Performance test of the KM3NeT track reconstruction software on ANTARES Monte Carlo data

(1)

MSc Physics and Astronomy

Gravitation, Astro-, and Particle Physics Amsterdam

(GRAPPA)

Master Thesis

Performance test of the KM3NeT track

reconstruction software on ANTARES Monte

Carlo data

by

Maarten Hammer

10525319

May 28, 2021 60 ECTS

September 2019 through May 2021

Examiner/Supervisor: Examiner:

Prof. dr. Maarten de Jong Prof. dr. ir. Paul de Jong

Nikhef Amsterdam KM3NeT ANTARES

(2)

Abstract

Event reconstruction constitutes the first and thereby essential part in the analysis of the data from a neutrino telescope. Any improvement in the event reconstruction will effectively improve the performance of the neutrino telescope. For ANTARES, the so called AAFit application is used to reconstruct the neutrino directions from the recorded data. These neutrino directions are subsequently used for searches of neutrino point sources in the sky. For KM3NeT, a new software framework, called Jpp, has been developed for this purpose. This framework uses a more thorough approach to the various steps in the reconstruction process. For this research, the Jpp software framework is modified such that it can be applied to ANTARES data. Standard Monte Carlo simulations of the detector response are used to evaluate the performance of Jpp and to compare it to that obtained with AAfit.

Before event selection is applied, the event rate of correctly recon-structed neutrino events in Jpp is 30% higher than AAfit using the same hit preselection. After event selection, the event rate depends on the cho-sen event purity (fraction of neutrinos in the final event sample). For an event purity of 90%, the performance obtained with Jpp is similar. Re-laxing this constraint to 80 (70)%, yields an increase of the neutrino event rate of about 20 (30)% compared to AAfit. There still is a potential to further increase the neutrino event rates if more efficient event selection criteria are found in the future. If the hit preselection is expanded, the yields are up to 95% higher before cuts; similar with 90% purity; and up to 50% higher if purity is relaxed to 65%. The present and possi-ble future improvements could retroactively improve the performance the ANTARES detector.

(3)

1 Introduction

1.1 Why do we use neutrino telescopes?

In astro-particle physics all sorts of telescopes are used to scour the sky for discoveries. Traditional telescopes rely on the detection of some form of elec-tromagnetic radiation. Neutrino telescopes do not rely on elecelec-tromagnetic ra-diation, but on neutrinos emitted by sources in the Universe. Neutrinos are not deflected by electromagnetic fields and very little affected by radiation or mat-ter. Thus, neutrinos are excellent probes for the observation of the sky but this comes with the challenge to detect them and measure their direction, energy and flavour [1].

1.2 Neutrino detectors and improvements

Neutrinos cannot be detected directly as they only interact via the weak force. Indirect detection must be used to observe neutrinos. But when neutrinos weakly couple to matter, charged particles can be produced. The charged par-ticles can then be used to indirectly detect the neutrino.

The ANTARES and KM3NeT neutrino telescopes make use of Cherenkov radiation for neutrino detection. Cherenkov radiation is produced when charged particles move faster than light in a medium. ANTARES and KM3NeT detect this light using photosensitive detectors called photo-multiplier tubes (PMT). These detectors constitute large arrays of PMTs placed in the Mediterranean Sea. The reconstruction of the particles produced in a neutrino interaction makes it possible to indirectly measure the neutrinos.

1.3 Effective volume, angular resolution and research goal

The performance of a neutrino telescope can be expressed in terms of its effec-tive volume and its angular resolution. As such, a good approach to qualify a telescope is to study these two quantities. By improving the effective volume, the number of detected neutrinos is increased. By improving the angular reso-lution, the pointing of the telescope is increased. This is the motivation behind the construction of the much bigger KM3NeT detector following the operation of the relatively small ANTARES detector.

In this paper a synergistic approach is used to improve the ANTARES neu-trino telescope. For KM3NeT a new software framework has been written known as ”Jpp”. This framework includes event reconstruction algorithms. An im-provement in neutrino event reconstruction could increase the effective volume of the detector or increase the angular resolution. In this paper, ANTARES Monte Carlo data are used to compare the performance with the KM3NeT software framework and the original ”AAfit” algorithm.

(6)

1.4 Thesis layout

In chapter 2, the underlying neutrino astrophysics is briefly described. In chap-ter 3, the ANTARES and KM3NeT detectors as well as the detection principle are introduced. In chapter 4, the neutrino event reconstruction with AAfit and Jpp is explained, as well as some test statistics used in the results section. In chapter 5, the modifications applied to Jpp are explained such that Jpp can be applied to ANTARES data. In chapter 6, the performances of both recon-struction methods are presented. Finally, in chapter 7, the results and future prospects are discussed.

(7)

2 Neutrino Astrophysics

In this chapter, the basics of the sources and detection of neutrinos as well as possible backgrounds are presented.

2.1 Neutrino Sources

Neutrinos can be produced in many places, for example in the cosmos as well as man-made nuclear reactors and natural decays of radio-active elements in the Earth [2]. Neutrino astronomy is the field of research in which neutrinos from the cosmos are studied. In 2013 the first astrophysical neutrino flux was detected by IceCube [3, 4]. In this section, I will present the most relevant neutrino sources for the ANTARES detector. One generally classifies neutrinos from cosmic sources as signal and all other events as background [5]. At the energies of interest, neutrinos and muons produced by cosmic-rays interactions in the Earth’ atmosphere constitute the dominant background [6]. In figure 1 the neutrino flux covering a wide range of energies is presented.

Figure 1: Grand Unified Neutrino Spectrum at Earth, integrated over direc-tions and summed over flavors. Solid lines represent neutrinos and dashed lines represent anti-neutrinos as presented by E. Vitagliano et al. [7].

Signal Neutrino Sources High-energy neutrino point sources in the cosmos

constitute the ”golden” signal. The list of possible sources includes active-galactic nuclei (AGNs), gamma-ray bursts (GRBs), galaxy clusters, starburst galaxies and cosmogenic neutrinos. [6]. In figure 2, the expected flux of these neutrino sources is displayed for the relevant energy range of ANTARES which is from 20 GeV up to and beyond 10 TeV [8].

(8)

Figure 2: Cumulative neutrino flux predicted for various sources as presented by K. Murase for the IceCube neutrino observatory [2].

At the time of writing, no neutrino point source has been detected with sufficient significance to be considered a discovery [9, 10, 11]. In the future, KM3NeT/ARCA could yield a measurement with a 3σ significance for the most intense sources within 6 years of operation [12].

Background Neutrino Sources With reference to the neutrino spectrum

shown in figure 1 it can be concluded that the relevant neutrino background at the energies of interest is due to the atmospheric neutrinos. Atmospheric neu-trinos are produced by cosmic-ray interactions in the Earths’ atmosphere [13]. In addition, muons are produced which may enter the detector from above. The abundance of muons also constitute a background to neutrinos due to possible inaccuracies in the data analysis.

(9)

2.2 Neutrino Interactions

Neutrinos can only interact with matter via the weak force. These interactions can be split into current and neutral-current interactions. The charged-current neutrino-matter interactions can be summarised as follows:

W νl(νl) l−(l+) u(d) d(u) W νl l− νe e−

In this, νl is the l-neutrino with l the lepton flavor (electron, muon or tau).

The diagram to the left is the charged-current neutrino-quark interaction and the diagram to the right the charged-current neutrino-electron reaction. Finally there is also an interaction called the Glashow resonance, which corresponds to the s-Channel equivalent of the diagram on the right [14].

W−

e−

νe νl

l−

The neutral-current neutrino-matter interactions can be summarized as follows:

Z

νl(νl) νl(νl)

f f

(10)

2.3 Cherenkov Radiation

Cherenkov radiation is produced when particles move through a medium faster than the speed of light. The speed of light in water is about 73% of the speed of light in vacuum. Particles, however, can move faster than this (but not faster than the speed of light in vacuum) [15]. When neutrinos interact with a nucleon in the water of the Mediterranean Sea, charged particles can be produced. If the neutrino has enough energy, these particles can have a velocity above the speed of light in water. As a result, Cherenkov radiation will be produced. The detection of this light makes it possible to see neutrinos from the cosmos. This Cherenkov radiation is emitted at a particular angle known as the Cherenkov angle: cos(θC) = c/n β = 1 βn (1)

Here, c refers to the speed of light in vacuum, β the particle velocity as a fraction of to c and n the index of refraction of the medium. In figure 3 the signature ”Cherenkov cone” as well as the Cherenkov angle are shown schematically in relation to the motion of a particle.

Figure 3: Cherenkov radiation schematically shown [16]. Motion of the particle is to the right.

The refractive index nmof a medium m is defined as

nm=

c cm

(11)

In this, cmrefers to the speed of light in the medium.

Combining equation 1 and 2 this can be combined to: θC= arccos ₁ βn = arccos ₁ vp c c cw = arccos cw vp (3) Here c and cwrefer to the speed of light in vacuum and water, vpis the velocity

of the particle. Plugging in the numbers for seawater and highly relativistic particles, n ≈ 1.364, and β ≈ 1, we get θC ≈ 42.5◦.

2.4 Atmospheric muons and background

For the neutrino telescopes (section 3.1 and 3.2), Cherenkov light is used to detect neutrinos but there are more light sources in the Mediterranean Sea. The primary backgrounds of these two neutrino detectors are due to40_Kdecays

and bioluminescence. In addition, Cherenkov light will be produced by muons produced in the atmosphere above the detector that reach the detector.

(12)

3 Neutrino Detection

In the following sections, the two neutrino telescopes relevant to this work are briefly described, highlighting the similarities and differences between them.

3.1 ANTARES

The ANTARES telescope is a deep-sea neutrino detector consisting of an array of about 900 photo-multiplier tubes (PMTs), deployed off the coast of Toulon, France [8]. A PMT is the light sensor that is used to measure Cherenkov ra-diation. The PMTs are mounted in pressure resistant glass spheres which are arranged along 12 vertical strings that are anchored to the seabed. Each (nom-inal) string consists of 25 stories. Each storey constitutes a node with three PMTs. The PMTs have a diameter of about 10” and a field of view of about 70◦

(measured from the pointing direction). The PMTs are pointed at an angle of 45◦_{below the horizon. As such, they have an excellent acceptance for neutrinos}

passing through the Earth. Each storey is 14.5m above the lower one, with the highest storey about 450m above the seabed. The strings cover an area of about 0.1 km2

For a neutrino telescope, the Earth acts as an passive filter. Muons loose energy when passing through matter but neutrinos do not. So, muons will generally stop somewhere in the Earth before reaching the detector. However, high-energy muons produced in the atmosphere above the detector may actually reach the detector. As the PMTs are pointed towards the seabed, they effectively see less light from these muons than from the products of an interaction of a neutrino that passed through the Earth. As neutrinos are far more likely to pass through the Earth, this filter does not apply.

All data from the PMTs are set to shore where they are filtered in real time. This is known as the ”All-data-to-shore” concept. The filtered data are stored for further analysis. The main reconstruction algorithm that is applied to the data is called AAfit, which is described in Section 4.

3.2 KM3NeT

Similarly to ANTARES, the KM3NeT telescope is a deep-sea neutrino detec-tor. KM3NeT currently is under construction and will consist of two detectors, namely ARCA and ORCA. The ORCA detector is situated near the ANTARES detector off the shore of Toulon, France. The ARCA detector is situated off the coast of Sicily, Italy [5].

The biggest difference between ANTARES and KM3NeT is the size and technology of the detector. When finalized, the ORCA detector will consist of a block of 115 strings. These strings consist of 18 so-called digital optical modules (DOMs). Each of these DOMs houses 31 3” PMTs. ARCA will consist of two of these blocks for a total of 230 strings [17].

(13)

3.3 Detection principle

For both detectors, a 3D-array of PMTs is used to detect the Cherenkov light produced by charged particles. A relativistic charged particle produces a Cherenkov cone along its trajectory. The PMTs record the light from the Cherenkov cone as it moves through the detector. The track of the particle can then be recon-structed from the times of the signals of the PMTs in the detector. The signal of a PMT is commonly referred to as ”hit”. In KM3NeT, a hit consists of a time and a so-called time-over-threshold [5, 8]. Time-over-threshold is the time that the signal from the PMT is above a certain threshold. In figure 4, a typical PMT signal is shown [18].

Figure 4: Typical PMT signal. Ti is the hit time and the time-over-threshold

is equal to (Tf - Ti).

The known positions and orientations of the PMTs and the recorded hit times and times-over-threshold are input to the reconstruction of the trajectories of a charged particles. The trajectory of a muon is very long (O(km)) for the energies of interest. As a consequence, the angular resolution for a muon and thereby for the incident neutrino is better than for other particles. Hence, the accurate reconstruction of muon trajectories is a key in neutrino astronomy. In figure 5, a schematic representation is shown of a muon moving through the detector. The hit times are used to fit a straight line to the data. A more detailed explanation on how these hit times are used in the fit is presented in section 4.2.1 and 4.2.2 for AAfit and Jpp, respectively.

(14)

Figure 5: Schematic representation of a muon trajectory in the ANTARES detector. The spheres correspond the PMTs that detect photons displayed in black, in green is the incident neutrino and in red is the trajectory of the muon passing through the detector.

3.4 Monte Carlo Simulations

In this report, Monte Carlo simulations are used to study the performances of the different algorithm used for the reconstruction of events in the detector. Monte Carlo simulation is an approach where a large number of random samplings from a probability distribution is used to efficiently determine certain quantities [19]. In the procedure, a data set contains so-called ”true values” which can be compared to values obtained with the track reconstruction applications. So, a comparison of the true muon track with the reconstructed muon track yields an estimate of the angular resolution of the telescope. The angular resolution is usually defined by the distribution of the angles between the true track and the reconstructed track. Such simulations provide a method to study the

(15)

perfor-mance of a detector while taking into account the specifications of the detector and the environment [20].

The Monte Carlo simulations used in this report are produced in a so-called run-by-run approach. In this, the actual conditions of each data-taking run are simulated. The list of conditions includes the duration of the run, the bioluminescence at the time of the day and the active or defective PMTs. For each data-taking run, a corresponding Monte Carlo run is created with the same conditions. For this analysis, run-by-run version 3 is used.

The interactions of neutrinos and anti-neutrinos are simulated using GEN-HEN (GENerator of High-Energy Neutrinos v7r1) [19]. The list of possible neutrino interactions includes the diagrams shown in section 2.2.

The atmospheric muons are simulated using MUPAGE (v3r5) [21, 22]. In this, a set of parametric formulas is used which has been tuned to data from the MACRO underground experiment[21]. This makes it possible to simulate a much larger number of muons than with a full simulation such as in CORSIKA [20, 23]. A comparison of MUPAGE with ANTARES data has previously been published [20]. The detector response to the Cherenkov light is simulated using the km3 software (v5r1) [24]. This part of the simulation includes the energy loss of a muon as well as light production, propagation and detection. The light propagation involves scattering as well as absorption. The light detection involves the quantum efficiency, the photo-cathode area and field of view of the PMT. Finally, the electronics and data acquisition system are simulated using TriggerEfficiency.

In these MC Simulations a weight factor is implemented. For the atmo-spheric muons a weight factor 3 has to be implemented to match the Monte Carlo runs to Data taking runs. For neutrinos runs the weight per event is calculated differently. A so-called w2 and w3 is provided in the Monte Carlo files. These weight factors w2 and w3 are calculated as follows [25]:

w2 = V · Iθ· IE· Eγ· σ(E) · ρ · NA· Pearth· F (4)

w3 = w2· Φearth (5)

With V is the generation volume, Iθ the angular phase space factor, IE the

energy phase space factor, E is the generated neutrino energy, γ is the spectral weight of this energy such that Eγ is the reciprocal of the generation spectrum

evaluated at the generated neutrino energy, σ(E) the neutrino cross section, NA

Avogadro’s number, ρ · NA is the density of target nucleons, F the amount of

seconds in a year and Pearththe transmission probability, and Φearththe Bartol

flux [26]. For a full explanation see [25]. To obtain the weight of a specific event, it then has to be normalized as follows:

wevent=

w3

#events· run duration (6) With #events being the amount of events generated in a specific run and run duration being the lifetime of that run in years.

(16)

4 Track Reconstruction

Track reconstruction refers to the fitting of a muon track model to the (Monte Carlo) data. In track reconstruction, one looks at the Cerenkov light cone produced by muons (see section 2.3) and reconstruct the track from which it follows. The reconstruction performs a fitting algorithm to the data to recreate the original energy and direction of the tracks these muons.

4.1 Test statistics

4.1.1 Angular deviation

A good test statistic for the angular resolution of a neutrino telescope is the angular deviation of the reconstructed track. This is defined as:

cos θ = ~u · ~v k~uk ∗ k~vk

Where the resulting angle θ is the angle between two tracks, commonly re-ferred to as the angular deviation. In this case, ~u is the true track and ~v the reconstructed track.

4.1.2 Zenith angle

The zenith angle is defined as the angle between the reconstructed track and the vertical [27]. The zenith angle is used for an additional test statistic as well as an event selection parameter.

4.1.3 Signal purity

For event selection comparison a so called signal purity test is applied. The signal purity P is defined as follows:

P = Nν+ N¯ν Nν+ Nν¯+ Nµ

· 100% (7)

with Nν+ Nν¯ as the amount of neutrinos and anti neutrinos in the final data

set and Nµ as the amount of atmospheric muons.

4.2 Applications

ANTARES data are analyzed using the AAFit reconstruction chain. In this report, an alternative reconstruction chain has been applied to the ANTARES data. This alternative is based on the Jpp software framework developed for KM3NeT and uses different fitting algorithms. In the following subsections, the key features of each reconstruction chain are presented.

(17)

4.2.1 AAFit

The AAFit reconstruction chain consists of four consecutive steps in which each step uses the results of the previous step as starting values and the final step produces the most accurate result. The four steps of the reconstruction are as follows. First, a linear fit is applied to the data, commonly referred to as ”prefit” Then, an M-estimator fit is applied and after that, a maximum likelihood fit. The M-Estimator fit and maximum likelihood fit are repeated a number of times with modifications to the starting values given by the prefit. Finally, a maximum likelihood fit with an improved probability density function (PDF) is applied to the best result obtained from the previous step [28]. As a result, the following five independent parameters of the track are found: position ~

p ≡ (px, py, pz), the direction ~d ≡ (dx, dy, dz) = (sin θ cos φ, sin θ sin φ, cos θ)

with θ and φ the zenith and azimuth angle, respectively. Figure 6 shows the reconstruction schematically.

Figure 6: The AAfit reconstruction chain presented schematically.

Prefit The first step in the chain is a linear fit that requires no prior starting

point and is used to get a rough estimation of the track using a subset of the hits. Only hits that are part of a local coincidence are used. A hit is considered part of a local coincidence if one or more other hits occur in the same storey within a predefined time window (typically 25 ns). This improve the signal-to-noise ratio of the data [28]. The linear fit is defined as follows: [28, 29].

(18)

y = HΘ (8)         x1 y1 z1 x2 .. zn         =         1 ct1 0 0 0 0 0 0 1 ct1 0 0 0 0 0 0 1 ct1 1 ct2 0 0 0 0 . . . . 0 0 0 0 1 ctn                 px dx py dy pz dz         (9)

with y as a vector with the known positions of the PMTs that recorded a hit, Θ as a vector of the unknown track parameters and H a matrix with the hit times. A covariance matrix V is used to store the error estimates on the PMT positions. This equation is then used to find the track parameters ˆΘ by minimising the χ2.

χ2= [y − H ˆΘ]TV−1[y − H ˆΘ] (10) This directly provides an estimate of the track parameters [28, 29]:

ˆ

Θ = [HTV−1H]−1HTV−1y (11)

M-Estimator Following the prefit, an M-Estimator fit is made. For this,

all hits that are compatible with the previously fitted track are selected. The compatibility is based on a time window of ±150ns around the expected time and a maximal distance of ±100m from the track. In addition, hits with a large amplitude are included [28]. An M-Estimator fit uses a modified χ2 to reduce

the effect of outliers on the result[30]. The M-Estimator used in AAfit is [28, 29]: g = −X i 2κ r 1 + ai(ti− ti exp) 2 2 + (1 − κ)fang(θi)

where tiis the time of the hit, aiis the amplitude, ti expthe expected time, κ an

arbitrary weight factor (0.05) and fang(θi)the assumed angular response

func-tion of the PMT. This M-Estimator is then minimized to improve the previous estimates of the track parameters [28, 29].

Maximum likelihood fit For the next step, a maximum likelihood fit is

used. The likelihood of the event is defined as the product of the likelihoods of the hits:

P (event|track) ≡Y

i

P (hiti|~p, ~d)

In this, the measured times ti of the hits are compared to the expected times

based on the track parameters using the probability density function shown in figure 7. If multiple maxima exist, the fit will generally converge to the closest

(19)

local maximum. To increase the probability to find the global maximum, the fit is therefore repeated with modified starting values.

Figure 7: The original PDF used in the maximum likelihood fit in AAfit [28].

4.2.2 Jpp

For the reconstruction in Jpp, a modular approach to the problem has been adopted. The so called ”JChain” of applications is used to reconstruct the track of the muon. This chain consists of a several applications [31]. Just like AAfit, a linear fit called JPrefit is first applied to the data. After that, an M-Estimator fit called JSimplex is applied to improve the fit results. After that, the main fitting application called JGandalf is applied, in which performs a maximum likelihood fit is made using a 4-dimensional PDF. Following JGandalf, JStart is used to find a vertex position along the reconstructed track. Finally, an estimate of the muon energy estimator is made. In figure 8, a schematic view of the reconstruction chain is shown and in figure 10, the topology of the track reconstruction [32].

JPrefit In JPrefit a linear fit is used as in AAfit. However, a more rigorous

solution to the start value problem has been adopted. In this, the full solid angle is covered by a set of approximately equidistant directions, referred to as grid. The typical grid angle is set to 3◦_{. The grid then consists of 7,200 equidistant}

(20)

Figure 8: The Jpp reconstruction chain presented schematically. directions. For each direction in this grid, a selection of the hits is made using a cluster algorithm followed by a linear fit to the selected hits. This removes the assumption that the PMTs are along the muon trajectory as in AAfit. For this fit, the distance of closest approach is used to determine the expected arrival time (see figure 10).

tj = tf it+ z c + tan(θc) Rj c , (12) R = q (xi_{− x} f it)2+ (yi− yf it)2. (13)

In this, R is distance of closest approach, c the speed of light in vacuum and θc is the Cherenkov angle. Pairs of equation 12 are then used to build the

corresponding H and Θ matrices:

y = HΘ =             2(x2− x1) 2(y2− y1) −2(t02− t01) 2(x3− x2) 2(y3− y2) −2(t03− t02) . . . . . . 2(x1− xn) 2(y1− yn) −2(t01− t0n)                   xf it yf it t0_{f it}       , (14)

In this, only three fit parameters appear, namely xf it, yf it and t0f it. The

co-variance matrix V now includes the uncertainty due to the finite grid angle. Applying equation 11 for each direction yields one or possibly no solution.

To reduce the number of fits in subsequent processing steps, the solutions are evaluated. Only a limited number of solutions with the highest quality are then selected. The quality Q is set to the number of degrees of freedom NDF = NHits − 5in the fit, corrected for the reduced χ2 as follows:

Q =NDF − 1 4

χ2

NDF (15)

A higher quality Q is indicative of a better solution. The number of solutions selected for the following steps is set to 24.

(21)

JGandalf JGandalf takes the fits produced in the previous steps as start

values and applies a maximum likelihood fit to unbiased data. The maximisation algorithm is based on a custom implementation of the Levenberg-Markquardt method [33, 34]. This method combines gradient descent [35] and Newtons method [36] using a control parameter λ to balance between these methods. At λ = 0 the Newton method is used whereas at λ = ∞, the gradient descent method is used. The time residuals are evaluated against a 4-dimensional PDF which depends on the closest distance approach R, the orientation of the PMT (θ,φ) and the time of the hit. In figure 9, an example of the PDF is shown. Compared to the AAfit, no compromise is used in the PDF.

L =Y i dP (hiti|~p, ~d) dt (Ri, θi, φi, ∆t) (16) where Ri corresponds to the distance of closest approach, θ and φ to the

orien-tation of the PMT and ∆t is the time residual (see figure 10). In the following, the quality parameter Q = L is used.

Figure 9: PDFs used by JGandalf as a function of time for a PMT located at a distance of 50m. The labels refer to the PMT orientations compared to the muon track as shown in figure 10 and table 1 [32].

(22)

6

z R t (0, 0, 0) t (R, 0, 0) t (0, 0, z) θC 6 - * z0 x0 y0 J J J J J J ] P P P P t φ θ N E S W E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

Figure 10: Topology of a muon or shower producing light that is detected on a PMT. The muon or shower direction is pointed along the z−axis and the PMT is located at position (R, 0, 0). The zenith and azimuth angle of the orientation of the PMT are denoted by θ and φ, respectively. The wind rose is used for PMT orientation, in table 1 the four directions are defined. Courtesy of M. De Jong [32] θ φ label 0 0 N North π/2 0 E East π 0 S South π/2 π WWest

(23)

5 Changes made to the Jpp software framework

In the following section, I will describe the most important changes made to the KM3NeT software framework in order to analyze the data produced with the ANTARES detector.

The calibrated ANTARES data are stored in the so-called .i3 data format which has originally been developed for IceCube [37]. This data format is part of the IceTray software framework which is used to write and read data. The IceTray software framework has been redistributed for ANTARES under the name SeaTray [38].

The raw KM3NeT data are stored in the KM3NeT online data format [5]. These data can directly be analyzed using the Jpp software framework. In order to analyze the ANTARES data with the Jpp software framework, two main options are possible. Either you modify the Jpp software framework so that .i3 data can be used as input or you change the format of the data such that the Jpp software framework can read the data. For this work a combination of both options is pursued.

The main reason for this, is that both Jpp and SeaTray require very specific dependencies on other software packages to work, which complicates to combine these software frameworks in the same environment. So, I changed the format of the SeaTray data to a generic format, which can then be read by the Jpp software framework.

5.1 Modifying the data format

First, the .i3 files were modified to ASCII formatted files within the SeaTray environment. The output files contain calibrated data, a header and, if applica-ble, Monte Carlo true data. The header contains information such as the time of the run, the duration of the run and reconstruction results from previous analyses. A full example of this file format is shown in appendix A. These ASCII formatted files were then imported and converted to the KM3NeT of-fline data format in the Jpp environment. A further improvement would be to directly generate KM3NeT offline data from the source .i3 files, but the double conversion is lossless and takes a little amount of computer time compared to other applications.

5.2 Modifying the software framework

The next step is to adopt the Jpp software framework such that it accepts the KM3NeT offline format. To achieve this, a new set of applications is written, using the same Jpp header files and fit functions. These fitting functions nor-mally operate on the KM3NeT online data format. In these functions the online data are converted to calibrated hits and and for JPrefit and JSimplex, a list of coincidence hits is created as well. These lists are then used for the remainder of the fit function. The fit results of the algorithm are converted into a tem-porary data format called JEvt so that they can be stored in an intermediate

(24)

output file. Eventually, the final results are then converted to the KM3NeT offline format for analysis.

For this report, modifications are made to the input and output step of this process but they do not alter the original fitting algorithms. As stated before, the modifications are made such that KM3NeT Offline data are used for intermediate storage of hit data. The reconstruction algorithms require a list of calibrated hits and for JPrefit and JSimplex, a list of coincidence hits. Thus, converting the KM3NeT offline data to these lists is sufficient to apply the algorithm to the ANTARES data. The results of these algorithms are stored in the output file alongside the KM3NeT offline data format. The refreshed JChain can be seen in figure 11.

Figure 11: The Jpp reconstruction chain using the KM3NeT offline data format presented schematically. The original reconstruction chain using the KM3NeT online data format is presented in figure 8.

5.3 Coincidence difference

A small difference exists between KM3NeT [5] and ANTARES [8] in the handling of coincidences. For both detectors, coincidences are used to improve the signal-to-noise ratio of the hits and to reduce the computational overhead in the first step(s). For Jpp, JSimplex and JPrefit use coincidence hits and for AAfit the prefit uses coincidence hits. In general, unbiased hits are referred to level 0 (L0) hits. For KM3NeT, a level 1 (L1) hit is defined as a coincidence of hits from the same optical module within a specific time window. For ANTARES, the L1 hits are defined as coincidence of hits in the same storey, as well as hits with a sufficiently large amplitude (typically 3 p.e. equivalent). A so called L1 hit builder is created for Jpp that can be applied to ANTARES data.

5.4 Result verification

A few tests were performed to ensure correct execution of the code. To ensure that the output of the code is identical for the initial input file types, multiple applications were created. First, the consistency of the input to the fitting was verified. The list of L0 hits and the list of L1 hits produced via the KM3NeT online data format are compared to the lists produced via the KM3NeT offline data format. After extensive testing, this comparison showed identical results for

(25)

the two procedures. This implies that the fitting algorithm will yield identical results in either scenario. Secondly, an application is made that accepts the output produced by any fitting algorithm and displays the fit results as well as the Monte Carlo true data. An example output is shown in appendix B.

5.5 Adjusted Quality Parameter

In ANTARES, the standard reconstruction algorithm is AAfit which is described in section 4.2.1. In AAfit, the list of quality parameters includes Λ and β [28]. These are defined as follows:

Λ = log(L) NDF + 0.1(NComp− 1) (17) β = q sin2(ˆθ)ˆσ2 φσˆ 2 θ (18) 1 ˆ σ2_θ = − ∂2_{log L} ∂θ2 (19) 1 ˆ σ2_φ = − ∂2_{log L} ∂φ2 (20)

where β incorporates the estimated angular error in zenith and azimuth direction to a single parameter; Λ incorporates the likelihood of the fit L, the number of degrees of freedom NDF and the number of fits that are compatible with the best fit NComp. Compatible means that one of the 9 solutions of AAfit produces

a track within 1◦ of the best-fit track.

In Jpp, I use the quality fit parameter and the KM3NeT β equivalent as quality parameters. I have modified the quality parameter to include additional fits similar to way Λ uses NComp to improve the original quality. The adjusted

quality parameter is based on a Gaussian distribution seen in equation 21. g(x) = 1 σ√2πexp −1 2 (x − µ)2 σ2 (21) I have used the Gaussian distribution to increase or decrease the original quality parameter Q0≡ Q depending on how similar alternative solutions are.

In JGandalf a list of solutions is reported, sorted by quality. The first solution has the highest quality and the last solution has the smallest quality. Initially I only used the primary solution, but by looking at alternative solutions in more detail, a more efficient event selection can be obtained. The improved quality evaluation used can be expressed as:

(26)

Qi≡ NDFi− 1 4 χ2 i NDFi (22) Q0 = Q0 n Y i=1 (1 + f (Q0, Qi)g( ˆr0, ˆri)) (23) f (Q0, Qi) = 2 √ π 1 √ Q0 exp −(Q0− Qi) 2 Q0 (24) g( ˆr0, ˆri) = 2 √ π exp −arccos( ˆr0· ˆri) 2 1◦ −1 e (25) In this, equation Q0 _{is the adjusted quality parameter. It is equal to the initial}

quality Q0multiplied by a series of factors. ˆriis the direction of the i-th solution

of the fitting algorithm. Function f is a normalized probability density function for Qi<= Q0as Qi will always be smaller than Q0due to sorting by likelihood.

Function g without the offset is normalized to all possible angles θi,0 > 0. As

such: Z Q0 −∞ f (Q0, Qi)dQi≡ 1 (26) Z ∞ 0 g( ˆr0, ˆri) + 2 e√πd ˆri≡ 1 (27) Function f will always have a positive value, and is used to determine the magnitude of the value change of Qi with respect to Q0, function g can be

either positive or negative depending on the angle between track i and the original track, see equation 28. As such, it determines both the magnitude of change of Qiwith respect to Q0and it determines whether the change is positive

or negative.

g( ˆr0, ˆri) > 0 for arccos( ˆr0· ˆri) < 1◦ (28)

g( ˆr0, ˆri) ≡ 0 for arccos( ˆr0· ˆri) = 1◦ (29)

g( ˆr0, ˆri) < 0 for arccos( ˆr0· ˆri) > 1◦ (30)

A diagram of the effect of this function is presented in table 2. A computational example, as well as a comparison to Q is presented in appendix E.

f (Q0, Qi) Qi≈ Q0 Qi<< Q0 g( ˆr0, ˆri) ˆ ri∼ ˆr0 Q0> Q0 Q0≈ Q0 ˆ ri ˆr0 Q0< Q0 Q0≈ Q0

Table 2: An qualitative overview what happens to the adjusted quality param-eter Q0 _{when solutions i are similar or different to the best fit solution.}

(27)

An inherent flaw of quality parameter Q0 is that it is dependent on two

input parameters of the reconstruction, namely: gridAngle, which is the distance between each equidistant angle on the solid angle; and numberOfPrefits, which is (after quality sorting) the amount of prefits subsequent fitting algorithms use as starting values. When the grid angle is changed, the total amount of prefits JPrefit calculates will also change. For a grid angle of 3◦, about 7200 prefits

are calculated, approximately 3◦_{apart. When a (local) minimum is bigger than}

the grid angle, multiple solutions will be found with comparable quality, which affects Q0_{. If the number of prefits is changed, more solutions will be generated.}

As such, parameter n in equation 24 will increase and more products will be taken.

The dependency on the grid angle is more significant than that on the num-ber of prefits, as each additional fit has a lower quality than the one before it and the effect of each additional solution is scaled by it’s quality. As such, the parameter Q0 _{should be optimised for a given grid angle and number of prefits.}

(28)

6 Results

In the this section, the results of the tests are shown. The list of tests and parameters used for this report includes:

• The angular deviation as described in section 4.1.1; • The zenith angle of the track as described in section 4.1.2;

• The quality parameter Λ and β for AAFit as described in section 5.5; • The reconstructed vertex parameter ~r(x, y, z);

• The reduced quality parameter ΛJ pp= _NDFL ; and

• The quality parameter Q0, Q and β

0 for Jpp as described in section 5.5

and 4.2.2.

For certain plots, a distinction is made between ”correctly” and ”incorrectly” reconstructed tracks. The muon is considered correctly reconstructed if the angular deviation is less than 10◦from the true value and otherwise incorrectly

reconstructed.

For all tests, the same run-by-run version 3 of the Monte Carlo simulations for the ANTARES detector are used. The analysis has been applied to version 4 as well. However, a problem in these simulations was found. The impact of this is presented in appendix D. The data includes runs from muon-neutrino interactions, anti muon-neutrino interactions and atmospheric muons. For the analysis using AAfit and Jpp, the same Monte Carlo files are used. For the results of the atmospheric muon and neutrino fluxes, a limited data set is used that corresponds to a statistical uncertainty of about 10% lifetime of the experi-ment. For the results of correct versus incorrect reconstruction, a larger data set is used. For the study of the event selection and atmospheric muons, a lifetime of 50.4 days is used; for the study of the angular resolution, a lifetime of 313.9 days is used.

The selection of events based on a limited validity range of a parameter is commonly referred to as a ”cut”. In tables 7 and 3, the selection parameters are presented with their respective cuts.

(29)

6.1 AAfit Reconstruction results

Parameter Cut-off value Description

θz < 90◦ angle between the zenith and the recon-_{structed track presented in section 4.1.2.}

Λ > −5.2 AAfit quality parameter presented in sec-tion 5.5.

β < 1.0◦

expected angular uncertainty from the AAfit reconstruction presented in section 5.5.

Table 3: The standard event selection parameters for the AAfit reconstruction. As stated in sections 5.5 and 4.1.2, the event selection parameters for AAfit are Λ , β as well as the zenith direction. The two primary objectives of these event selection parameters are to limit the angular deviation and to reduce the amount of atmospheric muons in the neutrino sample. The following plots are presented to validate the standard cut values presented in table 3. Using these cuts AAfit yields a median angular deviation of 0.5◦ and an event purity of

P = 90%.

From figures 12b and 13b, it can be seen that by cutting around Λ < −5 and β < 1◦_{, the amount of incorrectly reconstructed tracks is indeed reduced}

significantly. This indicates that the previous cut values for Λ , β and θz are

still appropriate.

(a) The AAfit Λ distribution of atmo-spheric muons and neutrinos . Number of events are not to scale.

(b) The AAFit Λ distributions of cor-rectly reconstructed neutrinos and incor-rectly reconstructed neutrinos .

(30)

(a) The AAfit β distributions of atmo-spheric muons and neutrinos. Number of events are not to scale.

(b) The AAFit β distributions of cor-rectly reconstructed neutrinos and incor-rectly reconstructed neutrinos .

Figure 13: Event rates with respect to AAfit quality parameter β.

Figure 14: The AAfit zenith angle distributions of atmospheric muons and neutrinos. Number of events are not to scale.

(31)

6.2 Event Selection

I have created an event selection application that is used to determine the op-timal event selection parameters, given a starting value of event selection. The application circles around this starting value. Starting values were determined manually by analysing the plots in figure 15.

For this, the primary test statistics are the event purity described in section 4.1.3 and the angular deviation described in section 4.1.1. For this study a lifetime of 50.4 days is used and the events are weighed according to the weight factor shown in section 3.4. For the evaluation of the AAfit event rate, purity and angular deviation, the standard AAfit cuts are applied. The values obtained are summarised in table 4.

In table 6 and 5 various event selection cuts are shown sorted by purity. The event rate for Jpp corresponds to the number of neutrino events remaining with respect to the post-event selection AAfit values, as seen in table 4. As such, AAfit event rate is per definition 1. As expected, the angular deviation and event rate decrease and purity increases with stricter event selection. The event selection is presented according two cases, namely:

• Only coincidences are considered for JPrefitOffline, see section 5.3; • JPrefitOffline uses both coincidence hits, as well as non-coincidence hits

(so called L0 hits).

Zenith ΛAAf it β Event Rate Purity Angular deviation

90 -5.2 1◦ _≡100% _0.90 _0.5

Table 4: Event selection values of AAFit. Table 5 and 6 are compared to the event rate, purity and angular deviation of this table.

Q0 _β

0 Q r(x,y) ΛJ pp Event Rate Purity Angular deviation

55 0.50◦ 60 270m 2.00 0.8 0.95 0.5 55 0.50◦ 55 290m 2.00 1 0.9 0.5 52 0.60◦ 55 285m 1.95 1.2 0.85 0.5 50 0.65◦ _{55 285m} _1.95 _1.3 _0.80 _0.5 55 0.70◦ _{50 290m} _2.00 _1.4 _0.75 _0.6 45 0.70◦ _{50 290m} _2.00 _1.5 _0.65 _0.6

Table 5: Various event selection criteria with respect to AAfit. For the case JPrefitOffline uses both L1 hits, as well as L0 hits (see section 5.3).

(32)

Q0 _β

0 Q r(x,y) ΛJ pp Event Rate Purity Angular deviation

50 0.50 50 290m 1.5 1.0 0.90 0.5

50 0.55◦ ₅₀ _290m _1.5 _1.1 _0.85 _0.5

45 0.60◦ ₅₀ _290m _1.5 _1.20 _0.80 _0.6

45 0.60◦ 45 289m 1.45 1.30 0.70 0.6

50 0.70◦ 40 290m 1.5 1.40 0.65 0.6

Table 6: Various event selection criteria with respect to AAfit. For the case JPrefitOffline uses only L1 hits (see section 5.3).

(33)

6.3 Jpp reconstruction results

The effect of the Jpp event selection has been studied. For each parameter, the effect on the muon rejection and the angular deviation is evaluated. For this, all plots and tables are obtained with JPrefitOnline being fed with only L1 hits as seen in the event selection table 6.

Parameter Cut-off value Description

θz < 90◦ angle between the zenith and the recon-_{structed track presented in section 4.1.2.}

Q > 50 quality of the track after the JGandalf re-construction.

Q0 > 50

custom quality parameter, based on the quality parameter of the JGandalf recon-struction (see section 5.5).

ΛJ P P > 1.5

quality parameter that normalizes the likelihood to number of degrees of free-dom.

β0 < 0.50◦ expected angular uncertainty from the_{JGandalf reconstruction.}

r(x, y) < 290m distance of the vertex from the center of_{the detector obtained from JStart.}

Table 7: The standard event selection parameters for the Jpp reconstruction. As no prior research has been made to determine the optimal event selection, the following section presents plots to support the event selection cuts listed in table 7. The two primary objectives of the event selection are to limit the angu-lar deviation and to reduce the amount of atmospheric muons in the neutrino sample. The results for the cut parameter are presented in figure 15. Each plot shows the dependence on a cut parameter as it would appear when all other cuts are applied. For Q0, and Q both parameters are ignored when plotting,

this is to highlight the minute differences between the two.

With signal preservation in mind, the cuts applied to the data are more conservative than the ones presented here. The cuts I landed on were considered using the following premises.

• Maximize event rate of correctly reconstructed neutrino events; • Minimize event rate of atmospheric neutrinos;

• Minimize event rate of incorrectly reconstructed neutrino events; and • Improve the median angular resolution of AAfit.

(34)

With the cuts given in table 7, the amount of atmospheric muons in is reduced to approximately one per day. Which gives us an event purity of P = 90 with a median angular deviation of 0.5◦. With more restrictive cuts, the angular resolution of the data could be improved but this will then be at the cost selection efficiency.

(35)

(a) Quality parameter Q (b) Quality parameter ΛJ pp

(c) Adjusted quality parameter Q0 _{(d) Quality parameter β} 0

(e) Vertex distance from the center of the

detector. (f) Zenith direction

Figure 15: All cutting parameters of the reconstructed track before the cut of the plot is applied, presented to demonstrate the effect of each cut.

(36)

6.4 Comparing Jpp and AAfit performances

(a) Only L1 hits used for JPrefit and

JSim-plex. (b) Both L0 and L1 hits used for JPrefitand JSimplex.

Figure 16: The angular deviation of the reconstructed neutrino tracks plotted for both AAfit and Jpp before any cuts are applied.

In figures 16b and 16a, the angular deviation is shown for the neutrino Monte Carlo data without event selection. For AAfit and Jpp, the standard cuts given in table 3 and 7 are applied. When these standard cuts are applied, the angular deviation distribution as presented in figure 17 is obtained. The standard cuts are used to restrict the purity to 90%. After cuts, the purity of the AAfit reconstruction is P = 90% with a median angular deviation of 0.5◦_.

(37)

(a) Only L1 hits used for JPrefit and

JSim-plex. (b) Both L0 and L1 hits used for JPrefitand JSimplex.

Figure 17: The angular deviation of the reconstructed neutrino tracks plotted for both AAfit and Jpp after the 90% purity cuts in table 4, 5 and 6 are applied. Muon events for Jpp are also plotted.

As can be seen in figures 16b and 16a, the number of correctly reconstructed neutrino events before cuts obtained with Jpp is about 30% more than obtained with AAfit when JPrefit is only given L1 coincidence hits, and about 95% more when JPrefit is given both L1 and L0 hits. As seen in table 5 and 6 Jpp can match the event rate of AAfit in both the case where only L1 hits are used, as well as the case where L1 and L0 hits are used for plotting. If purity constraints are relaxed for the Jpp data, the event rate for Jpp can be improved from 10% up to 50%. With the very minor reduction from 90% purity to 85% an improvement in event rate is found of 20% when L0 and L1 hits are considered in JPrefit.

(38)

7 Discussion

For this work, ANTARES Monte Carlo data have been analyzed with the KM3NeT Jpp software framework and the performance of Jpp has been eval-uated and compared to the ANTARES specific AAfit algorithm. This was done with two objectives in mind, namely: Can the angular resolution of the ANTARES detector be improved; and/or can the neutrino event rate be im-proved?

7.1 Applying ANTARES Monte Carlo data to the KM3NeT

software framework

The Jpp software has been modified and successfully applied to the ANTARES Monte Carlo data. This was achieved by first reformatting the ANTARES data into the so called KM3NeT offline format. The existing Jpp applications were then modified to adopt their I/O to this format. These modifications were realised by creating new applications as well as new analysis tools such that the results produced by each step in the Jpp chain can be properly be analysed. Finally, an evaluation was made using ANTARES Monte Carlo data.

7.2 Improving the event rate

As seen in figure 16, the Jpp software framework significantly improves the rate of correctly reconstructed neutrinos in the ANTARES detector. If the same hit preselection is applied as AAfit, i.e. only L1 hits, the correctly reconstructed neutrino rate is 30% higher in Jpp. However, if no hit preselection is applied to Jpp, i.e. L0 and L1 hits, the correctly reconstructed neutrino flux is improved by 95%.

When an event purity of 90% is imposed, the resulting event rate for AAfit and Jpp become comparable. If the purity constraint is relaxed, the significant gain in events can be maintained. Relaxing the purity constraint to 85% can yield 10% to 20% higher neutrino event rate and relaxing it to 80% can yield 20% to 30% higher neutrino event rate depending on the hit preselection used. This dependence of the gain on the event selection could be explained as follows. The gained events could be of less quality. Furthermore, it is also worth noting that for AAfit, a much more thorough search has been applied to find optimal event selection parameters. Finally, there are more parameters that can be used for the event selection, such as the reconstructed energy of the event.

A shortcoming of this research can be seen in figure 15f, the number of remaining muons in the final sample is low and consequently the statistical uncertainty high. The current cuts reduce the number of muons from O(107₎

to O(101₎. As the goal is to have around 1 detected muon per day, this can

only be resolved by using a larger lifetime of muon simulation at the cost of significantly more CPU time.

(39)

7.3 Improving the angular resolution

The angular resolution of the reconstructed Monte Carlo data was not improved by going from AAfit to Jpp. The median angular deviation of reconstructed tracks remained at about 0.5◦_{. This can be seen in the neutrino data without}

cuts in figure 16 as well as neutrino data with cuts in figure 17.

There are several explanations as to why no improvement is found. One explanation is that as more events are reconstructed, the extra events that were reconstructed with lower quality, with more background hits obfuscating the signal, or a lower amount of hits to begin with. As such, these hits will have gone from reconstructed incorrectly to almost correctly, while maintaining the median angular deviation at 0.5◦. Another explanation is that other systematic

errors in the ANTARES detector limit the potential improvement to the angular resolution severely.

7.4 Future tests and improvements.

Before Jpp is applied to ANTARES data in bulk, some future test are still to be applied. First of all, this study has only considered Monte Carlo simulated data. For this reason, it has only shown theoretical improvements. Improvement in the simulations might not imply improvements in actual detector data.

To provide proof of improvement, an excellent test would be a shadow of the moon analysis. In this, atmospheric muon data are used to search for the dip of muon flux created by the moon. In reference [39] and [40] it is shown that the moon has been observed in ANTARES data with 3.5σ significance when using AAFit. An improvement of this significance when the data are reprocessed using the Jpp software framework would indicate that the reconstruction is improved. Another possible improvement of the reconstruction software is to correct for the time slewing due to the threshold of the PMT. In figure 4 it can be seen that the recorded hit time is slightly later than the actual start of the analogue pulse. This is commonly referred to as time slewing. The delay is more significant if the analogue signal is smaller, and less significant if the signal is larger. Time slewing could readily be incorporated by using the amplitude (time-over-threshold) information in the data. This could potentially improve the time residuals of the hits and thereby improve the accuracy of the fit.

(40)

8 Acknowledgements

I would like to show my deepest appreciation to those who helped me write this thesis. First of all, I would like to thank Maarten de Jong, who has assisted me at every step in this journey. He has been instrumental for the writing of the applications to run this analysis. He has been very involved in correcting this paper and has donated a lot of his time guiding me. Next up is Paul de Jong, who has been generous enough to take time out of his busy schedule to grade this thesis and the accompanying presentation. Thirdly I would like to thank Thomas Eberl, who has provided curcial applications for pre-processing of the data provided.

Furthermore, I would like to thank the KM3NeT collaboration for provid-ing access to the Jpp software framework and the ANTARES collaboration for providing access to data collected by the ANTARES Telescope. I would also like to thank Nikhef for providing access to the Stoomboot Computing Cluster, enabling the analysis of a much larger dataset. And the CC-IN2P3 computing center for running the AAfit analysis on the ANTARES data as well as the conversion scripts provided by Thomas Eberl.

In addition to people who have assisted me professionally, I would also like to thank some people for assisting me in a personal manner. I would like to thank my parents, Freek and Karin, for supporting me both financially and emotionally during my entire educational journey. And I would like to thank my partner Els for always pushing me to be better, without you this thesis would not be what it is now. I would also like to thank my brother Coen, for providing all the occasions to blow off some steam. In conclusion I would like to thank all my close friends. First off the ones I’ve met at the UvA: Danny, Deanna, Ester, Jasper and Peter. And finally the ones I’ve met before the UvA: Alex, Raymond and Ruben.

(41)

References

[1] The KM3NeT Collaboration. Dependence of atmospheric muon flux on sea-water depth measured with the first km3net detection units. The European

Physical Journal C, 80(2), Feb 2020.

[2] Kohta Murase. On the origin of high-energy cosmic neutrinos. AIP

Con-ference Proceedings, 1666(1):040006, 2015.

[3] IceCube Collaboration. First observation of pev-energy neutrinos with ice-cube. Phys. Rev. Lett., 111:021103, Jul 2013.

[4] IceCube Collaboration. Evidence for high-energy extraterrestrial neutrinos at the icecube detector. Science, 342(6161), 2013.

[5] The KM3NeT Collaboration. Letter of intent for km3net 2.0. Journal of

Physics G: Nuclear and Particle Physics, 43(8):084001, Jun 2016.

[6] K. W. Melis. Studying the Universe from -3000 N. A. P. PhD thesis, Universiteit van Amsterdam, 2021.

[7] Edoardo Vitagliano, Irene Tamborra, and Georg Raffelt. Grand unified neutrino spectrum at earth: Sources and spectral components. Reviews of

Modern Physics, 92(4), Dec 2020.

[8] The ANTARES Collaboration. Antares: The first undersea neutrino telescope. Nuclear Instruments and Methods in Physics Research

Sec-tion A: Accelerators, Spectrometers, Detectors and Associated Equipment,

656(1):11–38, Nov 2011.

[9] Giulia Illuminati, Julien Aublin, and Sergio Navas. Searches for point-like sources of cosmic neutrinos with 11 years of antares data. In Proc. 36th

International Cosmic Ray Conference (ICRC, Madison, W.I. USA, July 2019), page 920, 08 2019.

[10] The ANTARES Collaboration. Antares search for point sources of neutri-nos using astrophysical catalogs: A likelihood analysis. The Astrophysical

Journal, 911(1):48, Apr 2021.

[11] R. Abbasi et al. IceCube Data for Neutrino Point-Source Searches Years 2008-2018. arxiv 2101.09836, 1 2021.

[12] The KM3NeT Collaboration. Sensitivity of the km3net/arca neutrino tele-scope to point-like neutrino sources. Astroparticle Physics, 111:100–110, Sep 2019.

[13] The ANTARES Collaboration. Measurement of the atmospheric νµenergy

spectrum from 100 gev to 200 tev with the antares telescope. The European

(42)

[14] Sheldon L. Glashow. Resonant scattering of antineutrinos. Phys. Rev., 118:316–317, Apr 1960.

[15] P. A. Cherenkov. Visible luminescence of pure liquids under the influence of γ-radiation. Dokl.Akad.Nauk, 93(10):385–388, 1934.

[16] Kazuyuki Sakaue, Mari Brameld, Ryunosuke Kuroda, Mariko Nishida, Yoshitaka Taira, Tomoyoshi Toida, Junji Urakawa, Masakazu Washio, and Ryo Yanagisawa. Investigation of the Coherent Cherenkov Radiation Using Tilted Electron Bunch. In 8th International Particle Accelerator

Confer-ence, 5 2017.

[17] The KM3NeT Collaboration. Event reconstruction for km3net/orca using convolutional neural networks. Journal of Instrumentation,

15(10):P10005–P10005, Oct 2020.

[18] Fabio Bellini, L. Cardani, Nicola Casali, Ioan Dafinei, Michela Marafini, S. Morganti, F. Orio, Davide Pinci, Gabriele Piperno, Daria Santone, C. Tomei, and Marco Vignati. Measurements and optimization of the light yield of a teo2 crystal. Journal of Instrumentation, 9, 06 2014.

[19] D. Bailey. Monte Carlo tools and analysis methods for understanding the

ANTARES experiment and predicting its sensitivity to dark matter. PhD

thesis, Oxford U., 2002.

[20] The ANTARES Collaboration. Monte carlo simulations for the antares underwater neutrino telescope. Journal of Cosmology and Astroparticle

Physics, 2021(01):064–064, Jan 2021.

[21] G. Carminati, M. Bazzotti, A. Margiotta, and M. Spurio. Atmospheric muons from parametric formulas: a fast generator for neutrino telescopes (mupage). Computer Physics Communications, 179(12):915–923, 2008. [22] Y. Becherini, A. Margiotta, M. Sioli, and M. Spurio. A parameterisation of

single and multiple muons in the deep water or ice. Astroparticle Physics, 25(1):1–13, 2006.

[23] D. Heck, J. Knapp, J. N. Capdevielle, G. Schatz, and T. Thouw.

COR-SIKA: a Monte Carlo code to simulate extensive air showers. NASA, 1998.

[24] S. Navas and L. Thompson. Km3 user guide and reference manual.

IN-TERNAL NOTE, 1999.

[25] A. L’Abbate, T. Montaruli, and I. Sokalski. Genhen v6: Antares neutrino generator extension to all neutrino flavors and inclusion of propagation through the earth. INTERNAL NOTE, 2004-10.

[26] T.K. Gaisser. Fluxes of atmospheric neutrinos and related cosmic rays.

(43)

[27] M.Z. Jacobson. Fundamentals of Atmospheric Modeling. Cambridge Uni-versity Press, 1999.

[28] A. J. Heijboer. Track Reconstruction and Point Source Searches with

ANTARES. PhD thesis, Universiteit van Amsterdam, 2004.

[29] E. L. Visser. Neutrinos from the Milkyway. PhD thesis, University of Leiden, 2015.

[30] P. Mukhopadhyay. An Introduction To Estimating Functions. Harrow: Alpha Science International, 2004.

[31] Karel Melis, Aart Heijboer, and Maarten de Jong. KM3NeT/ARCA Event Reconstruction Algorithms. INTERNAL NOTE, ICRC2017:950, 2018. [32] M. de Jong. The probability density function of the arrival time of light.

INTERNAL NOTE, 2019.

[33] K. Levenberg. A method for the solution of certain non-linear problems in least squares. Quart. Appl. Math., 2:164–168, 1944.

[34] D. W. Marquardt. An algorithm for least-squares estimation of nonlinear parameters. Journal of the Society for Industrial and Applied Mathematics, 11(2):431–441, 1962.

[35] A. CAUCHY. Methode generale pour la resolution des systemes d’equations simultanees. C.R. Acad. Sci. Paris, 25:536–538, 1847.

[36] Kunio Tanabe. Global analysius of continuous analogues of the levenberg-marquardt and newton-raphson methods for solving nonlinear equations.

Ann. Inst. Statist. Math., 37:189–203, 1885.

[37] T. R. De Young. Icetray: a software framework for icecube. CHEP, pages 463–466, 2005.

[38] C. Kopper, T Eberl, and A Kappes. A software framework for km3net.

Nucl. Instrum. Meth. A602, pages 107–110, 2009.

[39] Tommaso Chiarusi and Matteo Sanguineti. Moon shadow in ANTARES.

EPJ Web Conf., 207:07007, 2019.

[40] The ANTARES Collaboration. An algorithm for the reconstruction of neutrino-induced showers in the ANTARES neutrino telescope. The

(44)

A ASCII file format

The file format is as follows: start_event [event ID]

[Run Id] [EventID] [trigger] [Unix Time]

weights [Weight W2] [Weight W3] [number of events] nu [dx] [dy] [dz] [x] [y] [z] [E] [type] muon [dx] [dy] [dz] [x] [y] [z] [E] [type] aafit [dx] [dy] [dz] [x] [y] [z] [lambda] [beta] *fit [dx] [dy] [dz] [x] [y] [z] [*fit parameters]

hit 1 [String] [Floor] [PMT] [x] [y] [z] [dx] [dy] [dz] [time] [charge] [rate] hit 2 [String] [Floor] [PMT] [x] [y] [z] [dx] [dy] [dz] [time] [charge] [rate] hit 3 [String] [Floor] [PMT] [x] [y] [z] [dx] [dy] [dz] [time] [charge] [rate] ...

hit n [String] [Floor] [PMT] [x] [y] [z] [dx] [dy] [dz] [time] [charge] [rate] end_event

An example for the file format filled in is as follows: start_event 1 37132 6583 0 1226768175 2008-11-15 16:56:15.000,000,000,0 UTC weights 75840000000.0 89350000000.0 500000000.0 nu -0.926427179874 0.103927020178 0.361845070255 80.014 -80.768 90.118 6.53452 14 muon 0.942987206855 0.15248803345 0.295842064896 80.014 80.768 90.118 6.38061 -13 aafit 0.023321614704 0.988172690961 0.15156132464 33.9617035207 59.065656674 6.80891072423 -7.09301232329 0.00648542714615 gridfit 0.622039271233 0.711329344135 0.32722730512 25.1545056533 -39.7486275754 85.1235728283 7.59721262548 hit 1 9 2 0 -97.274529 8.267296 156.632892 0.683382 -0.181630 -0.707106 -1696.694034 1.675060 78.315735 hit 2 12 17 1 -11.597152 -100.157554 61.367108 0.606848 0.362955 -0.707106 2006.686230 1.723468 62.599182 hit 3 12 17 2 -12.598033 -100.172990 61.367108 0.617752 0.344068 -0.707106 -1365.206221 1.309569 54.988861 ... hit 232 1 22 2 4.278801 96.848412 125.043108 0.095547 0.700622 -0.707106 1960.109191 1.552381 63.591003 end_event

(45)

B JPrintEvt Examples

B.1 Example

The JPrintEvtAA is used to check fits in a text-based environment. This ap-plication prints JEvt data as follows:

event: [n]

neutrino [x] [y] [z] [dx] [dy] [dz] [T] muon [x] [y] [z] [dx] [dy] [dz] [T] number of fits [nfits]

fit [x] [y] [z] [dx] [dy] [dz] [E]

[ndf] [Chi2] [Lambda] [ang_res] [beta_0] 1 [step ID] [JPP_Version] [run_date]

2 [step ID] [JPP_Version] [run_date] ... [...]

n [step ID] [JPP_Version] [run_date] An example for the file format filled in is as follows: event: 96 neutrino -116.46 50.74 4.66 0.726 -0.315 0.611 muon -116.46 50.74 4.66 0.748 -0.299 0.593 number of fits 97 fit -204.89 85.11 -56.73 0.764 -0.301 0.571 35 51.7 1.5 0.2 0.0

1 1 13.0.0-137-g58ee9044 Fri Mar 26 15:08:51 2021 2 2 13.0.0-137-g58ee9044 Fri Mar 26 15:09:43 2021 3 3 13.0.0-137-g58ee9044 Fri Mar 26 15:10:01 2021 4 5 13.0.0-137-g58ee9044-D Fri Mar 26 15:11:57 2021

B.2 JStart vs JGandalf example

JStart uses the fit of JGandalf to move the start position to the one closest to the ”real” vertex. An example of an event that got moved closer to the real vertex is given here:

Only JPrefit, JSimplex and JGandalf applied to a specific event: event: 152 neutrino -387.66 -105.71 7.11 0.979 0.059 0.193 0.0 muon -263.65 -99.38 27.59 0.985 0.050 0.164 0.0 number of fits 72 fit 8.06 -87.12 71.21 0.987 0.046 0.152 26 44.9 1.7 0.0 -0.1 0.0 1 1 13.0.0-137-g58ee9044 Fri Mar 26 15:08:58 2021

2 2 13.0.0-137-g58ee9044 Fri Mar 26 15:09:44 2021 3 3 13.0.0-137-g58ee9044 Fri Mar 26 15:10:03 2021

(46)

JStart applied as well to the same event yields the following change: event: 152 neutrino -387.66 -105.71 7.11 0.979 0.059 0.193 0.0 muon -263.65 -99.38 27.59 0.985 0.050 0.164 0.0 number of fits 96 fit -263.43 -99.77 29.34 0.987 0.046 0.152 26 44.9 1.7 0.0 -0.1 0.0

1 1 13.0.0-137-g58ee9044 Fri Mar 26 15:08:58 2021 2 2 13.0.0-137-g58ee9044 Fri Mar 26 15:09:44 2021 3 3 13.0.0-137-g58ee9044 Fri Mar 26 15:10:03 2021 4 5 13.0.0-137-g58ee9044 Fri Mar 26 15:10:35 2021

As you can see the vertex position (x,y,z) is moved closer to the real vertex of the muon along the reconstructed track.

(47)

C Settings and data files used

For this analysis the following computers are used: The Nikhef Computer Bemm running Centos7.

- Used for final analysis and plotting.

The Nikhef Stoomboot Cluster Computer running Centos7. - Used for large scale JChain Processing.

The Lyon CC-IN2P3 Cluster Computer

- Used for the initial ANTARES AAfit processing and to turn .i3 files into ASCII files. These are the settings used in the reconstruction chain:

useL0 = 0 numberOfPrefits = 24 sigma_ns = 5.0 gridAngle_deg = 3.0 numberOfOutliers = 3 ctMin = 0.0 TMaxLocal_ns = 25 useL0 = 0 roadWidth_m = 150 ctMin = -1.0 R_Hz = 60e3 E_GeV = 1.0e3 TTS_ns = 2.0

These are the applications used in sequential order to process the Antares Data from ASCII files to plottable data (see appendix A for the input file layout).: JAsciiToOffline JMuonPrefitOffline JMuonSimplexOffline JMuonGandalfOffline JMuonStartOffline JMuonEnergyOffline JConvertEvtOffline

This is the standard so-called ”JChain” reconstruction chain used for Muon re-construction in Jpp. The ”Offline” suffix for each application is used to distin-guish it from the applications they were based on. For example: JMuonPrefitOf-fline uses the JMuonPrefit fitting algorithm with the Jpp OfJMuonPrefitOf-fline file reader and hit-builder. Following this JChain a final application specific fitting application can be used to plot any data or fit values. These offline versions of the JChain can be downloaded from my git repository: https://git.km3net.de/mhammer/antares-jpp. The script I used to obtain the ascii files shown in appendix A can be down-loaded from the git repository: https://git.km3net.de/mhammer/i3-conversion. But any script that outputs data in the style described in A could be used in this JChain.