
Inter calibration

27. Conclusions
The operation of 3 stations (16 counters) for 10 days will provide:
The determination of a possible offset with an accuracy ~ 0.05 deg
The determination of the absolute position with an accuracy ~ 0.6 m
Efficiency vs Energy and Zenith angle…
Resolution No!
The conclusion is that the operation of 3 such stations for 10 days will provide:
The determination of a possible offset with an accuracy ~ 0.05 deg
The determination of the absolute position of the ν-detector with an accuracy ~ 0.6 m
Calibration system and assuming that the n-Telescope resolution in determining the zenith angle of a muon track is about 0.1 degrees and the impact about 2 meters,