MSc Physics and Astronomy Gravitation and Astroparticle Physics Amsterdam Master Thesis Muonic event reconstruction in KM3NeT-ORCA written by Max Merlijn Briel UvA ID: 10606513 September 2019 60 EC 2018-2019 Supervisor/Examiner: Second Examiner Dr. Ronald Bruijn Dr. Kazu Carvalho Akiba Abstract The KM3NeT collaboration aims to solve the unknown neutrino mass ordering by mea- suring the direction and energy flux of atmospheric neutrinos. At a depth of over 2 kilometres in the Mediterranean Sea, it uses photomultiplier tubes (PMTs) to record Cherenkov radiation from the high-energy neutrino reaction products. A charged current interaction with a muon neutrino leaves a path, named a track, of photon hits through the detector. Using the hits and the properties of the PMTs, the direction of the track is approximated in a process called reconstruction and comprises two successive algorithms. The first generates a set of starting values for the second main algorithm, which uses a maximum likelihood method to find the best fitting track to the data. This research determines that the initial directional accuracy the main reconstruction has to be 10° or lower for the algorithm to achieve its full potential. Since the first algorithm only reaches this limit in 10% of the events, we implement new quality functions and likelihoods in the context of re-ranking and minimisation. They contain different parametrisations of the hit information, which have been developed for this work. We show that the ranking of the main algorithm is optimal in selecting the best track set, but a new likelihood improves their internal ranking. Minimisation with the new likelihoods increases the percentage below the limit up to 25%. A more complete likelihood is introduced with hit and no-hit information. Its like- lihood space shows potential, and minimisation with the truth parameters leads to a significant improvement in the mean directional error from 1:92° to 0:81° compared to the current main reconstruction. 60% of the reconstructed tracks are now at a sub-degree accuracy. However, its likelihood contains many local minima and the pre-reconstruction is not optimised for this comprehensive likelihood putting it at a disadvantage. With better optimisation of the full reconstruction chain, the extended algorithm could provide better constraints on the direction and the neutrino mass ordering. Contents 1 Introduction 3 2 Neutrino Oscillations 6 2.1 The History of the Neutrino . 6 2.1.1 β decay . 6 2.1.2 Neutrino Discoveries: νe νµ ντ ..................... 6 2.2 Neutrino Interactions . 7 2.3 Neutrino Oscillations . 8 2.4 Matter Oscillations . 11 2.4.1 Usage within KM3NeT-ORCA . 12 2.5 Current Parameter Constraints . 12 3 KM3NeT Infrastructure 14 3.1 Neutrino Telescopes: ARCA & ORCA . 14 3.1.1 Photomultiplier Tubes . 15 3.2 Detection Principle . 15 3.2.1 Cherenkov Emission . 15 3.2.2 Interaction Signatures . 16 3.3 Background Sources . 18 3.4 Data Acquisition . 18 3.5 Monte Carlo Simulation . 19 4 Current Muonic Event Reconstruction and PDFs 20 4.1 Track Parameters . 20 4.2 Maximum Likelihood Method . 21 4.3 PMT's Probability Density Functions . 21 4.3.1 Light Emission . 22 4.3.2 Light Propagation . 23 4.3.3 Light Detection . 24 4.3.4 Direct and Indirect Light as PDFs . 25 4.4 The Pre-reconstruction: JPrefit . 27 4.5 The Main Reconstruction: JGandalf . 28 4.6 Other Algorithms: JStart & JEnergy . 28 4.7 Intrinsic Limits of the Reconstruction . 28 5 Evaluation of JGandalf's Input 30 5.1 The Positions of JGandalf's Minima . 30 5.2 Quantifying JGandalf's Directional Input . 32 5.2.1 Deviates from the True Direction . 32 5.2.2 Deviates using JPrefit tracks . 33 5.3 JGandalf's Input Limits . 36 1 5.4 Analysis of JPrefit’s Output . 36 6 Improvements to JGandalf's Input 38 6.1 Optimising JPrefit’s Quality Function . 38 6.2 Introducing the New Likelihoods . 39 6.3 Parametrisation of np.e. ............................ 41 6.4 Re-ranking of JPrefit tracks . 45 6.5 Minimisation . 47 6.6 Discussion of Input Improvements . 49 7 JGandalf Upgraded: JMerlin 52 7.1 JMerlin's Likelihood Space . 52 7.2 Re-ranking of JPrefit and JGandalf tracks . 54 7.3 Minimisation . 54 7.4 JMerlin's Input Requirements . 55 8 Discussion & Conclusion 59 8.1 Analysis of JPrefit and JGandalf . 59 8.2 Upgrading JPrefit’s output . 59 8.3 Extending JGandalf: JMerlin . 60 8.4 Future Improvements . 61 8.5 Conclusion . 62 Appendices 63 A Shower Emission Profiles 64 B JGandalf −LL Scans 66 C Global Minimum Scans 70 D JPrefit Quality Factor Exploration 71 E M-Estimator 73 F Parametrisation of PDFs 76 F.1 Individual Distance parametrisation . 76 F.2 Angle parametrisation . 78 G JGandalf vs JGandalfx vs JMerlin 92 2 Chapter 1 Introduction The Standard Model is the best description of the subatomic world. It contains the 12 known particles, their antiparticles, three fundamental forces with their 4 gauge bosons, and generates mass using a single scalar boson [1{3]. The theory results from many years of theoretical and experimental research and has predicted the existence of new particles, such as the W ±/Z bosons [4{7], gluon [8{11], and the Higgs [12, 13]. The model, however, is incomplete and contains only three of the four fundamental forces. Gravity has been difficult to merge with the microscopic scale of particles. At this moment, its extreme weakness allows it to be safely ignored in experimental predictions [1]. More pressing issues with the Standard Model are at the small scales, such as neutrino masses. Early neutrino experiments, sensitive to only solar electron neutrinos, measured fewer interactions than predicted [14{20]. The most natural explanation was an in-flight flavour change of the neutrino [21]. For example, when an electron neutrino (νe) is created with energy Eν and travels a distance L, it has a probability to be detected as a muon neutrino (νµ). Through the transition νe ! νµ, muon neutrinos appear in the detector, while electron neutrinos disappear, resulting in less than expected νe. Experiments measuring all three neutrino types were consistent with predictions and confirmed the neutrino mixing [22{30]. As a result, neutrinos are massive, which is in contrast with the massless Standard Model neutrinos. The mass states of the three neutrinos have to be unique and the flavour states are a linear combination of these mass eigenstates [31, 32]. The current neutrino oscillation framework comprises three flavours (νe, νµ, ντ ) and three mass eigenstates (ν1, ν2, ν3), although it is still an open question whether more non- interacting neutrinos exist [33]. Eν and L, and a set of constants determine the mixing probability. Most of them are contained within the Pontecorvo-Maki-Nakagawa-Sakata matrix (PMNS matrix) [31,32], which parametrises the mixing using three mixing angles and one CP violating phase, similar to the quark sector [34,35]. The other constants are the squared mass differences between the mass eigenstates. With three eigenstates, two mass differences are independent. So far, experiments are unable to measure the sign of one of the mass differences, which results in a degeneracy in the mass ordering. This is known as the Mass Hierarchy problem, also named the Mass Ordering problem. A promising method for determining the neutrino mass ordering is to exploit the effect of matter on the oscillation probability of neutrinos and antineutrinos [36], which alters the oscillation probability depending on energy, distance travelled, and the electron 3 density of the matter traversed. The ORCA (Oscillation Research with Cosmics in the Abyss) telescope of the KM3NeT (Cubic Kilometer Neutrino telescope) infrastructures plans to use this method with neutrinos and antineutrinos produced by cosmic rays. Cosmic rays are highly energetic charged particles that hit the atmosphere and create a shower of particles including νe/µ and ν¯e/µ. These atmospheric neutrinos oscillate through the Earth and create high-energy interaction products, such as muons, taus, and electrons. ORCA's detector structure is optimised for the 3 to 20 GeV range, where matter effects have a strong presence. It is, however, unable to distinguish between neutrino flavour of the interaction directly. Instead, the detector can only separate two interaction signatures: showers and tracks. Neutrinos interacting with hadrons or electrons through the neutral current cause the former, while charged current interactions from electron neutrinos result in a similar signal. Tracks, on the other hand, are caused by muons that travel far through the detector. They originate from charged current muon neutrino interactions, but the decay of a tau can also generate muons. This thesis focuses on muonic events because of the excellent directional information provided by the long path of the muon through the detector. The muon's direction links back to the amount of matter traversed by the neutrino. Together with the neutrino's energy, they are essential in determining the mixing angles, mass differences, and mass ordering. To balance the extremely small neutrino interaction rate, the detector will encompass 5 megatons of sea water. At a depth of over 2 kilometres in the Mediterranean Sea, the ORCA detector uses photomultiplier tubes (PMTs) housed in pressure-resistant glass spheres called Digital Optical Modules (DOM) to record Cherenkov radiation from the high-energy reaction products. When a photon is registered on a PMT, it records a hit containing the time and duration of the measured signal. From a collection of such hits in combination with the direction and orientation of the PMTs (an event), we approximate the original path of the muon through the detector. This process is called reconstruction and consists of two successive algorithms: JPrefit and JGandalf.