1. on behalf of the NEMO Collaboration
Monte Carlo simulation studies of the timing calibration accuracy required by the NEMO underwater neutrino telescope
R. Megna
on behalf of the NEMO Collaboration
VLVnT08 - Toulon, France, April 2008

2. Summary The NEMO-Project Timing calibration accuracy simulation
NEMO angular resolution VS muon energy (and PMTs hit number) by a timing calibration error
Background effect on the NEMO angular resolution about its mean value in the Capo Passero site
The String configuration
Background effect on the String apparatus angular resolution about its mean value in the Capo Passero site
Comparison angular resolution between NEMO and String apparatus
VLVnT08 - Toulon, France, April 2008

3. The NEMO-Project
The NEMO Collaboration is conducting a long term R&D activity toward the installation of a km3 apparatus in the Mediterranean Sea.
Capo Passero site:
80 km SE off shore from the Sicilian coast at 3500 m depth
average speed sea current = 3 cm/s (speed maximum < 12 cm/s)
average optical background due to 40K and bioluminescence = 28.5 kHz
absorption length = 70 m (at 440 nm)
attenuation length = 36 m (at 440 nm)
40 m
Tower
Secondary JB
Electro optical cable to shore
Primary JB
140 m
1140 m
Layout neutrino telescope:
81 towers
18 floors/tower
4 optical modules/floor
5832 PMTs
volume = 0.88 km3
20 m

4. Causes of errors Track reconstruction of muons
If an astrophysical neutrino of the muon interacts near the detector, it will generate an “observable” muon by Weak Charge Current interaction.
The underwater neutrino telescope NEMO will be optimize to reconstruction muons track, by Čerenkov light.
The tracks reconstruction will be on the acquisition times of the optical modules.
But, what are the causes of uncertainty when we want to reconstruct a muon track?
Dispersion of light in the water > 1 ns
Positioning error of the optical modules ~ 0.5 ns
Photon’s point impact on the optical module ~ 0.5 ns
Formation of signal in the PMT ~ 1.5 ns
Front-End electronics error ~ 0.3 ns
VLVnT08 - Toulon, France, April 2008

5. Timing calibration accuracy
We want to determine the timing calibration accuracy required by the NEMO underwater neutrino telescope.
The question is: which value timing calibration accuracy is tolerable, because the apparatus performance is not significantly changed?
We have studied the issue for the angular resolution by Monte Carlo simulation.
VLVnT08 - Toulon, France, April 2008

6. The NEMO simulation codes spring by Antares simulation codes
The Simulation
The NEMO simulation codes spring by Antares simulation codes
gendet (v1r2)
gentra (v5r5)
km3 (v2r1)
modk40 (v4r8)
reco (v4r4)
+ timing calibration improvements
1 km
can
detector
About 5 ·104 up-going muons events on the “can” (surface generation) have generated each MC, with:
isotropic distribution in  angle (azimuthal)
isotropic distribution -1< cos  < 0 ( = zenithal angle)
energy spectrum index = -1
range energy 1 TeV ÷ 1 PeV
up-going muons
VLVnT08 - Toulon, France, April 2008

7. Timing calibration accuracy simulation
+ 0.2 ns
- 0.5 ns
- 0.8 ns
+ 0.9 ns
- 0.3 ns
For each 5832 PMTs we have assigned a timing calibration error (ε), smaller than a maximum error (εmax): | ε | < εmax
εmax = 1, 2, 3, and 5 ns
Exemple of the case with < 1 ns timing calibration error
track reconstruction with timing calibration error = 0 ns
We have defined the angular resolution NEMO apparatus by the median of distribution angle () difference, between the track reconstruction with timing calibration error = 0 ns and the track reconstruction with error > 0 ns (1, 2, 3, and 5 ns) α
track reconstruction with timing calibration error > 0 ns
VLVnT08 - Toulon, France, April 2008

8. NEMO angular resolution VS muon energy
We selected optical background due to 40K and bioluminescence = 30 kHz.
εmax = 0 ns offset is the NEMO apparatus with timing calibration error = 0 ns, etc.
If timing calibration error increases, the angular resolution reduces even a ~ 2 factor.
The εmax = 1 ns offset is agreement to εmax = 0 ns offset. The small differences are compatibles with Half Width At Half-Maximum distributions  angle (HWHM ~ 0.04° ÷ 0.02° at E = 1 TeV ÷ 1 PeV for 0 ns and 1 ns offset).
Moreover a timing calibration error less than 1 ns is compatible if compared by errors in the list of the uncertainty causes on the reconstruct a muon track.
VLVnT08 - Toulon, France, April 2008

9. NEMO angular resolution VS hit_PMT
We had studied the angular resolution NEMO apparatus VS PMTs hit number, with optical background = 30 kHz.
If PMTs hit number is:
Nhit < 50 (1st bin), we have not good reconstruction tracks (median ~ 3°)
50 < Nhit < 100 (2nd bin), we have a good angular resolution (~ 0.1°)
Nhit > 100 (3th, 4th, 5th bin), we have a very good angular resolution (< 0.1°)
The effects of timing calibration error are evidents in all bins. The case with εmax = 1 ns offset is agreement to εmax = 0 ns offset.
Nhit > 50 corresponds to E > 20 TeV
VLVnT08 - Toulon, France, April 2008

10. Comparison background effect on the angular resolution about its mean value in the CP site
We had studied the angular resolution NEMO apparatus VS E , with optical background = 20 kHz and 35 kHz (about its mean value in the CP site).
If we compare the two different background effects on the angular resolution, there are:
differences in the median even a 2 factor about, at low energy (< some tens TeV)
at high energy there are small differences (> some tens TeV)
In both cases, the εmax = 1 ns offset is agreement to εmax = 0 ns offset. The small differences are compatibles with Half Width At Half-Maximum distributions  angle.
VLVnT08 - Toulon, France, April 2008

11. The String configuration
In the String configuration we had replaced the NEMO tower with a string
Layout neutrino telescope:
81 strings
36 floors/string
2 optical modules/floor
5832 PMTs
volume = 0.88 km3
140 m
20 m
String
Secondary JB
Electro optical cable to shore
Primary JB
140 m
1140 m
VLVnT08 - Toulon, France, April 2008

12. Comparison background effect on the angular resolution about its mean value in the CP site (String apparatus)
The angular resolution of the string apparatus is worse of the NEMO apparatus, particularly at low energy.
If we compare the two different background effects on the angular resolution, there are:
differences in the median even a 2 factor about, at low energy (< some tens TeV)
at high energy there are small differences (> some tens TeV)
The effects of timing calibration error are evidents at high energy (> some tens TeV).
VLVnT08 - Toulon, France, April 2008

13. Comparison NEMO and String apparatus
The comparison between NEMO apparatus and string apparatus points up:
angular resolution NEMO better than string apparatus (about a 2÷3 factor), particularly at low and medium energy (less than some tens TeV), only at high energy is almost the same (great than 100 TeV)
the two different background effects on the angular resolution are evidents at low energy and are zero only at high energy
VLVnT08 - Toulon, France, April 2008

14. Conclusions
The NEMO angular resolution reduces even a ~ 2 factor if timing calibration error increases in the range 0 ÷ 5 ns, with the mean value background in the CP site. The case with 1 ns offset error is agreement to 0 ns offset error.
The NEMO angular resolution is ~ 0.1° if 50 < Nhit < (E > 20 TeV) and it is < 0.1° if Nhit > 100.
The study background variation at 20 kHz and 35 kHz points up NEMO angular resolution reduces a 2 factor about at low energy. The almost same differences has the string apparatus.
The comparison NEMO and String apparatus points up angular resolution NEMO better than String apparatus, particularly at low and medium energy by about a 2÷3 factor.
VLVnT08 - Toulon, France, April 2008

15. Matrix of the timing calibration error (case with < 1 ns)
With nearly 6000 PMTs is awaiting a Gaussian distribution by timing calibration error. The Gaussian distribution is truncated because we can decreases the timing calibration error if it passed a fixed value. Also we have verified that using not truncated Gaussian the angular resolution changes its value in the same range values of the Half Width At Half-Maximum.
Every 5832 PMTs we have assigned a timing calibration error
Gaussian distribution truncated
VLVnT08 - Toulon, France, April 2008

16. Median variation Median variation ≈10 %
Half Width At Half-Maximum distributions  angle
Average and standard deviation obtained from 10 MC changing all the seeds generation (generation track, propagation light, matrix of the timing calibration error, etc.)
Median variation ≈10 %
1 ns offset is agreement to 0 ns offset
Median variation 5% ÷ 25%
VLVnT08 - Toulon, France, April 2008

17. Average PMTs hit number VS muon energy
< PMTs > ≈ 50 ÷ 100 ↔ Eµ ≈ 20 ÷ 100 TeV < PMTs > > 100 ↔ Eµ > 100 TeV
VLVnT08 - Toulon, France, April 2008

18. A typical output Monte Carlo simulation
1 - 3 TeV
TeV
TeV
TeV
TeV
TeV
TeV
entries
θ(degree)
VLVnT08 - Toulon, France, April 2008

19. A few characteristics in the Capo Passero site
Optical background (PMT 10”)
Temperature – Salinity – Attenuation and absorption length at 440 nm (December 1999 ÷ July 2003)
Comparison between attenuation and absorption length with Smith and Baker’s curves sea water pure.
VLVnT08 - Toulon, France, April 2008

20. Autors: R. Megna on behalf of the NEMO Collaboration
Title: Monte Carlo simulation studies of the timing calibration
accuracy required by the NEMO underwater neutrino telescope
Abstract:
The results of Monte Carlo simulation studies of the timing calibration
accuracy required by the NEMO underwater neutrino telescope are presented. The NEMO Collaboration is conducting a long term R&D activity toward the installation of a km3 apparatus in the Mediterranean Sea. An optimal site has been found and characterized at 3500 m depth off the Sicilian coast. Monte Carlo simulation shows that the angular resolution of the telescope remains approximately unchanged if the offset errors of timing calibration are less than 1 ns. This value is
tolerable because the apparatus performance is not significantly changed when such inaccuracies are added to the other sources of error (e.g., the accuracy position of optical modules). We also discuss about the optical background rate effect on the angular resolution of the apparatus.
VLVnT08 - Toulon, France, April 2008