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Alma Mater Studiorum · Universita diBologna
FACOLTA DI SCIENZE MATEMATICHE, FISICHE E NATURALI
Scuola di Scienze
Dipartimento di Fisica e Astronomia
Corso di Laurea Magistrale in Fisica
Selection of showering events andbackground suppression in ANTARES:comparison between the effects using
two different Monte Carlo version
Relatore:Prof. Maurizio SpurioCorrelatore:Dr. Federico Versari
Presentata da:Walid Idrissi Ibnsalih
Anno Accademico 2017/18
2
Abstract
Al momento ANTARES e il piu grande telescopio di neutrini sottomarino ed
e situato nel Mar Meditteraneo, circa 40 km a largo di Tolone, Francia, ad
una profondita di 2450 m in fondo al mare. Lo scopo principale di ANTARES
e quello di poter osservare neutrini di alta energia riconducibili a sorgenti as-
trofisiche. Un fondo irriducibile del rivelatore e rappresentato dai muoni atmos-
ferici, prodotti dalle interazioni dei raggi cosmici con i nuclei dell’atmosfera. La
collaborazione ANTARES fa largo uso di simulazioni Monte Carlo e recente-
mente e stata rilasciata una nuova versione della simulazione che tiene conto di
effetti di invecchiamento del rivelatore al fine di migliorare l’accordo tra la sim-
ulazione ed i dati. In questa tesi, utilizzando eventi di neutrini di tipo sciame, si
sono confrontate la vecchia e la nuova simulazione Monte Carlo, in particolare
ci si e concentrati sulla reiezione del fondo dovuto ai muoni atmosferici.
Contents
1 Atmospheric neutrinos 7
1.1 Cosmic Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1.1 Energy spectrum . . . . . . . . . . . . . . . . . . . . . . . 8
1.1.2 Mechanism of acceleration . . . . . . . . . . . . . . . . . . 10
1.2 Atmospheric shower . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.2.1 Atmospheric neutrinos flux . . . . . . . . . . . . . . . . . 13
1.2.2 Neutrino interaction . . . . . . . . . . . . . . . . . . . . . 16
1.2.3 Neutrino oscillation . . . . . . . . . . . . . . . . . . . . . 17
2 Neutrino telescope and ANTARES 21
2.1 Cherenkov effect . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Topology of events . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.1 Track events . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.2 Shower event . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.3 Double-bang event . . . . . . . . . . . . . . . . . . . . . . 25
2.3 ANTARES experiment . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3.1 Junction box . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3.2 ANTARES line component . . . . . . . . . . . . . . . . . 28
2.3.3 Data acquisition . . . . . . . . . . . . . . . . . . . . . . . 31
2.4 Sea water properties . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.4.1 Propagation light . . . . . . . . . . . . . . . . . . . . . . . 34
2.4.2 Optical background . . . . . . . . . . . . . . . . . . . . . 36
2.4.3 Biofouling and sedimentation . . . . . . . . . . . . . . . . 37
2.5 Effective Area Aeffν . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3 Reconstruction algorithms 41
3.1 TANTRA algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.1.1 Hit selection . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.1.2 Position reconstruction . . . . . . . . . . . . . . . . . . . 42
3.1.3 Direction reconstruction and energy estimator . . . . . . . 43
3.2 Track algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3
4 CONTENTS
3.2.1 AAfit reconstruction . . . . . . . . . . . . . . . . . . . . . 44
3.3 Gridfit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4 Monte Carlo ANTARES 51
4.1 Detector can . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2 Generation of physics events . . . . . . . . . . . . . . . . . . . . . 52
4.2.1 Simulation of atmospheric muons . . . . . . . . . . . . . . 52
4.2.2 Simulation of neutrinos . . . . . . . . . . . . . . . . . . . 53
4.3 Light emission and propagation . . . . . . . . . . . . . . . . . . . 56
4.4 Simulation of data acquisition . . . . . . . . . . . . . . . . . . . . 58
4.5 Run-by-run approach . . . . . . . . . . . . . . . . . . . . . . . . . 58
5 Monte Carlo v3 and v4 63
5.1 Event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.2 Event selection rbr v3 . . . . . . . . . . . . . . . . . . . . . . . . 65
5.3 Event selection rbr v4 . . . . . . . . . . . . . . . . . . . . . . . . 66
5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Introduction
This thesis is carried out with the ANTARES collaboration, the largest neu-
trino telescope in the Northern hemisphere. The ANTARES (acronym for As-
tronomy with a Neutrino Telescope and Abyss environmental RESearch) neu-
trino telescope is a three-dimensional array of photomultipliers distributed over
12 lines, installed at a depth of 2475 meters in Meditterean sea. The main
purpose of this Collaboration is to observe the neutrinos emitted by the as-
trophysical objects, like AGN, GRB, and supernova remnants. Therefore, the
study of these neutrinos can solve important questions: the sources or the mech-
anism of acceleration of cosmic rays.
High energy neutrinos interact (via weak interaction) with one of the nucleons
of the medium would produce charged particle. Cherenkov photons can then
be detected by a lattice of photomultipliers. An irreducible background for the
detector is represented by atmospheric muons, produced by the interactions be-
tween the cosmic rays and the nucleus of the atmosphere.
In order to reduce the events of atmospheric muons, studies with Monte Carlo
simulations have been performed. The main purpose of this thesis is to compare
the efficiency in rejecting muon events between the old simulation version and
the one currently produced. This thesis is divided as follows. In Chapter 1 we
introduced the theoretical aspects of the subject, such as cosmic rays and in
particular atmospheric neutrinos. In Chapter 2 the ANTARES neutrino tele-
scope is presented. A description of the reconstruction algorithms for the shower
and track events are presented in Chapter 3. Finally in Chapter 4 there is a
description of the Monte Carlo simulations of ANTARES, and the last Chapter
5 reports the results made by comparing two different versions of Monte Carlo.
5
6 CONTENTS
Chapter 1
Atmospheric neutrinos
Atmospheric neutrinos are produced by the interaction of primary cosmic rays
with the nuclei of the Earth’s atmosphere. Since they are the main argument
of this thesis a short theoretical digression in this chapter is illustrated, starting
from cosmic rays1.
1.1 Cosmic Rays
Cosmic Rays (CRs) are high-energy particles accelerated by astrophysical sources.
They are generally divided into two categories: primary CRs, i. e. the particles
that reach the Earth’s surface, and the secondary CRs, i. e. the product of the
interaction between primary CRs and the Earth’s atmosphere. The primary
ones are mainly composed of protons and ionized light nuclei. In particular, the
abundance is divided into the following percentages: 85% protons, 14% alphe
nuclei, 1% electrons and the rest are nuclei with mass greater than that of he-
lium. The chemical composition in these cosmic rays is practically identical to
that within the Solar System, except for elements such as Li-Be-B and Sc-Ti-V-
Cr-Mn, see figure 1.1. In fact Li-Be-B are relatively more abundant in CRs than
in the Solar System by several orders of magnitude, because these element act
as catalysts for nuclear reactions within the stars (for the first group of elements
is the CNO cycle). So the enhancement in their relative abundance in the CRs
for the first group is given from the collisions, spallation processes (fragmetation
process), between element such C,N,O and the interstellar medium (ISM).
1Since in literature is used the acronym CR, also in this thesis is reported.
7
8 CHAPTER 1. ATMOSPHERIC NEUTRINOS
Figure 1.1: The imagine represent the relative (to Si = 100) abundance as
function of the number atomic Z [3]. There is evident difference about the
abundance between the CRs (bue line) and Solar System (red line) for the two
groups of element(Li-Be-B and Sc-Ti-V-Cr-Mn).
1.1.1 Energy spectrum
The energy of the CRs can be extend from the MeV to the 1020 eV. Below 1014
eV are possible to detect CRs with satellite and balloon experiments, instead at
higher energies only indirect measurements are available because the CRs flux
is too low.
The energy spectrum above 109 eV can be represented according to the following
power law:
dN
dE= k · E−α (m−2sr−1s−1GeV −1) (1.1)
where k is a normalization factor and α is the spectral index. In the represen-
tation on a double logarithmic scale it becomes a straight line with an angular
coefficient of α. Depending on the energy region considered, as shown in figure
1.1. COSMIC RAYS 9
1.2, the slope of the energy spectrum changes.
Figure 1.2: The differential energy spectrum of CRs, in units
m−2sr−1s−1GeV −1, from 109 eV to 1020 eV [12].
The flux can be divided in different region:
• For energies below 1015 eV the spectral index α is approximately 2.7;
• At energy 3 · 1015 eV, α ' 3.1,this region is so-called knee. The accel-
eration mechanism until this energy it can be explain with the Fermi’s
mechanism [6], see § 1.1.2. Many hypothesis support that CRs with a
energy until to 1015 eV are originated within the galaxy;
• For energies above to 3 ·1019 eV the value of α becomes ∼ 2.7 again. This
region is called ankle;
• A cut-off at 6 · 1019 eV is present, as expected to the so-called GZK phe-
nomenon (Greisen Zatsepin Kuz’min). This phenomenon describes a inter-
cation between CRs and Cosmic Microwave Background (CMB) photons
10 CHAPTER 1. ATMOSPHERIC NEUTRINOS
[7]:
p+ γCMB → ∆+ → π+ + n (1.2)
CRs at top of the atmosphere are distrubeted isotropically, because the
charged particles are deflected by the Galactic magnetic field (∼ 3 µG) and
extra-galactic (∼ nG). Only very high energy particle comes directly from origin
source.
The motion of a charged particle in a magnetic field can be described with
Larmor radius [14]:
RL =mv⊥|q|B
(1.3)
As can be seen from the equation, the radius is linearly dependent on the
energy of the particle. The low energy or higher charge CRs are spread through-
out in the Galaxy for a long time. Therefore very high energy (above 1018 eV)
CRs are bent with a radius compatible with the height of the Milky Way (∼200
pc). This model is called the leaky box model.
1.1.2 Mechanism of acceleration
As mentioned previously, Enrico Fermi [4] firstly suggested the CRs mechanism
acceleration through iterative scattering processes. In this model low-energy
CRs, trapped in a magnetic field inhomogeneities, can reach high energies af-
ter a large number of interaction with shock waves. These shock waves can
produced in many extreme enviorements such as supernova remnants or black
holes.
In particular there are two models for CRs acceleration. The first model as
referred to as ”Fermi second order acceleration”, whereas the second is of-
ten called ”Fermi first order acceleration”. In the first work Fermi assumed
that the charged particles are accelerated by elastic scattering with turbulence
structures or clouds of gas moving with a characteristic velocity. The gain of en-
ergy for the particles in this model is proportional to β2, where β is the velocity
of the cloud in units of the velocity of light in vacuum [5]:
<∆E
E>' (4/3)β2 (1.4)
In the second work, where reach a higher efficiency, the particle is accelerated
if encouter a shock front or is moving between two clouds. In this case the gain
energy is proportional to β.
A possible envoriment for Fermi first order mechanism acceleration (fig. 1.3)
is a supernova remnants, where after explosion a shock front is built and the
1.1. COSMIC RAYS 11
particles can be accereleted. The acceleration mechanism due to the supernova
explosion can explain some features of the energy spectrum of CRs, for example
the change slope at knee of the CRs spectrum energy.
Figure 1.3: In the left part is depicted the second order Fermi acceleration
model. Therefore in right part is depicted the first order Fermi acceleration
model, where the plane shock wave is labelled with VS [29].
The precence of the knee can be explain with the Z dependence (charge of
nuclei) of the maximum energy achievable for the particles [12]:
Emax ≈ 300 · Z TeV (1.5)
As shown in figure 1.4, the chemical composition becomes heavier for value
above the knee. The protons can be accelerated to up ≈ 1015 − 1016 eV.
The energy spectrum of particles accelerated via Fermi mechanisms is de-
scribed for all types of charged particles by an unbroken power law with spectral
index α ≈ 2. This model can describe the acceleration mechanism for CRs be-
low the knee, but fails when to describe the CRs energy spectrum above the
knee. So additional model can be taken account for galactic source:
12 CHAPTER 1. ATMOSPHERIC NEUTRINOS
Figure 1.4: The interpretation of the CRs knee as due the correlation between
the maximum energy achievable for the particles and the nuclear charge Z. The
flux for all nuclear species decreas until to a given cut-off, that depends to the
nuclear charge. The plot represents the behavior for proton, Si (Z=14) and iron
(Z=26) [12].
• Pulsar is a neutron star with a strong magnetic field (1011−1012 Gauss).
Indeed, the rotation axis doesn’t coincide with the direction of magnetic
field of the NS. The rotation of these magnetic field around the axis of
rotation produce a strong electric fields through Faraday’s law. These
fields can accelerate the charged particles up to ≈ 1018 eV;
• Microquasars are binary systems composed by a normal star and a com-
pact object as black hole, neutron star or pulsar. These system can emit
relativistic jets or elettromagnetic radiation. The precence of these jets
produce a strong elettromagnetic fields, so charged particles according to
the hypotheses can be accelerated until a energy ≈ 1016 eV;
A possible extra-galactic source for acceleration of CRs are AGNs (Active
Galactic Nuclei). AGNs are very powerful source of elettromagnetic radiation
and jets matter. Often a supermassive black hole in the center of these galaxies
is present. Some models hypothesizes that AGNs are possible candidate to
1.2. ATMOSPHERIC SHOWER 13
accelerate CRs to the ultra-high energy.
1.2 Atmospheric shower
When a primary CRs enter inside the Earth’s atmosphere interact with the nu-
clei and produce a large cascade of subatomic particles, the so-called air shower.
These particles are referred as secondary CRs.
The interaction between the primary CRs and the nucleon produces firstly
hadronic particle such as kaons and pions:
p+N → π±, π0,K±,K0, ...... (1.6)
Charged pions and kaons can either initiate further interactions or decay,
and the competition between these process is function of the energy.
The charged kaons and pions produce leptonic component like neutrino and
muon via decay, while neutral pions produce a elettromagnetic cascade via de-
cay π0 → γγ. Therefore, the atmospheric shower is composed of a hadronic,
electromagnetic and muonic component.
1.2.1 Atmospheric neutrinos flux
Up to ≈ 100 TeV, muons and neutrinos in the atmosphere are produced mainly
by decays of charged pions and kaons:
π+(K+)→ µ+ν (1.7)
π−(K−)→ µ−ν (1.8)
Analytically, the differential flux of muons at sea level can be derived [12]:
Φµ(E) = KE−α
(Aπ
1 + (BπEεπ )cosθ+
AK
1 + (BKEεK)cosθ
)(1.9)
Where Aπ and AK depend on the ratio of muons produced by kaons and
muons and can be derived from Monte Carlo computations. The quantity εicorresponds to the energy at which the hadron interaction and decay lengths
are equal. Below these energies hadrons are more likely to decay, while at
higher energies, due to relativistic reasons, the probability to intercact with the
atmosphere is greater than the decay process. The characteristic decay constant
(εi) for pions and kaons is [12]:
επ ' 115 GeV
εK ' 850 GeV (1.10)
14 CHAPTER 1. ATMOSPHERIC NEUTRINOS
Figure 1.5: The atmospheric muon flux at ground in function of the muon energy
[43].
Due to the kinematics of two-body decay, neutrinos and muons have a different
energy spectrum. The muons obtain more energy than the neutrinos, for this
reasons the spectrum of neutrinos is given with a expression similar to 1.9, but
shifted toward for lower energies. The neutrino atmospheric flux can be write:
Φν(Eν) = AνE−α
(1
1 + (aEνεπ )cosθ+
B
1 + ( bEνεK )cosθ
)(1.11)
This flux, with units expressed in (m−2sr−1s−1GeV −1), is called ”conven-
tional atmospheric neutrino flux”. The scale factor Aν , the balance factor B,
which depends on the ratio of muons produced by kaons and pions, and the a,
b coefficients are parameters which can be derived from Monte Carlo compu-
tation. An analytical description of the neutrino spectrum above 100 GeV is
1.2. ATMOSPHERIC SHOWER 15
provided by the Volkova parametrisation [39], and also provided by the Barr
et al.[42] and Honda et al. calculations [41]. The comparison between these
models is represented in fig. 1.6.
At low energies the uncertainties of the atmospheric neutrino flux are dominated
by uncertainties of hadronic interaction processes, while the uncertainties in the
calculations arise from the limited knowledge of the composition of the primary
CRs. In high-energy approximation of neutrinos, (Eν >> εi), the flux can be
approximated with:
Φν(E) = A′
ν · E−γ (1.12)
with spectral index that can be rewritten as:
γ = α+ 1 (1.13)
Also the decay of muons produces neutrinos in atmosphere :
µ± → e±νeνµ (1.14)
At very high energies, another neutrino production mechanism is possible.
The charmed particles, produced by the interaction of the primary CRs with
the atmospheric nuclei, also decay to neutrinos.
The lifetime of charmed particles is approximately 5 to 6 orders of magnitude
smaller than pions and kaons, and for this reason there is no competition be-
tween the loss energy with collision and the decays. The cross section to product
charmed particles in a collision proton-nucleon is small, therefore this channel to
produce neutrinos is expected important for energies above 100 TeV. The neu-
trino flux that also includes this phenomenon is called prompt neutrino flux.
Two fundamental propetiers for the flux can be deduced. Given the decay chain,
the first is:
Φνµ ∼ 2Φνe (1.15)
As the muon decay probability in the atmosphere decreases with increasing Eµ,
this condition (1.15) is true at low energies. Moreover the fluxes of electronic
neutrino and muonic neutrino are up-down symmetric (considering the Zenith
angle θ):
Φνi(Eν , θ) = Φνi(Eν , π − θ) i = e, ν (1.16)
This prediction is consequence of the isostropy CRs primary and the quasi-exact
spherical symmetry of the Earth. These assumptions are correct but don’t take
into account the oscillation of neutrinos, phenomenon predicted firstly by Bruno
Pontecorvo [38].
16 CHAPTER 1. ATMOSPHERIC NEUTRINOS
Figure 1.6: The energy spectrum of νe,νe,νµ and νµ calculated from the Honda,
Bartol and Battistoni model [41].
1.2.2 Neutrino interaction
Neutrinos can interact with matter only through weak interaction. The weak
process involve the exchange of gauge bosons such as W± and Z0. This process
have a small cross section, so for this reason neutrinos are very penetrate par-
ticles. For example neutrinos with an energy 1 TeV have an interaction length
of 250 · 109g/cm2.
Considering a nucleon N, neutrinos can perform two types of processes.
νl +N → l± +X (1.17)
With l indicating the leptonic flavour (e, µ and τ). These process are called
charged current weak intercation (CC), and W± bosons are involved. In the
final state are produced a lepton with the leptonic flavour associated and a
1.2. ATMOSPHERIC SHOWER 17
hadronic shower (X).
The second type that can occur is neutral current weak intercation (NC), where
the gauge boson Z0 is involved:
νl +N → νl +X (1.18)
The differential cross-section for CC intercation can be written as:
d2σ
dxdy=
2GFMEνπ
(M2W
Q2 +M2W
)[xf(x,Q2) + xf(x,Q2)(1− y)2
](1.19)
The variable x is called Bjorken’s variable, which represents the fraction of
four-momentum transported by the parton, and y, which represents the fraction
of energy transferred by the neutrino to the lepton produced:
y =Eνl − ElEν
(1.20)
The term Q2 represents the fraction of energy transferred from the neutrino
to the charged lepton.
In the formula the functions f and f , which are the distributions of quarks and
antiquark within the nucleon, are present. Therefore, in order to have a correct
calculation of the cross sections, it is necessary to know these distributions.
Same calculation are similar to antineutrinos.
The neutral processes, however, can be written as:
d2σ
dxdy=
2GFMEνπ
(M2Z
Q2 +M2Z
)[xf0(x,Q2) + xf0(x,Q2)(1− y)2
](1.21)
The cross-section (represented in the figure 1.7) increases as the energy increases,
this means that the interaction length of neutrinos decreases with increasing
energy.
1.2.3 Neutrino oscillation
As has already been mentioned, neutrinos are subject to so-called neutrino
oscillation. The Standard Model predicts that neutrinos are neutral and mass-
less particles. According to the model, the neutrinos cannot change the leptonic
flavour, identified as Le,Lµ and Lτ . If the neutrinos are massive as suggested
by B.Pontecorvo, the change of the leptonic number becomes possible. This
is due because the ”weak flavor eigen states”(νl) are different from the masses
autostates νi, but a combination of them: νeνµντ
=
U11 U12 U13
U21 U22 U23
U31 U32 U33
ν1
ν2
ν3
(1.22)
18 CHAPTER 1. ATMOSPHERIC NEUTRINOS
Figure 1.7: The cross section of the intercation for all type of neutrino in function
with the energy [44].
The combination can be written:
|νl〉 =
+3∑i=0
Ul,i|νi〉 (1.23)
With Ul,i is the elements of the mixing matrix. It can be possible to determine
the probability that along the way the neutrino will change the flavour from l1to l2:
P1,2 = sin2(2θ1,2)sin2(1.27L
E∆m2) (1.24)
The various terms describe:
• θ1,2 is the mixing angle between neutrinos;
• ∆m is the difference between the neutrino masses;
1.2. ATMOSPHERIC SHOWER 19
• L is the length of the path from where the neutrino is produced to the
observation point.
The energy dependence of the neutrino should be noted.
20 CHAPTER 1. ATMOSPHERIC NEUTRINOS
Chapter 2
Neutrino telescope and
ANTARES
Many theories suppose that high-energy neutrinos are emitted in violent events
taking place in many astrophysical objects. The neutrinos originating from in-
teractions of CRs with the surrounding medium come from their origin source
without any deflection from magnetic fields Galaxy.
The possible detection of high energy neutrinos is limited by the fact that the
expected fluxes and the neutrino interaction cross-sections are very low. Very
large detectors are needed, ranging up to a cubic km of instrumented volume.
As proposed by M.A. Markov, it can be possible the use of large volumes of nat-
ural water. He proposed: ”to install detectors deep in a lake or in the sea and
to determine the direction of the charged particles with the help of Cherenkov
radiation” [1]. The main idea of detecting neutrinos with a neutrino telescope is
to observe downward through the Earth, because all other particles (as muon)
cannot penetrate it. Therefore, neutrinos that have crossed the Earth can in-
teract with the detector medium or the surroundings, and can produce the
corresponding charged lepton, see § 2.2. A 3D-array of PMTs allows the detec-
tion of the Cherenkov light released by ultra-relativistic particles crossing the
detector. From the Markov’s idea nowadays the km3 detectors are operating.
2.1 Cherenkov effect
When a charged particle traversing the medium, with a determineted refractive
index n, faster than the velocity of light in that medium, a electromagnetic
radiation is emitted. This radiation is called as ”Cherenkov radiation”.
The threshold for Cherenkov-effect is v > cn , corresponds to a threshold in the
21
22 CHAPTER 2. NEUTRINO TELESCOPE AND ANTARES
γ factor of the particle [19]:
γth =n√
n2 + 1(2.1)
This happens because the particle tends to polarize the medium, so the
atoms along the track become a electric dipoles. Varition time of these depoles
mean emission of light radiation [8]. An illustration of the phenomenon is given
in figure 2.1.
Figure 2.1: A simple illustration of Cherenkov emission. If the velocity of the
particle exceedes the velocity of light a coherent radiation is produced [20]
With simple geometric considerations this radiation is emitted at a angle
respectively to the track particle [2]:
cosθc =1
βn(2.2)
where θc is the Cherenkov angle, and β is the ratio between the velocity of
particle (v) and c, velocity of the light in vacuum. In water, with a refractive
index of n ∼ 1.33, considering a particle with relativistic energy, the angle of
emission is about 43◦.
The number of photons produced per unit of path and per unit of wavelength
is [2]:
2.2. TOPOLOGY OF EVENTS 23
d2N
dxdλ=
2παZ2
λ2sin2θc (2.3)
Detection Cherenkov light allows the trajectory of the particle to be recon-
structed.
2.2 Topology of events
A breif treatment of the processes of neutrinos that interact with matter is
proposed in paragraph § 1.2.2. There are three event topologies (as shown in
figure 2.2) in a neutrino telescope:
• track event;
• shower event;
• double-bang event by tau neutrino.
Figure 2.2: Event signature for all flavour of neutrinos: a) represent a charged
current interaction of νµ, b) double-bang event, by a neutrino ντ , c) shower
event from a CC interaction for νe and d) a NC interaction produced by all
flavours neutrino [13].
2.2.1 Track events
A high-energy muon can be produced by muon neutrino after CC interactions
with matter. The direction of the µ is highly correlated with the neutrino arrival
24 CHAPTER 2. NEUTRINO TELESCOPE AND ANTARES
direction and the average θνµ angle (fig. 2.3) between the incoming neutrino
and the induced muon is:
θνµ '0.7◦√Eν(TeV )
(2.4)
Using this event topology it can be possible to find the direction of neutrinos.
A muon can lose energy, in addition to the Cherenkov effect, via bremsstralung,
ionization and pair production. The energy loss per unit path length of the
muon is described with the following relation [14]:
dE
dX(Eµ) = α(Eµ) + β(Eµ) · Eµ (2.5)
where α(Eµ) is the parameter that describes the energy loss due to ionization
alone and the term β(Eµ) describes the radiative processes.
A critical energy Ec, depending on the traversed material, exists: above that
the radiative losses become larger than ionisation losses. In water this energy
is ∼ 500 GeV.
Defining Reff as the distance after which a muon of initial energy Eµ is still
above the energy Ethµ to be observed by the apparatus. This largely increases
the effective volume of the detector, neutrino interactions can happen far away
from the instrumented volume. Figure 2.4 shows the effective range (Reff ) in
the water.
However for the majority of high energy events, the interaction vertex is
far outside the detector. As a consequence only part of the muon track is
directly observed in the detector, this limits the capabilities of neutrino energy
reconstruction for track-like events.
2.2.2 Shower event
When a neutrino νe interact via CC process an electron or positron is created,
that produces a electromagnetic shower (see figure 2.2). A high energy electron
can radiate a photon via Bremsstrahlung. Consequent an electron-positron pair
is produced via pair production that itself will radiate via Bremsstrahlung again
and hence evolve a cascade of electrons, positrons and photons. If the energy
particles is above the thershold condition for Cherenkov radiation, the light is
emitted.
The longitudinal development of an electromagnetic shower is well understood
(fig. 2.5). For a radiation length (the distance which the electron loss ∼ e−1
energy only for radiation) ∼ 36 g/cm−2 in water, the maximum shower lies
2.2. TOPOLOGY OF EVENTS 25
Figure 2.3: The plot shows the average angle in function of neutrino’s energy.
For 1 TeV of energy neutrino the θνµ is approximately 0.7◦ [21].
between 0.6 m for 1 GeV and 7 m for 100 PeV. Therefore, given the size of
the detector, the showers are very compact so can be approximated like a point
source.
Unlike track events, shower events are characterized by worse angular resolution;
but the energy resolution is better compared to track events.
Hadronic showers are produced when a neutrino (of every flavour) interacts via
NC or CC.
2.2.3 Double-bang event
When a τ neutrino interacts via CC interaction, a τ lepton and hadronic shower
(see figure 2.2) are produced. Tauons are unstable particles, have a lifetime
about 2.9·10−13 s [24], and can decay producing various particles. Three relevant
decay scenarios are possible [21]:
26 CHAPTER 2. NEUTRINO TELESCOPE AND ANTARES
Figure 2.4: The effective range of muon in function of the energy. Different line
is relate to the different energy thersholds (from 1 to 106 GeV) [23].
τ → ν + ν + µ (17.4%) (2.6)
τ → ν + ν + e (17.9%) (2.7)
τ → ν +X (64.7%) (2.8)
The interaction of a τ neutrino with matter is associated with a double bang
signature (see Fig. 2.2). The first bang is defined by a hadronic shower, while
the second bang is caused by the short tauon lifetime. For high energy tauons,
due to the relativistic reason, is possible to observe a track between the two
bangs.
Below 1 PeV the hadronic and decay vertex are very closely, so is complicated
to discriminate them. If the τ decay starts or ends out of the instrumentad
volume, the event will have one shower less than the double-bang event. This
case is referred as lollipop event.
2.3. ANTARES EXPERIMENT 27
Figure 2.5: The plot shows the longitudinal distance for all topologies events in
function of the energy [25].
2.3 ANTARES experiment
ANTARES (acronym for Astronomy with a Neutrino Telescope and Abyss envi-
ronmental RESearch) is a neutrino telescope installed at a depth of 2475 meters
in Meditterean sea, 40 km from La Seyne-sur-Mer in the Gulf of Lion, Southern
France. The construction of the telescope started in 2006 with the first detec-
tion line. Between December 2007 and May 2008, it was then completed. Is
at present the largest neutrino telescope in the Northern hemisphere and the
largest under-water neutrino detector.
The telescope consists a three-dimensional array of 885 optical modules
(OMs) arranged in triplets (so called storey) distributed on 12 lines with a
vertical spacing of 14.5 m between (see figure 2.6). The lines are anchored on
the seabed and are held in tension by buoys located on the surface.
The total length of each line is 450 m and the separation between the lines
ranges from 60 to 75 m [12]. All lines are connected to a Junction Box on the
sea-bed, which is then connected to the shore station with a 42 km-long elec-
trooptical cable (the Main Electro-Optical Cable, MEOC). Besides the main
electro-optical cable provides the electrical power to the detector. In the shore
station the data are treated by a PC farm where they are filtered and then sent
28 CHAPTER 2. NEUTRINO TELESCOPE AND ANTARES
Figure 2.6: Schematic view of the ANTARES detector [26].
via the fibre optic network to be stored remotely at a computer centre in Lyon
[26].
2.3.1 Junction box
The Junction box (JB) is a pressure resistant titanium container mounted to the
JB Frame (see figure 2.7), so called JBF, and distributes the power supply,clock
signal and data trasmission to the 13 lines via interlink cables. The structure
of JB is based on a 1 m diameter titanium pressure sphere (fig. 2.8), whose
hemispheres are separated by a central titanium cylinder through which all
power and data connections pass to the exterior [26].
2.3.2 ANTARES line component
From bottom to top a line of ANTARES is composed:
• Bottom String Socket (BSS) is the connection between the line and a
dead weight which fixes the whole unit on the seabed. This module con-
2.3. ANTARES EXPERIMENT 29
Figure 2.7: This imagine shows the Junction box container and its frame [26].
tains a sub-module to control the string (SCM, String Control Module),
a component (SPM, string power Module) to supplement the power of all
the tools in the line and an acoustic signal emitter. The acoustic system
is used for both sending and receiving acoustic signals so that possible to
monitor the position of the line. The SCM contains the electronics capable
of transmitting data with the control room;
• Storey (fig. 2.9) is a titanium frame that carries three Optical Module
(OMs), see fig. 2.11, and many device for the positioning and calibrations.
The Optical Module consists of a pressure resistant glass sphere with 43
cm in diameter and 15 mm thick. Inside an Optical Module there is a
spherical PMT with a diameter of 25 cm, able to reach a gain of about
107 with a nominal voltage of 1760 Volts. A PMT can take a quantum
efficiency of 25 % in the wavelength range between 350 nm and 600 nm.
A cage of µ-metal is used to shield the PMT from the Earth’s magnetic
field, which modifies the transit-time of photoelectrons. The three OMs
are mounted on an OMF (Optical Module Frame), made of titanium,
30 CHAPTER 2. NEUTRINO TELESCOPE AND ANTARES
Figure 2.8: The Junction box [27]
and are orientated 45◦ downwards, to increase the detection of Cherenkov
light directed upwards. Additional device are present:
- LCM, Local Control Module, is the main electronic container on
each storey, where the PMT output is digitized by the Analog Ring Sam-
pler (ARS), see §2.3.3;
- Hydrophones The sea currents, typically with a 5 cm/s, can change
the lines their position by a few cm. This would result in a poor recon-
struction of the event. For this reason, an acoustic system is configured,
which uses the emitter placed in each BBS. The distance between the hy-
drophones, located somewhere on the line, and the BBS is obtained by
the speed of sound in the water. Therefore, through a triangulation sys-
tem, the position of the OMs can be obtained any time (about every two
minutes). At storey 1, 8, 14, 20 and 25 a receiver hydrophone is mounted
for acoustic positioning;
- Optical Beacons are LED Optical Beacons (LOB) placed for each
line at storey 2, 9, 15 and 21 in order to illuminate the OMs located above
2.3. ANTARES EXPERIMENT 31
Figure 2.9: A picture of ANTARES storey. The LED-beacon (blue) and the
hydrophone (ochre) for acoustic positioning are visible [27].
on the same line for time calibration issues.
• Buoy: Each line is pulled taught by a top buoy, made of composite syn-
tactic foam is mounted and with a density 0.5 g/cm3.
2.3.3 Data acquisition
The main purpose of the DAQ (data acquisition) is to digitize the analog input
signal from PMTs, thus obtaining useful information for the reconstruction of
the event (arrival time, signal amplitude, etc.). DAQ system is split in three
main part [20] [28]:
• digitize the analogue PMT signal;
• process the data stream online (on shore) and generate physics events by
applying triggers;
• store the information in an appropriate data format.
32 CHAPTER 2. NEUTRINO TELESCOPE AND ANTARES
Figure 2.10: The image shows a series of storeys in the laboratory, before the
deployment of the detector at sea [27].
The first part is devolped by two analogue ring samplers ARS, inside the
LCM. These work according to two precise parameters: the threshold charge
fixed at 0.3 photoelectrons, to eliminate effects due to dark current, and the
duration of the integration window ∼ 30-35 ns.
If there is a signal above the threshold ARS collects data for 30 ns, how-
ever follow a dead time of 200 ns. To prevent events losses, after a token
transmission (∼ 10-15 ns), the second ARS communicates with the PMT and
takes data, as shown in fig. 2.12. This communication protocol is called the
Token Ring Protocol.
The data is sent to the BBS, which is connected to the JB, so via the MEOC the
data are transferred to the central control. The ANTARES has tree different
2.3. ANTARES EXPERIMENT 33
Figure 2.11: The figure represents an optical module of Antares. Within this
glass ball is contained the PMT [27]
trigger:
• L0 (level zero): charge collection is more than the threshold, often is fixed
at 0.3 photoelectrons;
• L1 (First level trigger): hits with a large charge is identificated;
• L2 (Second level trigger): is a trigger logic algorithm that work on the L1
hits, after that the data are stored.
To reduce the amount of data, only hits above a threshold of 0.3 photoelec-
trons are taken. The corresponding L1 hits have typically a charge above 3 p.e.
or are defined as at least two L0 hits occurring on the same storey within 20 ns,
see fig. 2.13. This is due to reduce the optical background as 40K deacy and
bioluminescence. For L2 level there are two many physics algorithm:
• A 3D-directional scan logic trigger 3N, as referred five L1 hits in a time
window of 2.2 µs;
34 CHAPTER 2. NEUTRINO TELESCOPE AND ANTARES
Figure 2.12: Three peaks are observed in the picture: are related to the first
ARS, its switch to the second ARS and the first ARS after the dead time (200
ns) [26].
• A cluster logic trigger T3 trigger is a collection of two L1 hits on adjacent
storeys in 80 ns or two L1 hits on adjacent storeys in 160 ns. A trigger
logic level is defined as 2T3, based on the definition of a T3 cluster of hits,
that requires at least two T3 clusters within a time window of 2.2 µs.
2.4 Sea water properties
As explain previously ANTARES telescope is installed in deep water. The
knowledge of the optical properties of sea water at the ANTARES site is ex-
tremely important to understand the response of the detector.
2.4.1 Propagation light
When the photons propagate in water two phenomena can occur: dispersion
(scattering process) and absorption. Absorption reduces the intensity of Cherenkov
light, which results in a reduction of the total charge detected by PMTs. While
scattering changes the direction of the photons, modifying the distribution of
their arrival times to PMTs. Both phenomena lead to a misreconstruction of
2.4. SEA WATER PROPERTIES 35
Figure 2.13: An example of DAQ system, only signals above the L0 threshold
and fulfilling the SPE pattern have been sent to shore [29].
events. Given a wavelength λ, the propagation of light inside the medium is
described by the coefficient absorption a(λ), scattering b(λ) and attenuation
c(λ) coefficient [14]:
c(λ) = a(λ) + b(λ) (2.9)
For each phenomena a radiation lengths can be defined:
L(λ) = i(λ)−1 i = a, b, c (2.10)
These lengths represent the path after which the initial intensity I0 of beam is
reduced to a factor 1/e respectively for absorption, scattering and attenuation.
The light intensity has the following shape, depending on lengths:
Ii(x, λ) = I0e− xLi i = a, b, c (2.11)
Where x is the optical path (in meters) of the photons.
The measure (see figure 2.14) of the attenuation length in ANTARES site for a
wavelength λ = 446 nm is:
36 CHAPTER 2. NEUTRINO TELESCOPE AND ANTARES
Figure 2.14: The plot shows the absorption (blue dots) and effective scattering
(red line) length in different time. The black line is the effective scattering line
in a pure water [17].
Lc(λ) = 41± 1(stat)± 1(syst) m (2.12)
The measurement was repeated during the course of one year to understand
the time variability of water properties at the detector site.
2.4.2 Optical background
There are two main type of optical background on PMTs:
• Decays of radioactive elements;
• Bioluminescence light produced by living creatures;
40K decay is by far the dominant process among radioactive decays in sea water
[14]. Its decay channels are [15]:
40K →40 Ca+ e− + νe (89.3%) (2.13)40K + e− →40 Ar + νe + γ (10.7%) (2.14)
The electrons produced in the β-decay channel (first process) are often above
the threshold for Cherenkov light production. In the electron capture channel
2.4. SEA WATER PROPERTIES 37
(second process) fast electrons with subsequent Cherenkov light emission are
produced by Compton scattering of γ, released by the excited Ar nuclei [15].
The concentration of 40K in sea water is dependent by the salinity of the sea
water. Water salinity is almost constat in all over Mediterranean Sea, so on a
10-inch PMT the mean single rates from 40K decays is about 50 KHz.
The bioluminescence light is induced manly from two sources: glowing bacteria
Figure 2.15: The system configuration,for the second immersion, to the mea-
surement of the light transmission [16].
and flashes light produced by marine animals. This background source can be
more intense than 40K for several orders and appears as bursts in the counting
rates of PMTs.
Seasonal effects in bioluminescence can be present, for example during spring
a maximum intensity ∼ MHz single rates on PMTs can be observed. In these
period the detector may be switched-off to avoid data acquisition problems.
2.4.3 Biofouling and sedimentation
The OMs are exposed to sedimentation and adherence of bacteria (biofouling)
which reduce the light transmission through the glass sphere. These effects
on the ANTARES optical modules have been studied in [16]. The system for
38 CHAPTER 2. NEUTRINO TELESCOPE AND ANTARES
measuring light transmission, shown in 2.15, is housed in two 17′′
pressure
resistant glass spheres similar to those used for the OMs.
Figure 2.16: Light transmission as a function of time from the first immersion.
Curves are labeled according to the zenith (θ) and azimuthal angle (φ) of each
photodiode. At the bottom of the figure there is the current velocity [16].
One of them was equipped with 5 photo-detectors glued to the inner surface
of the sphere at various positions which were illuminated by two blue light LEDs
contained in the second sphere.
The light flux transmitted to each photodiode is measured in order to monitor
the effect of fouling on the two glass surfaces. The measurements went on during
immersions of several months and the results were extrapolated to longer periods
of time. There were in particular two immersions. For the first immersion the
photodetectors were glued to the lower sphere at different inclinations (zenith
angles of 0◦,20◦ and 40◦). Three photodetectors were placed at 20◦ on different
meridians to test for a possible azimuthal (φ) dependence of the fouling. For
the second immersion the photodetectors were placed at zenith angles ranging
from 50◦ to 90◦,fig. 2.15.
Figure 2.16 and 2.17, shows the loss of transparency respectivaly for the first
and second immersion.
The loss of transparency (figure 2.17) in the equatorial region of the OM is
2.5. EFFECTIVE AREA AEFFν 39
Figure 2.17: Light transmission as a function of time from the second immersion.
Each curves correspond to different photodiode zenith angle [16].
about 2% after one year, then shows some saturation effect.
Considering that the OMs of ANTARES point 45◦ downward, zenith angle of
135◦, the biofouling and the sedimentation should not represent a major problem
for the experiment.
2.5 Effective Area Aeffν
The effective area can be reffered as the ANTARES detection efficiency and can
be only calculated by Monte Carlo simulations. The effective area, convoluted
with the flux of neutrino, gives the event rate [12]:
NνT
=
∫dΦνdEν
Aeffν (Eν) dEν (2.15)
In general Aeffν depends on the neutrino cross-section, on the survival probabil-
ity of neutrinos crossing the Earth and on the daughter muon (in CC process)
detection. The effective area correspond to [12]:
Aeffν = A · Pνµ(Eν , Eµthr) · ε · e
−σ(Eν)ρNAZ(θ) cm2 (2.16)
40 CHAPTER 2. NEUTRINO TELESCOPE AND ANTARES
where the terms in equation rappresent:
Figure 2.18: The Aeffν in function of the neutrino energy for different ”water
model”. In up side the plot rappresent Aeffν with changing the absorption
lengths (λabs) and fixed the scattering lengths (λsca). In down side on the
contrary λsca is fixed [29]. Plot in right side are in non-log scale.
• A is the geometrical projected detector surface, expressed in cm2 units;
• ε is the fraction of muons with energy Eµthr that are detected;
• e−σ(Eν)ρNAZ(θ) describes the probability that a neutrino is absorbed when
crossing along Z(θ) in the Earth, θ is defined respect to the nadir;
• Pνµ(Eν , Eµthr) represents the probability that a neutrino with a energy Eν
produces a muon that can be observed at the detector with a residual
threshold energy Ethr [12].
In figure 2.18 is showed the effective area in function of the Eν .
Chapter 3
Reconstruction algorithms
The events, after trigger selection, are reconstructed to obtain the physics quan-
tities that are relevant for the analysis. The reconstruction algorithms for track
and shower events are presented in this chapter.
3.1 TANTRA algorithm
The TANTRA (Tino’s ANTARES Shower Reconstruction Algorithm) [31] al-
gorithm allows the reconstruction for position and energy of the shower-like
events. The reconstruction is performed principally in the following steps:
• Primaly there is a position hit selection, where is selected a set of
hits with the largest sum of associated charge compatible with a common
source of emission;
• A 4-dimensional least linear square pre-fit is performed for the shower
space-time position. After that an M-estimator fit for refinement is
accomplished;
• Shower hit selection: only hits compatible with the fitted position are
selected;
• In the last step there is the shower direction fit, which works with a
probability density funcion table based on log-likelihood minimisation to
determine the neutrino direction and energy.
3.1.1 Hit selection
The criterion selection for each pair of hits (i,j) is [31]:
|~ri − ~rj | ≥ cW · |ti − tj | (3.1)
41
42 CHAPTER 3. RECONSTRUCTION ALGORITHMS
where the terms are:
• ri is the position of the OM that hit i is observed;
• cW is the velocity of the light in the water, about ∼ 0.217288 m · s−1;
• ti is the time of hit i ;
3.1.2 Position reconstruction
After the hits selection, a sample of that is obtained. From N selected hits the
recostruction position of the shower vertex can be obtain assuming the following
quadratic system:
(~ri − ~rshower)2 = c2W · (ti − tshower)2 ∀i ∈ [1, N ] (3.2)
The ~rshower and tshower are defined as shower vertex position and time. This
system can be linearised by taking the difference between every pair of equations
i and j [31]:
(xi − xj) · xshower + (yi − yj) · yshower + (zi − zy) · zshower − c2W (ti − tj) · tshower
=1
2[x2i − x2
j + y2i − y2
j + z2i − z2
j − c2W (t2i − t2j )]
∀i, j : 1 ≤ i < j ≤ N(3.3)
The system can be represent as [31] [32]:
A~v = ~b (3.4)
where A can be written as:
A =
(x1 − x2) (y1 − y2) (z1 − z2) −cW (t1 − t2)...
......
...
(xN−1 − xN ) (yN−1 − yN ) (1zN−1 − zN ) −cW (tN−1 − tN )
(3.5)
The vector ~v::
~v =
xshoweryshowerzshower
cw · tshower
(3.6)
3.1. TANTRA ALGORITHM 43
Moreover ~b is:
~b =1
2
|~r12| − |~r2
2| − c2w(t21 − t22)...
| ~rN−12| − | ~rN 2| − c2w(t2N−1 − t2N )
(3.7)
To solve the eq. (3.4), a residual vector ~r is defined:
~r = A~v −~b (3.8)
The square of this vector has a χ2-like feature:
|~r|2 = (A~v)T (A~v) +~bT~b− 2(A~v)T~b (3.9)
A minimization to find a solution for eq.(3.4) needed [31], therefore:
~v = (ATA)−1AT~b (3.10)
An M-estimator fit with ~v is performed by minimising the following relation:
Mest =
NselectedHits∑i=1
qi ·√
1 +t2Res−i
2
(3.11)
where:
• qi is the charge of hit i ;
• tRes−i = ti - tshower - |~ri − ~rshower|/cw: the residual time of the hit i ;
3.1.3 Direction reconstruction and energy estimator
The energy and direction of the neutrino are determined by the minimisation
of the following negative log-likelihood (L) [31]:
−L =
NselectedHits∑i=1
log [Pq>0 (qi|Eν , di, φi, αi) + Pbg(qi)]
+
NunhitPMTs∑i=1
log [Pq=0 (Eν , di, φi)] (3.12)
with the varoius term indicating:
44 CHAPTER 3. RECONSTRUCTION ALGORITHMS
• Eν the energy of neutrino;
• di the distance between the vertex shower and PMT i , see figure 3.1;
• φi is the angle between the direction of particle and the direction of the
photons emitted;
• αi is the impact angle of photons on the PMT.
• Pq>0: the probability to observe a hit with a charge qi. This term is the
expectation value of the number of photons on a PMT, given the distance
between the shower vertex and the PMT, the photon emission angle and
photon impact angle. The number of photons expected is linear with the
neutrino’s energy. For N photons expected, the probabily to observe n
photons is described by the Poisson distribution:
P (n|N) =Nn
n!e−N (3.13)
• Pbg: the probability that the hit is caused by background, for example40K or bioluminescence;
• Pq=0: the probability for a PMT of not being hit. For N of photoelectron
expected, this term is written:
P (N) = P (q = 0|N) = e−N (3.14)
To define the PDFs, the MC simulation (see chap. 4) of showers in ANTARES
is used. This algorithm give the best performance for a shower reconstruction
ever achieved in a neutrino telescope. A resolution of the energy is about 5% -
10%, and the shower vertex is reconstructed with a error ∼ 1 meter.
3.2 Track algorithms
The track events provide a better angular relsolution than the shower events,
therefore can also be used to determine the origin of the event whether it is
a neutrino or an atmospheric muon. In this section two algorithms for track
reconstruction are described: AAfit [33] and GridFit [34].
3.2.1 AAfit reconstruction
To reconstruction the track of relativistic particle, the arrival time of a Cherenkov
photon to a PMT and the following five paramaters, see figure 3.3, are computed
[29]:
3.2. TRACK ALGORITHMS 45
Figure 3.1: Representation of the variables used in likelihood function.
• zenith angle (θ);
• azimuth angle (φ);
• the coordinate x of the point A, that is defined as the intersection with
the plan P;
• the coordinate y of the point A;
• t0 is the time when the muon cross A.
The expected time tiexp (arrival time) of a hit given muon position and
direction at an arbitrary time t0, can be written [33]:
tiexp = t0 +1
c
(Li −
ditanθc
)+
1
vg
disenθc
(3.15)
In the equation the term with Li describes the time that the muon travels
from the initial position to the point where the detected photons are emitted,
therefore the term with vg (the group velocity of light) is just the required time
46 CHAPTER 3. RECONSTRUCTION ALGORITHMS
Figure 3.2: Performance of TANTRA algorithm: on top left is plotted dis-
tance between the position of the neutrino interaction vertex and the recon-
structed shower position in function of energy. On top right there is the dis-
tance of the reconstructed shower position perpendicular to the neutrino axis.
On bottom left the ratio between the energy recontruction and the true en-
ergy. On bottom right the ratio between the directions of the reconstructed
shower and the MC neutrino [31].
for photons to reach the PMT. The difference between texp and the measured
arrival time (tmeas) of the photon defines the time residual [14]:
r = timeas − tiexp (3.16)
The track reconstruction method is based on a likelihood fit derived from
simulation. In this case the Probability Density Function (PDF) of the time
residuals is built under the assumption of Cherenkov emission from the track.
To obtain a optimal solution, before to improve the likelihood fit a series of
pre-fit algorithms of increasing sophistication are implemented [33] [29]:
• Linear pre-fit is a first linear fit independent of the starting point;
3.2. TRACK ALGORITHMS 47
Figure 3.3: Illustration of the variables used for AAfit recostruction [29].
• M-estimator fit: this step use the only the hits that are shorter than
distance 100 m from the fitted track (of course come from the previous
step). Moreover the hits should be on a ± 150 ns window with respect to
the expected time;
• A maximum likelihood fit with the original PDF;
• Repeation the previous step (9 time) with different starting points;
• Maximum likelihood fit with improved PDF.
The quality of the reconstruction can be estimated by the following variable:
Λ =logLNdof
+ 0.1(Ncomp − 1) (3.17)
where:
• logLNdof
is the log likelihood per degree of freedom;
• Ndof is the the number of starting points, i.e. the number of compatible
solution. For badly reconstructed events the Ncomp is 1 in average, and
for well reconstructed events it can be possible to find Ncomp = 9, in the
last case all the starting points have resulted in the same track.
48 CHAPTER 3. RECONSTRUCTION ALGORITHMS
3.3 Gridfit
Gridfit is a algorithm developed to optimise the track reconstruction for neutrino
with low energy [34]. The full solid angle in 500 different directions, a selection
hits compatible with a muon track performed. Consecutively a likelihood fit,
after various step, is performed. On order to separate muon from neutrino a
variable, called GridFit Ratio, is defined:
R =
∑up−going Nhits∑down−going Nhits
(3.18)
where∑up−going Nhits is the sum of the hits compatible with up-going direction
(from θ = 90◦ to θ = 0◦, with θ defined as the Zenith angle). Therefore∑down−going Nhits is the sum of all hits compatible with down-going direction.
This ratio for muon mostly is less than 1, as shown in figure 3.4, instead for
neutrinos the peak of the distribution is about 1.6 [34].
3.3. GRIDFIT 49
Figure 3.4: The distribution of Ratio for atmospheric muon, the peak distribu-
tion is about 0.6. Different plot is for different background rate: on top right is
120 kHz, on top left is 60 kHz, on bottom right is 240 kHz and on bottom left
is 180 kHz [34].
50 CHAPTER 3. RECONSTRUCTION ALGORITHMS
Chapter 4
Monte Carlo ANTARES
The Monte Carlo simulations are required to understand the behaviour the
detector and its physics. A software chain is schematised into three following
steps:
• Generation of physics event: particles (neutrinos and muons) are gen-
erated in proximity of the detector;
• Cherenkov light emission and propagation: particles are propagated
in the medium, and the Cherenkov light is simulated and propagated to
the OMs;
• Simulation of data acquisition: the PMT response and the optical
background is simulated. The data stream is created and the triggers are
applied.
4.1 Detector can
For the generation of the particles a sensitive volume of the detector is defined
as a cylinder containing the water region hosting the PMTs. This volume is
called can, see fig.4.1. The can defines the volume where the Cherenkov light in
the Monte Carlo is simulated. Outside this region Cherenkov photons produced
have a low probability to reach a PMT, and only particle energy losses during
propagation are considered.
51
52 CHAPTER 4. MONTE CARLO ANTARES
Figure 4.1: In figure the can is reppresents in yellow. It is anchored to the sea-
bed (in red) and containing the detector instrumented volume (in blue) [14].
4.2 Generation of physics events
4.2.1 Simulation of atmospheric muons
The most abundant signal for a neutrino telescope comes from high energy
muons that are produced in the extensive air showers via the interactions of CRs
with the nuclei of the upper atmosphere. Although the ANTARES telescope is
located at large depth under the sea, which acts as a shield, the atmospheric
muon flux is still intense at the active volume of the detector. The atmospheric
muons is an background for track reconstruction because their Cherenkov light
can mimic fake upward-going tracks. This kind of signatures can be confused
with the cosmic neutrino signal [14]. Most of them are rejected applying a
combination of geometrical and reconstruction quality cuts that select only well
reconstructed tracks moving upward. On the other side, atmospheric muons are
used to test the performance of analysis software, to monitor the detector and
to calculate the systematic uncertainties. Atmospheric muon bundles arriving
at the detector are accurately reproduced using a complete extensive air shower
simulation: the CORSIKA program [47]. With this package the interactions
4.2. GENERATION OF PHYSICS EVENTS 53
between the primary CRs and the atmospheric nuclei are simulated, than the
air shower is tracked, through the atmosphere, to the sea level.
The program offers a large choice for the input parameters, for example:
• Description of atmosphere;
• Hadronic interaction parameterisation;
• Chemical composition of the primary CR flux.
The propagation of the muons from the sea level to the detector was performed
using the MUSIC package [48] (MUon SImulation Code). This procedure gives
a precise description of atmospheric muons at the detector, but it has heavy re-
quirements in terms of CPU time and for this reason a different approch is has
been realized. In ANTARES atmospheric muon bundles are generated with
the MUPAGE software [46]. This simulation doesn’t take care of the full air
shower development, but is faster than the CORSIKA. The program uses a
parametric formulas to calculate the flux of muon bundles, taking into account
the muon multiplicity and the muon energy spectrum in a bundle [49]. The
parameterisations used in MUPAGE are extracted from a complete simulation
of events based on the results of the MACRO experiment at Gran Sasso, ex-
trapolated under the sea or under an ice layer [46].
The usage of parametric formulas allows the fast production of a large number
of Monte Carlo events, but there is the absence of flexibility in the definition of
the input parameters related to the primary composition and interaction. Even
if there are these limitations, the parametric simulation produces a reliable es-
timate of the atmospheric muon background.
4.2.2 Simulation of neutrinos
A dedicated package, called GENHEN (GENerator of High Energy Neutrinos),
has been developed by the ANTARES collaboration to cover the full range of
neutrino (all flavours), from a energy around 10 GeV (approximately the energy
thershold of muon detection) to multi-PeV.
The GENHEN has the following main feature:
• All neutrino interactions are simulated. At high energies the process rele-
vant is Deep Inelastic Scattering (DIS), therefore QuasiElastic (QE) and
Resonances (R) are the dominant processes at low energies;
• Events inside and outside the can are generated together;
• In case of inside events (volume events) hadronic and electromagnetic
showers at the interaction vertex are fully simulated, instead outside events
(surface events) high energy muons and tauons are tracked until they stop
or reach the surface of the can;
54 CHAPTER 4. MONTE CARLO ANTARES
• The effect of the different media, manly rocks and water, around the
detector are taking account;
• The generation spectrum of neutrino interactions is expressed with a power
law:
dN
dE= E−Γ (4.1)
This is referred to as interacting neutrino spectrum, which can be weighted
to different neutrino fluxes to produce the event rates.
The simulation strategy is based on the definition of a volume, referred gen-
eration volume, around the detector which contains all potentially detectable
neutrino interactions for the given energy range and simulate it within that vol-
ume.
The users firstly decide the maximum neutrino energy (Emax). This corre-
sponds to an upper limit on the energy of the muon (produced by a νµ via
CC processes) emerging from the interaction vertex, and to a maximum value
of the muon range, Rmax. If the event vertex is contained within the can the
information describing each particle is stored. For neutrino interactions outside
the can, only muons are propagated and the relevant information at the can
surface stored. The scheme of simulation proceeds (fig 4.2) as follow:
• A cylindrical volume (extending the can size) around the detector with a
radius Rmax is defined;
• The total binning neutrino spectrum is divided into equal N bins, between
Emin and Emax. The number of events for each bin is calculated.
• For each energy bin, using the maximum energy in that bin the maximum
muon range in rock and water is estimated.
• For each energy bin the numerical integration of the cross-section in LEPTO
[50] is performed. Therefore the generation for this energy range is ini-
tialised.
• In this step, the loop over the number of events in this scaled volume
(Nscaled) starts:
1. The energy of the interacting neutrino is sampled from the E−Γ spec-
trum within the energy range of this bin;
2. Within the scaled volume, the neutrino position is chosen;
3. If the position is outside the can the shortest distance from the neu-
trino vertex position to the can is estimated. In the case of this
distance is greater than the maximum muon range at that neutrino
energy, the muon don’t reach the can, and the event is rejected;
4.2. GENERATION OF PHYSICS EVENTS 55
Figure 4.2: The scheme of neutrino simulation with GENHEN [14].
4. The neutrino direction is sampled from an isotropic distribution. For
events outside the can, the distance of closest approach of the neu-
trino direction to the can is calculated comparing it to some user
specied distance;
5. For each event, the neutrino interaction is simulated to get the final
state particles produced at the neutrino interaction vertex;
6. At this step, for event inside the can all the properties of these par-
ticles are recorded (position, direction, energy, etc.). Therefore for
events outside only the properties of muons are kept;
7. For those events which are kept, the event weights are calculated
and all the event informations are written on disk.
• On completion of all the stages above, a record of each neutrino interaction
producing at least one particle at or inside the can is obtained.
As mentioned before the events can then be weighted properly to obtain the
effective rates at the detector in according to a specific model. Given a model
with Φ(Eν , θν), the global weight is:
ωglobal = ωgen · Φ(Eν , θν) (4.2)
56 CHAPTER 4. MONTE CARLO ANTARES
where ωgen is [14]:
ωgen =Vgen · ρNA · PEarth(E, θ) · Iθ · IE · EΓ · F
Ntotal(4.3)
The terms of equation (4.3) rapresent:
• V[m3] is the Generation volume;
• ρNA is the product between the target density (ρ) and the Avogadro’s
number (NA). This gives the the number of target nucleons per unit
volume;
• σ(Eν) [m2] is the total cross section of neutrino;
• PEarth(Eν ,θν) is the probability that the neutrino cross the Earth;
• Iθ [sr] = 2π(cosθmax − cosθmin) is the angular phase factor depending on
the specied range of cosθν ;
• IE is the enegy phase space factor depending on the input spectral index
(Γ). For Γ = 1, IE = ln(Emax/Emin) otherwise IE = (E1−Γmax−E1−Γ
min )/(1−Γ);
• F is the second in one year;
• Ntotal is the total number of the generated events.
4.3 Light emission and propagation
A specific package KM3 (a GEANT-based software developed in the ANTARES
context) has been developed for a full and quick simulation of the response of the
ANTARES detector. In particular is simulated the production and propagation
of Cherenkov light inducted by all long-lived particles which are stored as output
from the physics generators. The sea water doesn’t present inhomogeneities [14],
consequently it isn’t necessary a photon-by-photon simulation for the Cherenkov
light.
Thus the simulation is obtained with the creation of ’photon tables’ that store
the numbers and the arrival times of the photons. Moreover the tables contains
the probability that each photons give a hit on a PMT. This probability depends
by 5 parameters:
• The distance of the PMT from the particle;
• The 3 angles defining the direction of the photons with respect to the
particle and to the PMT;
4.3. LIGHT EMISSION AND PROPAGATION 57
Figure 4.3: Graphical representation of the concentrical shells used for building
the hit probability tables [14].
• The photon arrival time on the PMT.
The first step for the generation of the photon tables is the simulation of the
light emitted along the path of muon, at step of 1 m. The photon tracking
is performed considering the composition and the density of the water at the
experimental site and its optical properties: absorption and scattering lengths.
The result is a set of tables recording the photon properties: position, direction,
wavelength and time when they cross spherical shells of increasing radii centered
around the track segment, see fig.4.3.
The probability for each Cherenkov photon to reach a PMT is extracted from
these ’photon tables’. Similar tables are calculated for electromagnetic showers.
The hadronic showers are treated differently, due manly for the large number
of charged particles produced at the interaction vertex and the high stochas-
tic variability in the composition of the shower. Therefore the computation
of scattering tables for each single particle would require an event-by-event
simulation and a huge amount of CPU time. A different approch is used:
the ’multi particle approximation’. Each particle of shower is treated as
a electron. The electron ’photon tables’ are used in association with oppor-
58 CHAPTER 4. MONTE CARLO ANTARES
tune weights, evaluated for each hadron after many complete photon tracking
simulations.
4.4 Simulation of data acquisition
The software in ANTARES used for the simulation of detector response is Trig-
gerEfficiency. This program is performed to adding the hits of physical event
with the hits of optical background, for simulation of the electronics and trig-
gering of events. There are two strategies to add the optical background:
• The optical background can be generated in according to a Poissonian
distribution with a fixed rate chosen by the users;
• The amount of background light can be extracted from a real data run.
In the first approch the background of 40K (manly) is reproduced, because the
rate is essentially constant. The second approach allows for a more realistic sim-
ulation of the environment situation, because is taken into account for seasonal
variations occurring as a consequence of biological activities and for inefficiency
of the OMs, due to the ageing of the PMTs and to the biofouling on the OM’s
surfaces.
The program simulates the DAQ system as described in §2.3.3. Starting from the
number of photons impinging on the OM an analogue pulse at the PMT anode
is simulated whose charge follows a Gaussian distribution. In order to simulate
the time resolution (for single photo-electron signals is 1.3 ns and decreases for
higher amplitudes), the hit times are smeared using a Gaussian function, with
a width [14]:
σ = 1.3ns/√Nγ (4.4)
where Nγ is the number of simultaneously detected photons.
4.5 Run-by-run approach
In order to reproduce the current detector status at the time of data taking a
Monte Carlo strategy, the so called run-by-run, is used in ANTARES. For each
physics run an analogous MC run is produced using the informations extracted
directly from the data. This approch is achieved to take into account the vari-
ations of the environmental conditions under the sea and the periodical change
of the rates registered at the detector due to the biological and physical phe-
nomena. In addition, not all detector elements take data continuously, due of
temporary or permanent malfunctioning of optical modules or lack of connection
to some part of the apparatus. At the moment, the run-by-run version 4 (rbr
4.5. RUN-BY-RUN APPROACH 59
v4) is produced. Compared to the old version (rbr v3), v4 has new important
features:
• The water model of Capo Passero is used;
• 85% OM collection efficiency;
• Efficiency reduction tables according to the measured 40K coincidence
rates.
Comparing the time evolution of the measured atmospheric muon rate in the
data sample of ANTARES to the simulated rate, a discrepancy between the two
time series has emerged. Same result is noted for neutrino induced events. The
loss of efficiency of the OMs has been analyzed using the measurement of 40K.
This signal is constant and stable (see section 2.4.2), therefore can be used as a
reference.
This study has been performed in [15]. In order to monitor the status of the
whole detector from 2008 to 2017, the average photon detection efficiency as a
function of time has been determined. An average decrease of the OM efficiency
by 20% is observed, as shown in fig 4.4. The results of this study implicate
a realistic simulation of the OM efficiencies in each data taking run. For the
rbr v4 this feature is computed for both muons and neutrinos. For neutrinos
simulation this efficiency shows a good data/MC agreement, instead for muons
this correction cannot reproduce a time dependent behaviour in the data/MC
[52]. The rate of muons event was calculated as:
Rate[Hz] =NselectedEventsRunDuration[s]
(4.5)
where NselectedEvents are the number of events (of muons) that are passed the
following selection (AAfit variables):
• Downgoing events (Zenith < 90◦);
• Λ > −6.5;
• β < 1◦, where β indicates the direction error =√σ2θ + σ2
φsin2(θ) ;
• Trigger 3N.
As shown in fig.4.5, the data/MC is time dependent. This means that the
simulation for muons isn’t able to reproduce the behaviour of data. To correct
the MC behaviour according to the observed data rates, a specific procedure
was used:
• To find the rate loss as function of time, a fit of data/MC ratio is per-
formed;
60 CHAPTER 4. MONTE CARLO ANTARES
Figure 4.4: Relative OM efficiency averaged over the whole detector from 2009
to 2017. The blue arrows indicate the periods in which high voltage tuning of
the PMTs has been performed [15].
• Find the correlation between a given efficiency reduction in the MC sim-
ulation and the rate loss;
Combining them the efficiency correction as function of time was obtained [52]:
EfficiencyCorrection =−0.00013 · (dateMJD) + 8.077− 0.99
−1.598(4.6)
This correction has to be applied in addition to the correction that comes from
the 40K study, to remove the time dependence of the rate loss of atmospheric
muon events.
4.5. RUN-BY-RUN APPROACH 61
Figure 4.5: Data/MC ratio, one point per run, as a function of time. Three
regions are indicated: first platau, linear decreasing and second plateau [52].
62 CHAPTER 4. MONTE CARLO ANTARES
Chapter 5
Monte Carlo v3 and v4
One of the goal of this thesis is the preliminary study of selection criteria that
can allow a separation between interactions of atmospheric neutrinos producing
a showers and the background of atmospheric muons. As discussed in Chap-
ter 2, showering events are induced by charged current interactions of electron
neutrinos and neutral current interaction of all neutrino flavours. Atmospheric
electron neutrinos are characterized at high energies (above 1 TeV) by a flux
that is more than one order of magnitude smaller than that of muon neutrinos,
with a soft spectral index, Γ ∼ 3.7. The neutrino interactions we are searching
for must be well contained within the detector fiducial volume; the huge flux
of atmospheric muons represents a background that can be almost irreducible.
This work try to estimate how the atmospheric muon flux can be reduced using
different selection criteria. A selection procedure optimized for cosmic electron
neutrinos (characterized by a harder spectral index, Γ ∼ 2, and a flux higher
than that of atmospheric neutrinos at energies higher than 50 TeV, was defined
in [53]. This selection was optimized with the Monte Carlo simulation of the
signal and of the background defined as “rbr v3” in the previous chapter. In this
chapter, it is presented the effect of the same chain of cuts but applied on the
new version of Monte Carlo: the rbr v4. That version includes the correction
for the muon efficiency described in §4.5. The comparison of the effect of the
cuts on the two Monte Carlo versions are presented.
5.1 Event selection
In order to reduce the background given by atmospheric muons, a chain of cuts
has been defined. The description of this selection cut is presented:
63
64 CHAPTER 5. MONTE CARLO V3 AND V4
• Trigger selection: only the events that pass 3N or T3 trigger are selected
T3 or 3N (5.1)
• Contaiment selection: Only events inside a cylindrical volume around
the detector center with a radius ρ and height z are selected
ρtantra < 300 and |ztantra| < 250 (5.2)
The radius and height considered are those reconstructed with the Tantra
algorithm.
• Mestimator selection: A definition of the variable Mestimator was re-
ported in §3.1.2. When a atmospheric muon is reconstructed with a shower
algorithm often a shower vertex that lie far away from the detector bound-
ary and have a large value for MEst. For this reason a cut is implemeted
as follow:
Mestimator < 1000 (5.3)
• Track-Veto: Event track-like are excluded by the follow selection:
Λ > −5.2 β < 1.0 cos(θ) > −0.1 (5.4)
where the variables are reconstructed by the AAfit algorithm.
• Up-going selection: Only the event up-going are selected:
cos(θzenith,tantra) > −0.1 (5.5)
where θ is the Zenith angle reconstructed by the Tantra algorithm.
• Angular error selection: this step requires that the angular error (for
Tantra algorithm) is:
βtantra < 10◦ (5.6)
• GridFit ratio: the GridFit Ratio variable is defined in 3.3. If it is
combined with the number of selected shower hits, this variable gives a
estimable suppression of atmospheric muon:(R
1.3
)3
+
(Nshower
150
)3
> 1 (5.7)
• MuonVeto selection: a likelihood function has been developed to im-
prove the discrimination between showers and atmospheric muons [53] [31].
This likelihood takes into consideration only the hits that coincide with
another hit on the same storey within 20 ns. The PDFs of this likelihood
depends by the following 3 parameters:
5.2. EVENT SELECTION RBR V3 65
– Time residual tres (see §3.1.2);
– N, number of hits that are in −20 < tres/ns < 60;
– The distance d of the hits to the reconstructed shower position;
The likelihood can be written as [53]:
L =∑hits
[log (Pshower/Pmuon) + Pshower − Pmuon] (5.8)
with Pshower = P (N, d, tres|shower) and Pmuon = P (N, d, tres|muon) are
the PDFs built with the Monte Carlo. This likelihood parameter can be
combined with the zenith angle. On events that have been reconstructed
as down-going, a harder likelihood-ratio cut can be applied:
L >
{400, cos(θAAfit) < −0.2
20, otherwise(5.9)
• Charge Ratio: when a muon is recostructed by an algorithm optimized
for shower, it is supposed that the hits induced by the muons arrive earlier
than predicted by a shower hypothesis. Qearly is defined as:
qi in −1000 ≤ tres/ns ≤ −40 (5.10)
and Qon−time:
qi in −30 ≤ tres/ns ≤ 1000 (5.11)
Therefore the charge ratio between Qearly and Qon−time has been studied,
and a selection to improve the shower selection:
log(Qearly/Qon−time) < −1.3 (5.12)
5.2 Event selection rbr v3
In order to test the performances of the algorithm to discriminate (TANTRA)
the shower events from the atmospheric muons, a selection of events with the
criteria exposed previously was performed with the version rbr v3 of Monte
Carlo ANTARES. The selection of events is published in [53], the results are
reported in the following table:
66 CHAPTER 5. MONTE CARLO V3 AND V4
Criterion Condition εatm.µ εatm.ν→any
Triggered 3N or T3 100 % 100 %
Contaiment ρshower < 300m, |zshower| < 250m 53 % 81 %
M-estimator MEst < 1000 40% 66%
Track Veto not selected as muon candidate 40 % 59 %
Up-going cos(θshower) > −0.1 18 % 44 %
Error Estimator βshower < 10◦ 0.66 % 5.0 %
GridFit Ratio(R1.3
)3+(Nshower
150
)3> 1 0.057 % 4.2%
MuonVeto L > 20 or L > 400 if cos(θAAfit) < −0.2 2.9 · 10−4 % 0.41 %
ChargeRatio log(Qearly/Qon−time) < −1.3 1.1 · 10−5 % 0.31 %
Events in 301 days 18.8 163
In the table the first two columns rapresent the name of the criterion and the
applied condition. The effect on the atmospheric muon is presented in column
3 (εatmµ ), while for atmospheric neutrino is shown in column 4 (εatmoν ). The
efficiencies are the ratio of the number of events that passed a cut and the
number of events after the trigger selection:
εi =npassedntriggered
i = µ, ν (5.13)
As shown on the table above, after applying these selection criteria to the
ANTARES data with an effective life time of 1690 days, is expected to ob-
tain 163 of atmospheric neutrinos. Therefore, the events of atmospheric muon
has been reduced by six orders of magnitudes.
5.3 Event selection rbr v4
The main purpose of this thesis is to calculate the efficiency (eq. 5.13) of the
selection chain for the new version of Monte Carlo ANTARES (rbr v4), in order
to compare with the rbr v3. Therefore the following step was performed:
• A sample of Monte Carlo files are chosen. Only the runs that contained
all types of particles (even all types of processes) were taken into account
(νe CC, νe NC, νµ CC, νµ NC, µ);
• The run ending with 0 are selected. This allows to test a 10% subsample
of the data set leaving blinded the remaining 90%.;
• The lifetime of MC files is 2774 days, instead the lifetime for data is 310
days. Therefore the MC is scaled to the data;
• The selection chain described in the section §5.1 is applied;
5.3. EVENT SELECTION RBR V4 67
Figure 5.1: Likelihood Ratio (Muon-Veto) distribution for atmospheric neutri-
nos (red), atmospheric muons (gray), showers caused by astrophysical neutrinos
(orange), and data (black) [53]. The distribution is plotted after the Gridfit Ra-
tio cut and all previous cuts listed in § 5.1.
Figure 5.2: The Likelihood Ratio distribution after the MuonVeto (rbr v3)[53].
• After each cut a plot of the Likelihood Ratio is produced.
In this section the plots of the Likelihood Ratio distribution are shown. These
68 CHAPTER 5. MONTE CARLO V3 AND V4
plots have been realized to every step of the selection chain in order to observe
the change of the distribution. All plots are shown with the 0-runs data (black
line), the atmospheric muons (grey line) and the atmospheric neutrinos (red
line). Analyzing the plots obtained with v4
(a) Likelihood distribution without cut (b) Likelihood distribution after trigger selec-
tion
(c) Likelihood distribution after contaiment
cut
(d) Likelihood distribution after Mestimator
cut
Figure 5.3: Starting from the plot on the top left side are applied all cuts of the
cut-chain that are the trigger, the contaiment and the Mestimator.The selection
step is shown below each plot. Furthermore, for each plot is showed the ratio
between the data (0-runs) and the Monte Carlo.
5.3. EVENT SELECTION RBR V4 69
(a) Likelihood distribution after Track-Veto (b) Likelihood distribution after up going se-
lection
(c) Likelihood distribution after angular error
selection
(d) Likelihood distribution after GridFit ra-
tio
Figure 5.4: Starting from the plot on the top-left side are applied cuts of the
cut-chain that are the Track-Veto, the up-going selection, the angular error
selection and the GridFit-Ratio. Furthermore, for each plot is showed the ratio
between the data (0-runs) and the Monte Carlo.
70 CHAPTER 5. MONTE CARLO V3 AND V4
(a)
Figure 5.5: The Likelihood distribution after the MuonVeto cut (rbr v4).
5.4. RESULTS 71
5.4 Results
The efficiencies obtained for the v4 are shown in the following tables. The first
table shows the efficiencies for atmospheric muons and neutrinos (either yielding
a shower or a track), in order to then compare with the table in § 5.2 :
Criterion Condition εatm.µ εatm.ν→any
Triggered 3N or T3 100 % 100 %
Contaiment ρshower < 300m, |zshower| < 250m 58 % 32 %
M-estimator MEst < 1000 51% 29%
Track Veto not selected as muon candidate 51 % 28 %
Up-going cos(θshower) > −0.1 34 % 10%
Error Estimator βshower < 10◦ 10 % 4.1 %
GridFit Ratio(R1.3
)3+(Nshower
150
)3> 1 0.016 % 1.7%
MuonVeto L > 20 or L > 400 if cos(θAAfit) < −0.2 1.0 · 10−2 % 0.09%
ChargeRatio log(Qearly/Qon−time) < −1.3 9.3 · 10−3 % 0.07 %
While in the second table is reported the efficiency for atmospheric νe and νµ(CC and NC process):
Criterion Condition εatmoνe εatm.νµ
Triggered 3N or T3 100 % 100 %
Contaiment ρshower < 300m, |zshower| < 250m 24 % 33 %
M-estimator MEst < 1000 20% 29 %
Track Veto not selected as muon candidate 20% 29%
Up-going cos(θshower) > −0.1 8% 10%
Error Estimator βshower < 10◦ 4.6% 4%
GridFit Ratio(R1.3
)3+(Nshower
150
)3> 1 1.9% 1.7%
MuonVeto L > 20 or L > 400 if cos(θAAfit) < −0.2 0.1% 0.08%
ChargeRatio log(Qearly/Qon−time) < −1.3 0.1% 0.08%
The efficiency of the cuts between the two simulations is different. In particular,
in two precise cuts are observed a relevant difference:
• Contaiment: with this selection, a significant reduction in the number
of atmospheric neutrinos is observed for version v4. In version v3 80% of
neutrinos are observed, while with v4 only 32% of events remains. For
muons at this step, instead, there is almost an agreement between the two
versions.
• MuonVeto (and ChargeRatio): these cuts with the rbr v4 version
are less effective than with the rbr v3 version. Therefore with the v3
72 CHAPTER 5. MONTE CARLO V3 AND V4
was obtained a decrease of 10−5%, with v4 only a reduction of 10−3% is
obtained.
Therefore using the cut-chain proposed in [53] with the version rbr v4 is ob-
served a lower efficiency to reject the atmospheric muon events than the rbr v3.
The events of muons decrease for each cut, but a considerable reduction isn’t
achieved. Furthermore, as shown in fig.5.5, the number of neutrinos after the
cut-chain remains low with respect to muon events.
Conclusions
The ANTARES telescope was completed in 2008 and has taken data contin-
uously since then. In order to understand the detector’s response, a chian of
simulation (Monte Carlo) is performed. The main purpose of this thesis is to
make a comparison between two different Monte Carlo simulation of ANTARES:
the old version (rbr v3) and new version (rbr v4).
To accomplish this objective, a cut-chain optimized to reject atmospheric muons
was used as a comparison test. The variables used in this selection of events are
explained in this thesis. Applying these cuts we observe a difference between the
two versions of simulation: the efficiency to reject muon events is less in the new
version (v4) than in v3. Therefore with the version v4 the atmospheric muons
events remain higher than the atmospheric neutrino events, after the cut-chain.
In the end we are focused on the Likelihood Ratio: a function developed to
improve the discrimination between showers and atmospheric muons.
With the version v3, selecting with this Likelihood distribution it was possi-
ble to reduce of six orders of magnitude the background given by atmospheric
muons.
Instead for the v4 version selecting with this distribution is observed a reduction
in efficiency to reject atmospheric muons.
73
74 CHAPTER 5. MONTE CARLO V3 AND V4
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