Investigating possible biases in the efficiency determination of the KM3NeT detectors

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Searching for Neutrinos in the

Mediterranean Sea

Investigating possible biases in the efficiency

determination of the KM3NeT detectors

Pieter Julius Nicolaas Braat

11026936

Report Bachelor Project Physics and Astronomy

Size: 15 EC

Conducted between 02-04-2018 and 07-07-2018

Supervisor: Paul de Jong

Second examiner: Auke-Pieter Colijn

Faculty of Science

University of Amsterdam

NikHef Institute

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Scientific Summary

In modern day Neutrino Physics there still exist a lot of unknowns, such as the proposed existence of sterile neutrino’s, the mass hierarchy problem and the ques-tion whether or not neutrinos violate CP symmetry. KM3NeT is an internaques-tional collaboration which aims to answer two of these questions, by serving as a neu-trino telescope and by doing neuneu-trino oscillation physics in the Mediterranean Sea simultaneously. This to the extent of identifying highly energetic neutrino sources in the universe, and in order to provide a solution to the mass hierarchy problem. Neutrinos traversing sea water can undergo interactions via the weak inter-action, in which the interaction products produce light via Cherenkov radiation and Bremsstrahlung. This light can be measured using Photo-MultipliersTubes (PMTs), 31 of which are mounted on a Digital Optical Module (DOM) to allow for 3D reconstruction. This research focused on the relative efficiency determina-tion of these PMTs and on identifying possible biases in this determinadetermina-tion to the extent of understanding the accuracy of efficiency determination.

The relative efficiency determination makes use of the coincidence rates arising from the K40 optical background decays, as light coming from such decays is expected to hit multiple PMTs. The measured rate for a PMT pair is compared to a model that calculates the expected rate based on the separation angle between the PMTs. The relative efficiencies were determined to be between 0.8 and 1.3, with a mean value of about 1.15.

The parametrization of the K40 model is based on simulations, and was tested using data from the first deployed ORCA string. The model was found to under-estimate the measured data, indicating that the PMTs measure more light than expected from simulations. This finding was in accordance with the found mean value of about 1.15.

The measured coincidence rates are corrected for background, which consists of misidentified coincidence hits. The background rates can be determined via three methods; i) using the individual measured rates of the PMTs, ii) using the tails region of the coincidence spectrum and iii) using the measured hits that were not marked as coincidences.

In this research only the first two methods were tested, as the third requires a different data type. Comparing the two methods showed that the first method (‘rates’) shows a systematically higher efficiency (up to 3 %) with respect to the second method (‘tails’). An uncertainty up to 3% thus arises from the choice of background estimation methods.

The relation between the individual measured rates of a PMT and its corre-sponding determined relative efficiency was investigated and the two were shown to be correlated, proving that these rates can be used as a crosscheck channel for the determined efficiency. Deviations from this correlation were then used to check for biases in the efficiency determination. Deviations up to ±2% were seen,

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imposing a 2 % uncertainty on the determined efficiency.

Lastly the effect of malfunctioning PMTs was investigated, where a malfunc-tioning PMT was simulated by setting the measured rate of that PMT to 0. De-viations from the reference values, i.e. the original calibration, up to ±3% on average were seen, and were proposed to arise from an in-/decreased effect of the shadowing of the construction. Shadowing from the construction as a cause can be tested, as it is expected to be visible and similar for all runs. This can then be used to construct a blueprint which can be consulted in case of a malfunctioning PMT.

The various factors that impose an uncertainty on the determined relative ef-ficiencies are listed above, with an overall combined uncertainty of 5 % on the relative efficiency. For a more accurate reconstruction of the energy of the mea-sured particles, additional research is required, investigating the different back-ground estimation methods. A more accurate efficiency could also be determined by combining an efficiency determination based on both the single rates and the K40 background coincidence rates.

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Populair Wetenschappelijke

Samenvatting

In 1930 onderzocht Wolfgang Pauli betaverval en zag tot zijn verbazing dat de energie van het gevormde electron niet een vaste energie had, maar verschillende

energie¨en kon aannemen. Om toch de wet van behoud van energie staande te

houden, stelde hij een hypotetisch deeltje voor dat met bijna niks reageert en hij dus niet kon waarnemen. Dit deeltje zou een deel van de energie van het moederdeeltje overnemen en tijdens het verval ontsnappen. Pauli bleek hierin gelijk te hebben en dus een nieuw deeltje te hebben ontdekt. Dit deetje kennen we tegenwoordig als het neutrino.

Vandaag de dag bestaan er nog allerlei onbekende eigenschappen van dit neu-trino, zoals zijn precieze massa en het voorgestelde bestaan van een broertje van dit neutrino, dat met niks reageert: een zogenoemd steriel neutrino. KM3NeT is een internationale organisatie die zich bezighoudt met dit gebied van de natuurkunde (neutino fysica) door neutrino’s te detecteren in de Middellandse Zee.

Om deze neutrino’s te detecteren, gebruikt KM3NeT kleine detectoren die licht kunnen waarnemen. Deze detectoren meten echter niet allemaal evenveel licht, maar kunnen onderling tot wel 20 % verschillen. Hoeveel licht zo’n kleine detector meet ten opzichte van de totale hoeveelheid licht, wordt de efficientie van de detector genoemd, waarbij een gemiddelde detector een efficientie heeft van ongeveer 30 %. Hoeveel een specifieke detector meet ten opzichte van een gemiddelde detector, wordt de relatieve efficientie genoemd.

Om de moderne vraagstukken uit de neutrino fysica te kunnen beantwoorden, is het belangrijk om de energie van het gemeten neutrino heel nauwkeurig te bepalen en aangezien het gemeten aantal lichtflitjes schaalt met de energie van het neutrino, is het dus ook belangrijk om te weten hoeveel licht er in totaal uitgezonden is op basis van wat je gemeten hebt. Daarom is het belangrijk om de individuele relatieve efficienties nauwkeurig te bepalen. Mijn onderzoek richtte zich op de bepaling van deze relatieve efficienties, en op factoren die deze bepaling kunnen be¨ınvloeden.

De bepaling van de relatieve effici¨enties maakt gebruik van alle lichtflitjes die

meerdere (minstens 2) kleine detectoren binnen een korte tijd meten, en alleen

dan worden deze lichtflitsjes geregisteerd als signaal. Zo’n signaal wordt een

co¨ıncidentie genoemd. Soms worden er echter toevallig twee lichtflitjes uitgezonden binnen die korte tijd en dus foutief geregisteerd als signaal. Dit wordt achtergrond genoemd. In mijn onderzoek heb ik onder andere gekeken naar de invloed van de

bepaling van deze achtergrond op de bepaling van de effici¨enties en vond ik dat

manier waarop je deze achtergrond bepaalt verschillen op kan leveren tot 2 %. Om het aantal gemeten co¨ıncidenties te gebruiken voor het bepalen van de

re-latieve effici¨enties, wordt een model gebruikt dat het verwachte aantal co¨ıncidenties

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worden bepaald aan de hand van simulaties, en in dit onderzoek heb ik deze waar-den vergeleken. Ik vond hierbij dat de detectoren meer licht zien dan verwacht wordt op basis van de simulaties, en dit kan deels verklaard worden door de ver-schillende manieren waarop het aantal co¨ıncidenties bepaald wordt.

Ook heb ik onderzocht of het aantal individueel gemeten lichtflitjes - dit zijn dus lichtflitjes die maar door een detector gezien worden - gebruikt kan worden

om te controleren dat de bepaalde effici¨enties wel juist zijn. De verwachting was

hierbij dat het aantal individueel gemeten lichtflitjes groter is voor een detector

met een hogere effici¨entie en er bleek inderdaad een verband te zijn tussen de twee.

Tot slot heb ik onderzocht wat er gebeurt met de efficienties van de andere detectoren als een van de detectoren kapot gaat. Het bleek dat deze detectoren

een andere effici¨entie kregen bepaald (tot wel 3 % verschillend), dan wanneer er

geen detector kapot is. Dit is natuurkundig natuurlijk niet juist. Een mogelijke verklaring hiervoor is dat het effect van de constructie die gebruikt wordt om de detectoren op hun plaats te houden, groter wordt wanneer een van de detectoren kapot gaat.

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Introduction

Neutrinos are among the lightest particles described by the Standard Model of Particle Physics. These in 1930 by Wolfgang Pauli proposed particles are subject to the weak interacting force only and are therefore difficult to observe. Up to this day there still exist some unknown properties of these neutrinos, such as their exact mass - it was proven only recently that neutrinos are in fact not massless [1] -, whether it is its own anti-particle, a so called Majorana or Dirac fermion, and why only left-handed neutrinos (and right-handed anti-neutrinos) are observed.

KM3NeT is an international collaboration working on neutrino physics to pro-vide solutions to some of these current day questions. Its main objectives are to measure neutrino oscillations, to determine the neutrino mass hierarchy and to serve as a neutrino telescope for high energy neutrino sources in the universe. This research is done by measuring neutrino’s in the Mediterranean Sea using de-tector blocks that are referred to by ORCA/ARCA for these research objectives respectively. The KM3NeT experiment will be further discussed in the chapter 2. To provide a credible solutions to the research goals of KM3NeT, the energy of the detected particles must be determined. To do this energy reconstruction accurately, the efficiencies of the used detectors must be known accurately as well. This research investigated this accuracy by looking at the factors that can influence the determination of these efficiencies, as well as looking for possible biases in the determination method.

This thesis will explain first explain the method that KM3NeT uses to detect the neutrinos and the type of signatures that are observed. The second chapter will explain in more detail the research goals of KM3NeT, as well as the technical design and the optical background sources. The third chapter discusses the method that is used to determine the relative efficiencies of the detector, the influence of the background estimation method on this determination and will discribe the result of the testing of the model used for the determination. The fourth chapter focuses on the result of the biases investigation, by discussing the single rate versus determined efficiency relation, as well as the result of malfunctioning detectors on the determined efficiency. The last chapter concludes the thesis and provides an outlook for further research.

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Chapter 1 Neutrino Detection

As neutrinos are only subject to the weak interacting force, detecting these parti-cles is not trivial. KM3NeT is located in the Mediterranean Sea, and this location is chosen for the reason that neutrinos can undergo interactions that produce light, which can be detected. This light is known as Cherenkov radiation. This chapter will first explain how Cherenkov radiation is produced, and will secondly explain the type of interactions a neutrino can undergo in sea water.

1.1 Cherenkov radiation

Light travelling through a medium other than the vacuum will be slowed down, allowing particles to have velocities higher than the speed of light in this medium. If the medium is dielectric, charged particles travelling with such velocities will polarise the medium creating a electromagnetic disturbance in this medium. This disturbance is seen as light, and is therefore called Cherenkov radiation. [2]

1.2 Neutrino interactions

Neutrino interactions occur when a neutrino scatters on a nucleus in the sea water

via the weak interaction, i.e. the emission of a Z or W±-boson. These interactions

are called a neutral current (NC) and charged current (CC) interactions respec-tively. Since the neutrino’s of interest are highly energetic (starting from a few GeVs upwards), the emitted boson will cause the nucleus to fragment, causing a hadronic shower. The NC interaction conserves flavor so the neutrino after scat-tering remains unchanged. The detected signature (a hadronic shower from the nucleus fragmentation) is the same for all three neutrino flavors. NC interactions are thus independent of the flavor of the incoming neutrino.

In the case of a CC interaction the incoming neutrino converts to its flavor

cor-responding charged lepton while emitting a W±-boson. Depending on the flavor of

the incoming neutrino, the decay products will show a different event structure. In the case of an electron neutrino, the decay product will be an electron (or positron for anti-neutrino). This electron will radiate off photons as Bremsstrahlung and Cherenkov radiation. These photons can create an electron and positron pair via pair creation, as well as Compton scatter on the electron in the sea water. These processes will create an electromagnetic shower, and are thus classified as shower-like.

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CHAPTER 1. NEUTRINO DETECTION

The muon neutrino will form a muon in a CC event, which travels through the water and radiates off Cherenkov radiation along its trajectory. A muon neutrino CC interaction will thus leave a track-like signature in the detector.

In the case of a tau neutrino, a tau lepton is formed via the emission of a W±

-boson. This boson scatters on a nucleus, fragmenting it and creating a shower-like event. The formed tau lepton can decay via different decay modes in either a elec-tron, muon or hadrons. The muon then leaves a track-like signature in the detector (similar to the muon neutrino CC interaction). Both the electrons and hadrons will cause a shower-like event (electromagnetic, and hadronic respectively). This topology is therefore called a double bang event. The Feynman diagrams of the neutrino interactions are shown in figure 1.1. [3]

1.3 Event signatures

Neutrino events are categorised into two different signatures; track- and shower-like signatures. A track-shower-like signature is detected only for muon neutrino CC interactions. The signature is called track-like as the photons from Cherenkov radiation and Bremsstrahlung are emitted along the trajectory of the muon.

In a shower-like signature the incoming particle scatters on another particle, creating decay products. In this process some of the energy of the incoming particle is converted to mass of the decays products. These decay products themselves can

scatter on another particle, causing more decay products to be formed. This

process continues until the energy of the decay products is too low to create new particles, causing a cascade or shower of particles to be formed. A shower can be

identified as electromagnetic, i.e. a cascade of e+e− and photons, or as hadronic,

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CHAPTER 1. NEUTRINO DETECTION

(a) Neutral current (NC) events for all three neutrino flavors.

(b) Charged current (CC) events for the electron neutrino.

(c) Charged current (CC) events for the muon neutrino.

(d) Charged current (CC) events for the tau neutrino, where the tau lepton ei-ther decays hadronically, or to an elec-tron (82.6% of the interactions).

(e) Charged current (CC) events for the tau neutrino, in which the tau lepton decays to a muon (17.4% of all interac-tions).

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Chapter 2 The KM3NeT Experiment

As described in the introduction, KM3NeT aims to answer two different questions by detecting neutrinos in sea water. This chapter will explain in more depth the research goals of the KM3NeT experiment, as well as the detector design used to detect the neutrino interactions. Lastly, the most dominant optical background sources will be discussed.

2.1 Astroparticle Research using Cosmics in the

Abyss (ARCA)

The KM3NeT detector consists of two building blocks (ARCA/ORCA) that are used to focus on different aspects of neutrino physics. The aim of the ARCA experiment is to identify astronomical sources that produce highly energetic neu-trinos. Neutrinos are especially suited for this type of research as they are only subject to the weak interacting force, meaning that their trajectory is not deflected by gravitational or electromagnetic fields. As possible sources for these high ener-getic neutrino’s blazars and supernova remnants within Starbust galaxies or galaxy clusters are proposed.

To identify these astronomical sources, ARCA looks at the high energy neutrino spectrum (energies starting from 100 GeV upwards). To optimise for this research two detector blocks of 115 detector strings each are placed off-shore Sicily, Italy. The spacing between the detector strings is 90 meters, and the structure of the ARCA detector can be seen in figure 2.2a. The design of placing two detector blocks for the ARCA detector allows for better track reconstruction for the highly energetic neutrino, thus increasing the resolution of the neutrino telescope.

2.2 Oscillation Research using Cosmics in the

Abyss (ORCA)

The aim of the ORCA project is to provide a solution to the mass hierarchy problem. The observation of a deficiency in the expected flux of muon neutrino’s by the SuperKamiokande experiment led to the proposition of neutrino oscillations, which were rewarded with the Nobel prize for Physics in 2015. Neutrino oscillations have proven the neutrino’s to have a non zero mass [1].

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CHAPTER 2. THE KM3NET EXPERIMENT

Figure 2.1: This figure shows the different solutions to the mass hierarchy problem,

i.e. either normal hierarchy (NH, m1 < m2 < m3) or inverted hierarchy (IH,

m3 < m1 < m2). [4]

flavor B and arise from the fact that the neutrino flavor states are not eigenstates

of the vacuum, but superpositions of the so called mass eigenstates ν1, ν2 and

ν3. These mass eigenstates are eigenstates of the vacuum, with corresponding

eigenenergies of m1, m2 and m3 respectively.

Oscillation experiments are not able to determine the mass of these eigenstates,

but they can measure the absolute differences between them: ∆m2

ij = m2i − m2j,

where mi,j stands for the mass of the mass eigenstate νi,j respectively, where i, j ∈

{1, 2, 3}. Current day experiments have proven ∆m2

21 to be positive (m2 > m1),

so two possibilities of the mass hierarchy remain; either normal hierarchy (NH,

m1 < m2 < m3) or inverted hierarchy (IH, m3 < m1 < m2). Figure 2.1 shows

the two possible solutions graphically. ORCA aims to provide a solution to this so called mass hierarchy problem.

ORCA looks at neutrino’s of the low energy spectrum(∼ few GeVs), that have traversed the earth. Because the earths core has an higher electron density than the atmosphere, the atmospheric three generation neutrino flux ratio will change at these energies. This change can then be used to determine the mass differences squared, which provide a solution to the mass hierarchy problem.

The ORCA building block can be seen in figure 2.2b, and consists of 115 detector strings, spaced 20 meters apart placed off-shore Toulon, France. This spacing is optimised for the low energy neutrino range. For additional information on the ORCA/ARCA project I’d like to refer to the KM3NeT Letter of Intent. [4]

2.3 Building blocks

The ARCA/ORCA building blocks consist of 115 strings, or Detection Units (DUs) which function as a large detector by combining information from all strings. These strings consist of 18 Digital Optical Modules (DOMs) which are used to detect events, and a buoy on top and a power station on the sea floor to provide the DOMs with power. These DOMs contain 31 Photo-Multiplier Tubes (PMTs) that can each detect photons and turn them into an electrical signal. These PMTs are mounted in six rings (A to F), where ring A is the downwards pointing PMT, and rings B to F contain 6 PMTs each. The lower half of the DOM contains

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(a) The ARCA detector off-shore Sicily, Italy, consisting of 2 detection blocks of 115 detector strings spaced 90 meters apart.

(b) The ORCA detector off-shore Toulon, France, consisting of 1 detec-tion block of 115 detector strings spaced 20 meters apart.

Figure 2.2: The structure of the ARCA/ORCA building blocks respectively.

19 downwards facing PMTs (rings A to D), the upper half contains 12 upwards facing PMTs (rings E and F). The DU and DOM design respectively are shown in figure 2.3a.

Currently there are 2 deployed ARCA strings and 1 deployed ORCA string online. For this research ORCA data taking runs 3100 to 3110 are used, corre-sponding to data taken between 30/11/2017 9pm and 02/12/2017 9pm. Besides this data, ARCA runs 5010 and 5045 are used to cross-check between ORCA

and ARCA systematics. These runs are taken between 23/12/2016 6pm and

24/12/2016 12am, and between 01/01/2017 12pm and 6pm respectively.

2.3.1 Photo-MultiplierTubes

To detect the photons from neutrino interactions Photo-MultiplierTubes (PMTs) are used. An incoming photon falls onto the photocathode which is right behind the glass shielding, clearing an electron. This electron is then accelerated by a dynode, clearing more electrons when impacting the dynode. This process is repeated several times to increase the signal strength measured as output. Figure 2.3b shows the Hamamatsu PMTs used in the DOMs. [5]

2.4 Optical background

Besides neutrino interactions, other processes contribute to the amount of light seen in the detectors. This light is called the optical background. In this section the most dominant optical background sources are discussed.

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(a) (b)

Figure 2.3: A detection unit (DU) used in the KM3NeT experiment. A string (left) with 18 DOMs is installed in the sea, with a buoy mounted on top and a power station on the sea bed. The middle picture shows a detector module (DOM) with 31 Photo-MultiplierTubes (PMTs). The right picture shows an Hamamatsu PMT. [4]

2.4.1 Potassium-40

The largest contribution to the optical background comes from an unstable isotope of Potassium in the sea salt, Potassium-40 (K40). This isotope will decay into Calcium 40 via β-decay or into Argon-40 via electron capture. The decay schemes of K40 are as follows 40 19K → 4020Ca + β − + ¯νe (89.28%) 40 19K → 40 18Ar + γ (EC, 10.72%),

where in 89.28 % of the decays an electron and an anti-neutrino are emitted, and in 10.72 % a photon is emitted. [6]

The formed electron will typically have sufficient energy to emit Cherenkov radiation. The anti-neutrino however has a relatively low energy (≤ 1.3 MeV) and is not likely to interact (as the interaction cross section scales with the energy of the neutrino) and will thus not be measured. The photon formed in the electron capture decay mode will undergo Compton scattering until it has sufficient low energy to be absorbed by the photoelectric effect.

The K40 background amounts for a steady background rate of about 7 kHz per PMT. Due to the relatively short mean free path of the electrons, the Cherenkov light from K40 background is localised. Decays happening close a DOM can thus trigger multiple PMTs. When multiple PMTs are triggered within a certain time window, this is called a coincidence, where the multiplicity of the coincidence defines how many PMTs were hit. Figure 2.4 shows the optical background rates as a function of the expected multiplicity. As can be seen in the figure, K40 background events trigger up to 7 PMTs in coincidence, i.e. these events have

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background and signal as the signal is expected to trigger more PMTs than the K40 background. PMTs in coincidence 10 20 30 [Hz] Rate 6 − 10 3 − 10 1 3 10 6 10 _{L1F1: Data} L1F1: Total simulation L2F18: Data L2F18: Total simulation Random coincidences K simulation 40

L1F1: Atm. muon simulation L2F18: Atm. muon simulation

Figure 2.4: The multiplicity dependence of the K40 and atmospheric muons back-ground sources. The K40 backback-ground amounts for a rate of about 7kHz per PMT, with a multiplicity of at most 7. Atmospheric muons show a lower rate, but trigger more PMTs (up to 31) in coincidence due to their higher energy. [7]

2.4.2 Atmospheric muons

The second largest optical background source comes from atmospheric muons. These muons are formed when highly energetic nuclei from the universe enter the atmosphere, and scatter on an air molecule, creating a cascade of particles (a so called cosmic shower). Due to their low reactivity and relatively long lifetime they are able to reach the earths surface, where they give off background noise to the detector of a few Hz per PMT. The energy of these muons is higher than the K40 background, which causes higher multiplicities on the DOM and makes this background harder to distinguish from the signal.

2.4.3 Bioluminescence

The third largest background source comes from micro-organisms in the seawater, so called bioluminescence. These organisms can sometimes emit light a burst -in a localised area, that typically lasts for a few seconds. When happen-ing close to the detector these bursts cause a spontaneous increased rate of a few MHz, lasting for a few seconds compared to an overall average rate of a few kHz, as can be seen in figure 2.5. A high rate veto is therefore imposed on the PMTs to prevent excessive writing of data to shore. For bioluminescence bursts further away from the detector a lower rate is measured. [8]

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Figure 2.5: A bioluminescence burst shows a localised higher rate around 30 s. The high rate veto cuts the rate at 20 kHz to prevent excessive writing of data to shore. [8]

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Chapter 3 PMT Efficiency Determination

For the energy reconstruction of the detected particles it is important to accurately know the efficiencies of the individual PMTs. The PMTs have a different efficiency depending on the wavelength of the incoming light, with a maximum of 30% around 380 nm, as is shown in figure 3.1 [9]. Individual PMTs however can have efficiencies varying between the 25 and 35%. To account for these differences in efficiency, a new quantity is introduced, the so called relative Quantum Efficiency (rel. QE) which is defined as the efficiency of the PMT divided by the efficiency of a reference PMT.

This chapter discusses the method that is used to determine these relative QE’s and discusses the influence of different background estimation methods on this determination. Lastly, the model that is used for the efficiency determination is tested.

3.1 Efficiency determination method

3.1.1 Theory

The light from K40 decays provides the detector with a steady background rate, where light from a K40 decay is expected to hit multiple PMTs thus causing a coincidence to be detected. Due to intrinsic PMT properties the coincidence hits

Figure 3.1: This figure shows the Quantum Efficiency dependence of a Hamamatsu PMT as a function of the wavelength. [9]

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CHAPTER 3. PMT EFFICIENCY DETERMINATION

Figure 3.2: This figure shows the expected distribution of the differences in arrival time of the coincidences on the two PMTs of a PMT pair.

are not measured simultaneously, but with a certain difference in arrival time. This difference in arrival time is determined as the time that the first PMT of the PMT pair registers a hit minus the time that the second PMT registers a hit, i.e.

∆tar. = thit,1− thit,2.

The distribution of these differences for all measured coincidences provides information on the PMT properties. Firstly, the mean value of these differences is shifted from zero due to the individual time offsets of the corresponding PMTs. Besides the time offsets, the arrival time is spread out due a spread in the transit time, i.e. the time between the moment that the photon reaches the PMT and the moment that a electrical signal is sent. Lastly differences in the total number of measured hits - provided the separation angle between the PMTs of a PMT pair is the same - amount for differences in the PMT efficiencies.

Figure 3.2 shows the expected distribution of the difference in arrival time of an arbitrary PMT pair, where

µ = t0,1− t0,2,

σ ∝ σ1∗ σ2,

Area = Rate ∗ QE1∗ QE2, (3.1)

and t0,i corresponds to the time offset, σi to the transit time spread and QEi

to the relative efficiency of PMT i. The indices 1, 2 correspond to the first and second PMT of the PMT pair respectively. Both the time offsets and the transit time spreads are of the order of a few nanoseconds, and the relative efficiency lies between 0.8 < QE < 1.3.

As this thesis focuses on biases in the efficiency determination, only the deter-mination of this PMT property will be discussed. For this deterdeter-mination a model depending on the separation angle θ between the PMTs is postulated,

40_K

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where pi, i ∈ {1, 2, 3, 4} are parameters used to parametrize this model [3]. The

values of these parameters are determined by simulations, and are displayed in ta-ble ?? [10]. Figure 3.3 shows the expected rate based on this model as a function

of the separation angle, with the parameters pi set as in the efficiency

determina-tion. This model is used to calculate the expected rate, which can then be used to determine the relative efficiencies (using eqn 3.1).

K40_rate(θ) = Exp[p1 + cos(θ) (p2 + cosθ (p3 + p4 cosθ))]

0 50 100 150 separation angle [degrees]

0 2 4 6 8 10 rate [Hz]

Figure 3.3: This figure shows the expected K40 coincidence rate as a function of the separation angle θ between the PMTs of a PMT pair.

3.1.2 Software implementation

Events are registered when at least one PMT measures a photon, and these are stored every 0.1 second in so called time slices. The time slices also store additional information, such as the PMTs that where hit by a certain event. The data streams that contain all measured hits are called L0 data streams. L1 data streams store only coincidence events, which are events when at least two PMTs measure a hit within a certain set time frame. Both L0 and L1 data streams can be used for the efficiency determination, as only the coincidence events are used. The analyses performed for this thesis made use of L1 data streams only.

The coincidence rates are determined from the total number stored events in the time slices divided by the livetime of that PMT pair. The livetime of a PMT pair is defined as the time that the PMTs were measuring properly, which means that a non-zero, below the High Rate Veto rate was stored in the time slices. These coincidence rates are then sorted for every PMT pair (1/2 ∗ 31 ∗ 30 = 465 pairs in total), where the indices of the PMT pairs correspond to a smaller separation angle for an higher index.

The coincidence rates contain some background, due to uncorrelated photons hitting a PMT pair within the set time window. This background can be estimated in three distinct ways, which will be discussed in section 3.2. After the background estimation a constant background rate is subtracted from the measured signal. A Gaussian distribution scaled by the expected rate from equation 3.2 is then fitted to every PMT pair, and the determined parameters are combined to determine the properties of the individual PMTs. The JMonitorK40 and JFitK40 programs from the JPP software are designed to perform this determination [11] [12]. Figure 3.4a

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(3.4b) shows the measured coincidence rates for all PMT pairs on a DOM, and the determined relative efficiencies of all PMTs for all 18 DOMs of the first deployed ORCA string respectively. This determination was done using ORCA run 3104.

(a) DOMs 2 4 6 8 10 12 14 16 18 PMTs 22 A1 14 B1 19 B2 25 B3 24 B4 26 B5 18 B6 13 C1 21 C2 29 C3 28 C4 20 C5 17 C6 12 D1 15 D2 23 D3 30 D4 27 D5 16 D6 10 E1 6 E2 3 E3 2 E4 1 E5 11 E6 9 F1 8 F2 4 F3 0 F4 5 F5 7 F6 0 0.2 0.4 0.6 0.8 1 1.2 QE (b)

Figure 3.4: This figure shows the measured coincidence rates for all PMTs on a DOM (left) and the determined relative efficiency of all PMTs of all 18 DOMs of the first deployed ORCA string (right). This determination was done using ORCA run 3104.

3.2 Influence of background estimation method

The method used to estimate the background can influence the determination of the quantum efficiency, as an under-/overestimation in background noise can result in a higher/lower efficiency due to an over/underestimated rate. To determine the PMT efficiencies accurately, it is therefore important to understand the influence of the different methods of estimating this background.

The background rate can be estimated via three different methods. The first method makes use of the measured rates of the PMTs with multiplicity 1, the so called single rates and is therefore referred to as the rates method. The sec-ond method estimates the background based on the coincidence rates in the high

difference in arrival time region (15 < |∆tar.| < 20 ns), i.e. the so called tails

region of the Gaussian distribution. This method is therefore referred to as the tails method.

The last method uses the measured hits that lie outside the set L1 time window for the background estimation, i.e. L0 hits only. These hits can be used to estimate the rate of random coincidences, and is therefore referred to as the random method [13]. This background estimation is not considered however, as these hits are only stored for L0 data. An analysis was performed to show the difference between the tails and rates method using ORCA run 3103.

Figure 3.5 shows the difference between the determined relative QE using the tails method minus the determined relative QE of the rates method and normalised on the relative efficiency of the rates method for all PMTs of all DOMs. As can

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CHAPTER 3. PMT EFFICIENCY DETERMINATION DOMs 2 4 6 8 10 12 14 16 18 PMTs 22 A1 14 B1 19 B2 25 B3 24 B4 26 B5 18 B6 13 C1 21 C2 29 C3 28 C4 20 C5 17 C6 12 D1 15 D2 23 D3 30 D4 27 D5 16 D6 10 E1 6 E2 3 E3 2 E4 1 E5 11 E6 9 F1 8 F2 4 F3 0 F4 5 F5 7 F6 0.035 − 0.03 − 0.025 − 0.02 − 0.015 − 0.01 − 0.005 − 0 0.005

(QE_tails - QE_rates) / QE_rates

Figure 3.5: This plot shows the difference in determined relative efficiency for all PMTs between the tails and random method.

be seen from the figure, the median of the difference is negative, indicating that the rates method determines an higher relative efficiency than the tails method.

This difference might be due to the fact that some of the signal in the tails region might be wrongly classified as background. This would result in an over-estimation in the background rate, causing a lower determined relative efficiency. A choice was made to use the rates background determination method for further investigations.

3.3 Testing of the K40 model parameters

The K40 model is used to determine the expected coincidence rate of a PMT pair given the separation angle between the PMTs that make up the pair, which can then be used to determine the relative efficiencies of the corresponding PMTs.

The values of the parametrization of the model pi are based on simulation using

OMGsim [10]. Wrongly determined values for these parameters can however lead to inaccurately determined relative efficiencies of the PMTs. The values of these parameters are therefore tested via two separate methods:

i) By comparing the K40 model to the data, corrected for their determined efficiency, and

ii) By fitting the model to the data (uncorrected) to find the best fit values of

the parameters pi.

The testing is done by plotting the mean coincidence rate per separation angle. This mean is determined by counting the number of times a coincidence rate was measured per separation angle, and fitting a Gaussian distribution to this distribution. ORCA runs 3100 to 3110 were used for this analysis.

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separation angle [degrees]

20 40 60 80 100 120 140 160 rate [Hz] 0 2 4 6 8 10

Mean coincidence rates

Figure 3.6: This figure shows the mean coincidence rates corrected for the deter-mined efficiency.

3.3.1 Method 1

Figure 3.6 shows the mean coincidence rates as a function of the separation angle, where the measured coincidence rates were corrected for the determined efficiency

before determining the mean. The K40 model with the values of pi set as used in

the efficiency determination is also drawn. The means of the coincidence rates lie above the K40 model, indicating that more light is measured by the PMTs than expected from the simulation.

3.3.2 Method 2

Figure 3.7 shows the determined mean coincidence rates, not corrected for the determined relative efficiency. The K40 model was fitted to this data, and the

values of the parameters pi can be found in table 3.1 together with the determined

values based on the simulation.

The determined values from the fit are not consistent with the data, which is in accordance with the result from the first method. The larger value of the parameter p1 from the fit result, which can be thought of as a scaling factor, seems consistent with the earlier notion that the PMTs measure more light than is expected from the simulation.

parameter simulation values fit values

p1 −1.07061 −0.633 ± 0.002

p2 3.17173 2.497 ± 0.007

p3 −1.35769 −0.298 ± 0.017

p4 1.6885 1.07 ± 0.02

Table 3.1: The determined values of the parameters pi of the K40 model based on

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separation angle [degrees]

20 40 60 80 100 120 140 160 rate [Hz] 0 2 4 6 8 10

Mean coincidence rates

Figure 3.7: This figure shows the mean coincidence rates as a function of the separation angle. The K40 model (eqn. 3.2) is fitted to these means and the values of the parameters are shown in table 3.1.

3.3.3 Conclusion

Looking at the data it can be concluded that the PMTs measure more light than is expected based on the simulation. This might partially be due to the difference in the determination of the total coincidence rate, that is compared to the K40 model. The total coincidence rate for this analysis is calculated from all measured hits, whereas the efficiency determination - that uses the simulation values - uses the area under the fitted Gaussian distribution. Differences in measured coincidences could arise from this difference.

Data points of the mean coincidence rate, based on determining the measured coincidence rate from the area and correcting for the determined relative efficiency would be expected to be in better accordance with the K40 model. It was chosen to base the testing on the data for this research and therefore to use all measured hits, rather than based on the result of the fit. Additional research could provide more insights in this difference, by performing both methods and comparing the two.

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Chapter 4 Biases in PMT Efficiency

Determination

The model that is used for the relative efficiency determination is based on simu-lations, not derived from theory. It could be that this model is therefore biased in certain ways. This chapter discusses these eventual biases by looking at the rela-tion between the single rates of a PMT and its determined relative efficiency. The effect of a malfunctioning PMT on the efficiency determination is also discussed.

4.1 Single Rates vs. QE

The single rate of a PMT is the total number of hits on that PMT with multiplicity 1, i.e. the hits that measured by this PMT only, divided by its livetime. The single rates are mostly dominated by random photons hitting the PMT, which could come from bioluminescence or K40 decays from further away. PMTs also contain a dark rate, which is defined as the rate that a PMT would measure in absence of any optical sources. This dark rate includes the thermal release of photons within the PMT.

A mean single rate of about 7 kHz is expected for every PMT, but due to statistics and PMT properties this rate may vary in different time slices. Some-times the high rate veto is triggered as a result of nearby bioluminescence bursts, causing a single rate of 20 kHz to be stored in the time slices.

Figure 4.1a shows the distribution of the measured single rates of a single PMT (PMT C6) for ORCA run 3104. The measured single rates for every time slice are stored in a histogram, and a Gaussian distribution is fitted to this data. The single rate of this specifc PMT is determined as the mean of this Gaussian. This analysis is performed by the JMonitorSingleRates and JFitSingleRates programs of the JPP software. [14] [15]

Figure 4.1b shows the single rates and the corresponding determined relative efficiency for all PMTs in ORCA run 3104. A linear relation is fitted to this data, where

SR = p0 + p1 ∗ QE

with p0 = 0.54 ± 0.03 kHz and p1 = 5.92 ± 0.03 kHz are determined to be the best fit values. The fit shows that the measured single rate and the determined relative efficiency of a PMT are indeed correlated. The parameter p0 represents the average dark rate of the PMTs.

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CHAPTER 4. BIASES IN PMT EFFICIENCY DETERMINATION 2 4 6 8 10 12 14 16 18 20 Rate [kHz] 0 20 40 60 80 100 3 10 × Number of Entries

Measured single rate PMT 17 (C6)

(a) This figure shows the single rate distribution for a single PMT (C6) for ORCA run 3104. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 QE [a.u.] 0 1 2 3 4 5 6 7 8 9 10 Single rate [kHz] Single rate vs. QE

(b) This figure shows the measured sin-gle rates and corresponding relative ef-ficiency (QE) for ORCA run 3104. A linear relation is fitted to the data.

This relation can thus be used to look for biases in the K40 model, as systematic deviations from this relation can point to such biases. The deviations ∆A are here determined by calculating the difference from the mean single rate and the mean relative efficiency, normalised on the difference from the mean efficiency, i.e.

∆A = (SR/<SR> − QE/<QE>) / (SR/<SR>),

where SR (<SR>) stands for the (mean) single rate, and QE (<QE>) for the (mean) determined relative efficiency. This analysis was done for both ORCA data (run 3104) and ARCA data (run 5045).

Figure 4.2 shows the result of this analysis, by showing the calculated deviations ∆A for all PMTs of all DOMs of the corresponding strings. One can seen that in the lowest DOM (DOM channel 1) a systematically lower single rate is measured for the downwards facing PMTs (rings A to D) of the ORCA string. This could be explained by the effect of the sea floor. As the single rates are expected to come mostly from photons from further away than the localised K40 decays the sea floor will not contribute to the single rate of the downwards facing PMTs. A lower single rate with respect to the determined efficiency can thus be explained.

Furthermore, the A and B ring tend to show positive differences in DOMs 4 to 12 for ORCA, indicating that they measure a systematically higher single rate than their determined efficiency, which might point to a bias. A possible explanation would be that the sea salt concentration is inhomogeniously spread in the seawater, thus providing a orientation dependent K40 rate.

The K40 model now assumes no orientation dependence in the expected back-ground rate, so that differences in measured coincidences are attributed only to differences in the PMT properties. These inhomogeneities might arise from fluctu-ating sea salt distributions in the water. Integrfluctu-ating over time would average out these inhomogeneities and might be a way to check this hypothesis. In a larger data sample, or combined data from multiple runs smaller deviations would be expected to be seen.

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CHAPTER 4. BIASES IN PMT EFFICIENCY DETERMINATION 2 4 6 8 10 12 14 16 18 DOMs 22 A1 14 B1 19 B2 25 B3 24 B4 26 B5 18 B6 13 C1 21 C2 29 C3 28 C4 20 C5 17 C6 12 D1 15 D2 23 D3 30 D4 27 D5 16 D6 10 E1 6 E2 3 E3 2 E4 1 E5 11 E6 9 F1 8 F2 4 F3 0 F4 5 F5 7 F6 PMTs ORCA 5 10 15 20 25 30 DOMs 22 A1 14 B1 19 B2 25 B3 24 B4 26 B5 18 B6 13 C1 21 C2 29 C3 28 C4 20 C5 17 C6 12 D1 15 D2 23 D3 30 D4 27 D5 16 D6 10 E1 6 E2 3 E3 2 E4 1 E5 11 E6 9 F1 8 F2 4 F3 0 F4 5 F5 7 F6 PMTs 0.2 − 0.15 − 0.1 − 0.05 − 0 0.05 0.1 0.15 0.2 ARCA

Figure 4.2: The figures show the asymmetry between the deviation of a individual measured single rate from the mean single rate and the deviation from an individual determined relative efficiency and the mean relative efficiency for ORCA (left) and ARCA (right). The color scale for both figures is the same.

4.2 Malfunctioning PMTs

Another way to check for biases is to investigate the result of malfunctioning PMTs on the efficiency determination. For the efficiency determination the coincidences between the PMT in question and all other 30 PMTs are compared. If certain PMTs were to be biased, i.e. influencing the efficiency determination in an un-physical way, and one of the unbiased PMTs were to malfunction, the effect of the biased PMTs would increase and would thus be visible when comparing with the original calibration. This analysis was done using ORCA run 3103.

Malfunctioning PMTs in this context are PMTs that measure nothing (for example due to a wiring problem) or PMTs that consistently store a rate above the HRV. In both these cases no data would stored, so that the measured rate is zero. PMTs that for some reason measure only partly their usual signal would (ideally) be corrected by the efficiency determination and this case is therefore not looked into.

4.2.1 Method

To simulate the malfunctioning of a PMT, the measured rate is manually set to zero. The efficiency determination has existing features to recognise zero rates as a malfunctioning PMT and sets the relative efficiency of the corresponding PMT to zero. The effect on other PMTs however has not yet been implemented and is therefore investigated.

To understand the effect of malfunctioning PMTs, the efficiencies are first determined using data and stored as reference values. The measured rates of a specific PMT are then switched off and the efficiency determination is rerun. The newly determined efficiencies are then compared to the reference values to calculate the change in efficiencies. In a unbiased model the efficiencies do not change, and are the newly determined efficiencies the same as the reference values. Nonzero differences on the other hand can point to a bias.

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CHAPTER 4. BIASES IN PMT EFFICIENCY DETERMINATION

22 A114 B119 B225 B324 B426 B518 B613 C121 C229 C328 C420 C517 C612 D115 D223 D330 D427 D516 D610 E16 E23 E32 E41 E511 E69 F18 F24 F30 F45 F57 F6

PMTs 22 A1 14 B1 19 B2 25 B3 24 B4 26 B5 18 B613 C1 21 C2 29 C3 28 C420 C5 17 C6 12 D1 15 D2 23 D3 30 D427 D5 16 D6 10 E16 E2 3 E3 2 E4 1 E5 11 E6 9 F1 8 F2 4 F3 0 F4 5 F5 7 F6 malfunctioning PMT 0.02 − 0.01 − 0 0.01 0.02 0.03 per malfunctioning PMT avg QE ∆

Figure 4.3: This figure shows the effect of an malfunctioning PMT on the other PMTs for ORCA run 3103. The changes shown are averaged over all 18 DOMs.

4.2.2 Result

Figure 4.3 shows the relative change in relative efficiency ∆QEavg when a specific

(malfunctioning) PMT is switched off, averaged over the 18 ORCA DOMs. De-viations between +3 and −2 % are seen, indicating that a malfunctioning PMT influences the efficiency determination of the remaining PMTs.

Diagonal patterns can be seen in the figure, indicating that the effect of the malfunction PMT is strongest on the nearest neighbour PMTs of the malfunction-ing PMT. These nearest neighbours are not in fact the PMT left or right on the same ring, but the PMTs diagonal in the ring above or below the malfunctioning PMT. This effect is expected, as the expected coincidence rate is largest for nearest neighbour PMT pairs and the efficiency determination is therefore most relying on these pairs.

To investigate the nearest neighbour dependence, the average change in ef-ficiency was plotted against the angular separation between the malfunctioning PMT and the corresponding PMT. This result is shown in figure 4.4. No correla-tion was found however, indicating that the bias might not arise from the model itself, but rather an external bias.

4.2.3 Conclusion

It was thus proposed that the changes in efficiency are partly due to the shadowing of the construction of the DOM. To keep the DOM in place in the sea water, it is placed in a harness which is connected to construction lines. The upper and lower half of the DOM are constructed separately and mounted together with tape to prevent them from deconstructing when deployed in the water. Figure 4.7 shows part of the construction of the DOM.

Some PMTs are more affected by the construction than others. The effect of the construction would come from shadowing in the region between two PMTs, as this region accounts for the highest coincidence rate. Shadowing in this region would cause a lower coincidence rate, leading to a lower determined efficiency.

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40 60 80 100 120 140 160

separation angle [degrees] 0.04 − 0.03 − 0.02 − 0.01 − 0 0.01 0.02 0.03 0.04 [a.u.] abs QE ∆

mean change in rel. QE vs angular separation

Figure 4.4: This figure shows the average change in determined efficiency ∆QEavg

as a function of the angular separation between the malfunctioning PMT and the PMT in question.

When now one PMT starts to malfunction, the determination of the efficiencies relies on the coincidence rates of the other PMTs, thus increasing the weight of the negative effect of the construction.

The simulation of malfunctioning PMTs thus shows the effect of the shadowing by the construction of the DOMs. If the construction is indeed causing these changes, they are expected to be the same for all runs, as the construction stays the same over time. Checking this would verify this hypothesis, and can also provide grounds for a solution. If the same procedure was carried out for multiple runs, and the change in efficiency was determined for each of these runs, then this could provide a blueprint that can be used to correct the efficiencies of the remaining PMTs if a PMT were to malfunction.

4.2.4 Effect of a malfunctioning upper half

To illustrate the effect of malfunctioning PMTs, a malfunctioning upper half of the DOM (rings E and F, corresponding to PMT channels 0 to 12) was simulated using ORCA run 3103. It was shown that the PMTs in the nearest neighbour ring ring D gain an increase in efficiency up to 8%. The PMTs in the next ring -C ring - show an decrease in their efficiency up to −3 %. This result is shown in figure 4.5.

The construction effect in this case comes from the tape between the D ring and the upper half of the DOM. This tape shadows some of the coincidences between the D and E ring, resulting in a lower rate for these PMT pairs, as can also be seen in figure 4.6. This figure shows that the coincidence rates between the D-and lower rings (B D-and C) are higher with respect to the model, than the rates between the D ring and the upper half of the DOM.

The efficiencies of the PMTs in the D ring are a result of the coincidence rates with the (shadowed )upper half and the (less shadowed) lower half. In the case that all PMTs are working accordingly, the efficiencies of the PMTs in the D

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CHAPTER 4. BIASES IN PMT EFFICIENCY DETERMINATION 2 4 6 8 10 12 14 16 18 DOMs 22 A1 14 B1 19 B2 25 B3 24 B4 26 B5 18 B613 C1 21 C2 29 C3 28 C4 20 C5 17 C612 D1 15 D2 23 D3 30 D4 27 D5 16 D610 E1 6 E2 3 E3 2 E4 1 E5 11 E69 F1 8 F2 4 F3 0 F4 5 F5 7 F6 PMTs 0.02 − 0 0.02 0.04 0.06 0.08 rel. QE ∆

Figure 4.5: This figure shows the change in relative efficiency ∆QE when the upper half of the DOM (rings E and F) is switched off for ORCA run 3103.

ring will thus somewhat underestimated. When now the upper half of the DOM is switched off, the lower coincidence rates are not taken into account, and the efficiency determination relies on the higher coincidence raters. The efficiencies of the D ring are thus no longer underestimated, and a increase in efficiency is observed. separation [degrees] 20 40 60 80 100 120 140 160 rate [Hz] 0 2 4 6 8 10 _BD CD DE DF rest Dring-pairs

Figure 4.6: This figure shows the measured coincidence rates as a function of the angular separation of the PMTs for ORCA run 3100. The coincidence rates of all pairs with a PMT in the D ring are marked.

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Figure 4.7: This figure shows the part of the construction of the DOM. The tape that holds the upper and lower half of the DOM together, as well as the harness used to keep the DOM in place are visible.

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Chapter 5 Discussion & Conclusion

5.1 Discussion

This research focused on the efficiency determination of the KM3NeT PMTs, and on possibles biases in this determination. This was done by looking at various aspects of this determination using ORCA runs 3100-3110 and ARCA run 5045. The relative efficiencies of the PMTs used showed to lie between the 0.8 and 1.3,

with a mean relative efficiency of about µQE = 1.15.

The influence of the method used for the estimation of the background in the efficiency determination was also investigated. It was shown that estimating the background based on the single rates of the PMTs (rates method) shows a sys-tematically higher relative efficiency than estimating the background based on the tails region of the difference in arrival time spread (tails method). This systematic difference was as large as 3.5%.

The parametrization of the K40 model used for the efficiency determination was also looked into. This model is based on simulations, and it was found that this model systematically underestimates the measured data, indicating that the PMTs measure more light than expected. This underestimation might arise from a difference in determination of the total coincidence rate between the model and this research. Additional research however is advised to verify the validity of the model.

The relation between the single rate and the determined relative efficiency of a PMT was investigated as well, in order to serve as a crosscheck channel for the determined efficiency. The two quantities were shown to be correlated, thus confirming that the measured single rate of a PMT can be used as a verification of the determined efficiency.

The deviations between the measured single rate and relative efficiencies were investigated, and some asymmetries in the difference between the deviation of an individual single rate from the mean and the deviation from an individual determined efficiency from the mean were observed. These asymmetries were seen in the downwards facing PMTs of the first DOM, which could be explained by the sea floor. Some other fluctuations up to ±2% were seen, which might be due to an inhomogeneous distribution of the K40 salt in the sea water, resulting in different coincidence rates depending on the orientation of the PMTs. Additional research could however look into this.

The effect of malfunctioning PMTs on the determined efficiencies was also in-vestigated. As it turned out, the determined efficiencies of other PMTs change

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CHAPTER 5. DISCUSSION & CONCLUSION

between the +3 and −2 % on average, depending on the orientation with respect to the malfunctioning PMT. It was proposed that this effect comes from the shad-owing of the construction of the DOM. To account for these changes in efficiency, assuming that the construction indeed is responsible, it was proposed to determine a blueprint that can be used to correct the neighbouring PMTs if a PMT were to malfunction.

The malfunctioning of a PMT showed that the construction does indeed influ-ence the measured coincidinflu-ence rate of a PMT pair. This means that the proposed K40 model, which assumes that any difference in measured coincidence rates is due to PMT properties, is oversimplified and should be corrected for the shadowing effect of the construction. Follow-up research can be done to simulate the effect of the construction, and its effect on the determined efficiencies.

5.2 Conclusion

The aim of this research was to investigate how accurately the efficiencies of the PMTs can be determined, and what factors might influence this accuracy. Those factors are listed above, together with their influence on the determined relative efficiency, which accounted for an uncertainty of up to 3.5 %. Combining these uncertainties yield an overall uncertainty of 5% on the determined efficiency. To accurately reconstruct the energy of the measured particles, a smaller uncertainty might be desirable. This can be achieved by additional research on the various background estimation methods or by combining an efficiency determination based on both the measured single rates and the K40 coincidence rates.

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Investigating possible biases in the efficiency determination of the KM3NeT detectors

Searching for Neutrinos in the

Mediterranean Sea