The Search for High Energy Tau Neutrinos Using the Icecube Neutrino Observatory

The Search for High Energy Tau Neutrinos using the IceCube Neutrino Observatory

By Logan James Wille

A dissertation submitted in partial fulﬁllment of the requirements for the degree of

Doctor of Philosophy

at the UNIVERSITY OF WISCONSIN–MADISON 2019

Date of ﬁnal oral examination: April 10th, 2019

The dissertation was approved by the following members of the Final Oral Committee: Vernon Barger, Professor, Physics Paolo Desiati, Senior Scientist, WIPAC Jay Gallagher, Emeritus Professor, Astronomy Francis Halzen, Professor, Physics Kael Hanson, Professor, Physics i

THE SEARCH FOR HIGH ENERGY TAU NEUTRINOS USING THE ICECUBE NEUTRINO OBSERVATORY

Logan James Wille

Under the supervision of Professor Francis Halzen At the University of Wisconsin-Madison

High energy neutrinos provide a new frontier of astrophysical and particle physics research. Astrophysical neutrinos are produced at the same sources as hadronic cosmic rays throughout the universe in many different accelerators. These neutrinos propagate a very long distance to reach the Earth during which they experience oscillations between the flavors, including tau neutrinos which are not produced at the source. Astrophysical tau neutrinos are a clear sign of neutrino oscillations, which can shed light on beyond standard model physics at energy scales and distance scales not yet explored. The signature of the BSM physics can be seen in the flavor ratio of astrophysical neutrinos. However, astrophysical tau neutrinos have not yet been observed by IceCube, this dissertation is on my work to observe astrophysical tau neutrinos. The work presented here is about an improved analysis to observe astrophysical tau neutrinos using novel observation techniques, a critical key in measuring the astrophysical neutrino flavor ratio. Neutrino oscillations, interactions, and observe techniques will be explored along with the methods to improve a previous analysis of IceCube data to observe neutrinos. The main signature used to observe tau neutrinos is a double pulse waveform, where a single DOM observes the Cherenkov light signals associated with both the tau neutrino interaction and the decay of the tau that it produced. This analysis focuses on observing O (100 TeV) tau neutrinos via double pulse waveforms in 8.5 years of data. The analysis observed two neutrino candidates and one probable muon background event which resulting in setting upper limits of tau neutrino flux at 1.1 10−18 E−2.19, 2.5 10−18 E−2.5, and 6.0−18 E−2.9GeV−1cm−2s−1sr−1. × × × × ×

Francis Halzen ii

ACKNOWLEDGMENTS

I first would like to thank my advisor, Francis Halzen, for his help navigating graduate school, allowing me freedom in my research, and understanding my passion for long fly fishing trips. I also want to thank my thesis committee for their time and comments on my dissertation. Thanks to Michelle Holland for helping navigate the graduate school’s rules and arguing on my behalf to the graduate school. To my Friday lunch group who have become my support structure, many thanks, I would not have been able to do this without you. Finally, thanks to my family who have supported my childhood dream to be a physicist.

Untitled. Homemade 6x9 pinhole camera. Logan J. Wille iii

TABLE OF CONTENTS

Page

LIST OF TABLES ...... v

LIST OF FIGURES ...... vi

1 Introduction ...... 1

2 Neutrino Physics ...... 3

2.1 Neutrino Interactions ...... 3 2.1.1 High Energy Lepton Interactions in Ice ...... 5 2.2 Neutrino Oscillations ...... 6

3 Neutrino Fluxes and Flavor Ratio ...... 9

3.1 Neutrino Production ...... 9 3.2 Tau Neutrinos and ﬂavor ratio ...... 12

4 The IceCube Neutrino Observatory ...... 17

5 Tau Neutrino event Selection ...... 22

5.1 General overview and motivation ...... 22 5.2 Double Pulse Algorithm and Local Coincidence ...... 23 5.2.1 The Local Coincidence DPA ...... 25 5.2.2 Local Coincidence Double Pulse Algorithm Veriﬁcation ...... 28 5.3 Topology Cuts ...... 32 5.4 Geometric Containment Cut ...... 36 5.5 Final Sample ...... 43

6 Forward Folding ...... 49

6.1 Forward Folding ...... 49 6.2 Sensitivity ...... 51 6.2.1 Feldman-Counsins Conﬁdence Interval ...... 54 6.3 Event P-Values ...... 57

7 Results ...... 61

7.1 Data Sample ...... 61 7.1.1 2014 Event ...... 62 7.1.2 2015 Event ...... 63 7.1.3 2017 Event ...... 65 7.2 Forward Folding Results ...... 66 7.3 Results Discussion ...... 67 iv

Page

8 Conclusions ...... 70

LIST OF REFERENCES ...... 72 v

LIST OF TABLES

Table Page

5.1 Comparison of the threshold values from the improved local coincidence method to the method used in the previous analysis. These are threshold values for declaring a waveform with two rising edges and a falling edge a double pulse...... 27

5.2 The expected rate of events in the 235 burn sample period...... 41

5.3 The Level 6 ﬁnal sample expected rate of events in the 235 burn sample period...... 44

5.4 The ﬁnal sample expected rate of events in the 8 years of data...... 44

6.1 The average upper limits from 1000 data challenge trials when using a systematic set to create the trial and ﬁtting with the baseline set. All of the systematic sets are close to the baseline set and within the 1 σ variablility of the baseline upper limit. The average upper limit are in units of GeV−1cm−2s−1sr−1...... 55

6.2 The 68% confidence actual coverage when considering the baseline set and systematic sets. All sets have under coverage, though none are significantly different than the baseline coverage. The under coverage issue will be solved by a Feldman Cousins scan, presented in the next section. . 56

7.1 The best fit values of the floating parameters for the three different assumed astrophysical flux spectrums. All astrophysical normalizations are in units of 10−18GeV−1cm−2s−1sr−1...... 67 vi

LIST OF FIGURES

Figure Page

2.1 The Feynman diagrams for charged-current and neutral-current neutrino interactions with a nucleon. The diﬀerence between the two is the weak boson exchanged and the outgoing lepton. .4

2.2 The charged-current and neutral-current cross sections for neutrinos on a single nucleus. The cross section uses CT10 NNLO parton distribution functions [1]. The orange ”This Work” line refers to my work on high energy behavior of cross sections in the paper [2]. The modiﬁcation to the cross section is not important for this work as that is at much higher energies than IceCube can observe...... 4

2.3 A pictorial representation of the neutrino basis projection into the mass eigenstate basis. Where each color represents the ﬂavor contribution to each mass state. This is shown in normal mass ordering. Figure taken from [3]...... 6

3.1 The all particle cosmic ray ﬂux spanning many orders of magnitude in energy. The existence of hadronic cosmic rays guarantees the existence of astrophysical neutrinos. Plot taken from [4]. . . 10

3.2 The decay change of a pion produced by cosmic ray interaction, note this can also be a p γ interaction. The pion decays to a muon and muon neutrino, this muon further decays into an electron, electron neutrino, and muon neutrino. The resulting ﬂavor ratio is 1:2:0...... 11

3.3 The fraction of the atmospheric neutrino ﬂux produced by pions, kaons, and charm particles as a function of energy. As the energy increases the parent particles start to interact with the environment, losing energy, before decaying, reducing the ﬂux of neutrinos from that parent at those energies. Plot from [5]...... 12

3.4 Atmospheric muon and neutrino ﬂux as a function of energy broken down by their parent particle. These ﬂuxes are calculated with SIBYLL 2.3 RC-1 and TIG cosmic ray model. Plots from [6]. . 13

3.5 The flavor ratio of astrophysical neutrinos at Earth. The plot shows the regions of flavor ratio assuming four different flavor ratios at production with current oscillation parameters uncertainties. Regardless of the production flavor ratio the flavor ratio at Earth is close to 1:1:1. Plot from [7]...... 14

3.6 The flux of astrophysical tau neutrinos assuming a 1:1:1 flavor ratio compared to the atmospheric tau neutrino flux [6]. The astrophysical flux is about at least 1.5 orders of magnitude larger than the atmospheric neutrino flux in the region of interest, > 100 TeV...... 15 vii

Figure Page

3.7 Four plots that show the regions of flavor ratio when including possible beyond standard model physics mechanisms to the oscillation mechanics. Each plot assumes a differing production flavor ratio, the most probable two are 1:2:0 or 0:1:0. Note that the allowed regions include flavor ratios that are far from 1:1:1. Plot taken from [7] ...... 16

4.1 The IceCube detector near the geographic south pole buried in the glacial ice. The grey dots between 1450 m and 2450 m are the DOMs that measure and record the light produced by particles interacting in the ice...... 18

4.2 Event view of the three event topologies in IceCube. The single cascade is a spherically symmetric event with a single point light source. The track event is elongated due to the long lived and traveling muon. The double cascade has two spherically symmetric light source, one from the hadronic interaction and the other from the tau decay...... 19

4.3 The waveform of a double pulse event created by a charged-current tau neutrino interacting in IceCube. This is compared to a single pulse waveform created by an electron neutrino interaction. 20

5.1 A double pulse waveform from a tau neutrino charged-current interaction is shown, it shows the ﬁrst pulse rising and fall edge along with the second pulse falling edge. A comparison is a single pulse from a electron neutrino interaction with only one pulse...... 24

5.2 The tau neutrino charged-current event rate versus electron charged current plus all ﬂavor neutral current event rate as a function of LC DPA parameter set thresholds are shown. Each dot is a diﬀerent parameter set, the color represents one the Amp2 parameter in that parameter set. . . 25

5.3 A scan of a promising region from Fig. 5.2, showing the 9:1 signal to single cascade background rate ratio line. Each dot is a diﬀerent parameter set, the color represents one the Amp2 parameter in that parameter set. The parameter set that obtained the highest double pulse signal rate while reaching the (:1 signal to single cascade event rate was chosen...... 26

5.4 The eﬀective area of the Local Coincidence DPA compared to the previous single DOM DPA used in PRD 93.022001. This analysis uses both, shown by the blue line...... 29

5.5 A monte carlo simulation tau neutrino event view is shown. This event passed the LC DPA but not the single DOM DPA, showing what potentially new events can be seen with this analysis. The two grey spheres are the two main losses, the initial neutrino interaction and hadronic decay of the tau lepton, which are 12 m apart. Inset are the two double pulse waveforms that were selected by the LC DPA...... 30

5.6 The distribution of simulated tau neutrinos binned by their true energy. This plot shows the double pulse starts being observable above 100 TeV...... 31

5.7 The total eﬀective livetime of the Corsika monte carlo atmospheric muon sample shown per cosmic ray primary particle. At low energies the statistics are lacking, ideally this would be greater than the livetime considered in the experiment. A saving grace is the muon energy is usually at least a factor of 10 to 100 less than the cosmic ray primary energy...... 32 viii

Figure Page

5.8 The comparison between the burn sample and Corsika simulated events using the six DPA parameters corresponding the the rising and falling edge slope and duration of the double pulses observed...... 33

5.9 The monte carlo expected event rate binned by the charge observed by IceCube compared to the 10% burn sample at level 4. The lower plot shows a ratio of the burn sample data to the simulated atmospheric muons. This level is dominated by atmospheric muons...... 34

5.10 The monte carlo expected event rate binned by the charge observed by IceCube compared to the 10% burn sample when only applying the pre-cuts and LC DPA. The lower plot shows a ratio of the burn sample data to the simulated atmospheric muons...... 35

5.11 The event rate of all simulated particles considered binned by the rLogL diﬀerence between the CscdLLh and SPEFit32 ﬁts compared to the burn sample. The majority of atmospheric muons have negative values whereas the majority of tau neutrinos have positive values. A cut is applied at -0.5, removing any events below this value...... 37

5.12 Distribution of simulated tau neutrinos after the level 5 cuts compared to the level 4 cuts. Overall the rate is reduced due to removing the muon decay mode of the tau lepton. In addition, the high energy tail above 3 PeV is reduced due to the elongation of the events at these energies. . . 38

5.13 The event rate of all simulated particles considered binned by the ﬁrst hit z variable. The majority of atmospheric muons interact at the top of the detector whereas the neutrinos have no dependence of the ﬁrst hit z. A cut is applied at 475, removing any events below this value. . . . 39

5.14 Two event views of burn sample events that represent the remaining atmospheric muon background. (a) is a muon event that passes through DeepCore, skewing the level 5 reconstructions. (b) is a muon event that clips a top corner of IceCube, making it appear cascade like, a muon event can also clip a bottom corner of IceCube...... 40

5.15 The Corsika atmospheric muon sample binned by the muon ratio, Rµ, and the L5 delta rLogL value. At large Rµ values, the event is dominated by a single muon. This plot shows that the sample is dominated by single muon events at level 5 that are cascade like...... 41

5.16 The distribution of the combined Corsika and Muongun sample as described in the text compared to a Corsika only sample and burn sample at level 5. The combined Corsika and Muongun sample agree with the burn sample better than the Corsika only sample...... 42

5.17 The level 5 no DeepCore ∆rLogL distribution of tau neutrinos, atmospheric muon simulated events, and burn sample events. A cut is applied at -0.15, removing all events below this value. . 42

5.18 The distribution of events in the detector using the R250PE CoG position. The atmospheric muons cluster near the edge, top and bottom corners. The pink shaded area are the regions that are removed by the containment cut...... 43

5.19 The expected rate of tau neutrino events as a function of true neutrino energy compared after the level 6 cuts. The overall rate is decreased by about 40% for all energies due to the reduced ﬁdicual volume of the containment cut...... 45 ix

Figure Page

5.20 The charge distribution of the ﬁnal sample after all cuts are applied. Above 104 PE the sample is dominated by tau neutrino events...... 46

5.21 The distribution of the signal tau neutrino, background neutrinos, and their ratio binned in MaxToT1 and Monopod reconstructed energy. Most of the tau neutrinos have reconstructed energies of a few 100 TeV to 1 PeV with at least 26.3 ns long MaxToT1. This can be seen especially in the right most plot, the ratio between the signal tau neutrino event rate to the total event rate is high in these regions...... 46

5.22 The tau-ness score distribution of the ﬁnal sample for the signal tau neutrino events and the background neutrinos. The tau neutrinos generally have large tau-ness scores, showing the tau- ness score does have an ability to show how signal-like the event is...... 47

5.23 The effective area for the three neutrino flavors at the final level of the analysis compared to the previous double pulse analysis this is based on. This analysis has an effective area a factor of 2 larger than the previous analysis, showing the improvements discussed in this section were effective...... 48

6.1 The neutrino monte carlo statistical error per bin relative to the events expected per bin for the chosen binning of the forward folding...... 50

6.2 The distribution of the tau neutrino normalization 90% upper limit for 1,000 data challenges for each assumed spectrum. The median upper limit value is shown for each spectrum as a vertical line...... 52

6.3 The distribution of the tau neutrino normalization 90% upper limit for 1,000 data challenges for each systematic error. The averages of each systematic is shown in the blue band. The 1 σ deviation of the baseline upper limits are shown as the vertical red lines. All of the systematic error averages are within the 1 σ band...... 53

6.4 The distribution of the TS values fo 10,000 Feldman Cousin trials using three diﬀerent example normalizations, 0.1, 1.0, and 5.0. The vertical lines are the point of 90% containment of the trials, those values are the critical values for determining the 90% conﬁdence interval when conducting the likelihood scan...... 57

6.5 The ∆ Log likelihood values found by the Feldman Cousins procedure to determine the 90% conﬁdence interval of the unblinding data. The values are shown for the three spectrums that will be used for the forward folding...... 58

6.6 The TS distribution of background neutrino events for the three diﬀerent spectrums used in this analysis. These distributions will be used to determine the p-value of any events found during the unblinding...... 60

7.1 The distribution of the ﬁnal level expected events compared to the three events observed after unblinding. The expected events assume an 1.01 10−18 E−2.19 GeV−1cm−2s−1sr−1 1:1:1 astrophysical ﬂux...... × . . . .× ...... 61 x

Figure Page

7.2 The two waveforms selected by the double pulse algoritm are shown. These waveforms are on neighboring DOMs and so pass the new local coincidence double pulse selection. The waveform recorded on DOM 20, 27 also passed the previous single DOM double pulse algorithm. The longer duration ﬁrst rising edge hints towards a signal tau neutrino event...... 62

7.3 Event view of the 2014 event, ”Pop Pop”. The interaction point is directly above the dust layer of IceCube that can potentially obscure an outgoing muon. The interaction appears to start inside of the detector volume, so a neutrino event is highly likely...... 63

7.4 The double pulse waveform recorded for this event. Only one DOM recorded a double pulse, the neighboring DOMs have no evident double pulse signature. The first pulse is sharp with a short duration first rising edge and falling edge, suggestive of a muon cherenkov light producing the first pulse. This would be inline with the track like event topology...... 64

7.5 The event view of the 2015 event, ”Britta”. This event starts inside of the detector going in a horizontal direction. There are a few hits on the left side of the detector that hint towards this event containing a muon that leaves the detector. This is in agreement with the p-value and tau-ness score suggesting this is a background event...... 64

7.6 The single waveform picked by the DPA to be classified as a double pulse. Similar to the 2015 event, this waveform has a sharp first peak characteristic of cherenkov light. The first pulse has a short duration first rising edge that tends to be associated with background events...... 65

7.7 The event view of the 2017 event, ”Star-Burns”. From this view it is clear the event is comprised of two atmospheric muons, arriving one after the other. The event on the right side arrives ﬁrst and contains the double pulse waveform, the event on the left arrives after the ﬁrst muon has left the detector...... 66

7.8 The likelihood scan of the tau neutrino astrophysical normalization plotted against the Feldman Cousins scan performed in Chapter 6. The point at which the likelihood curve crosses the critical value determines the 90% upper limit of the tau neutrino ﬂux, this point is denoted with a vertical red line...... 68 1

Chapter 1

Introduction

Neutrinos are one of the least understood known elementary particles, however we do know a substantial amount about neutrinos. Neutrinos are nearly massless, the smallest mass of any massive particle, have a very small interaction cross section, so small they can pass through the entire Earth, come in three different flavor types in between which they can change, and are produced at a variety of places including the sun, Earth atmophsere, galactic, and extra-galactic astrophysical bodies. Due to our lack of understanding of the particle and its unique properties, the neutrino is a very rich topic to study with the potential to affect many different subfields of physics. With the discovery of the diffuse astrophysical neutrinos by the IceCube Neutrino Observatory, that is neutrinos coming from many extra-galatic bodies and at very high energies above 100 TeV, we can explore topics of neutrino oscillations at whole new scales. Tau neutrinos are rarely produced in nature, however there may be a flux of astrophysical tau neutrinos coming from the oscillation of the other astrophysical neutrinos. In this context, measuring tau neutrinos can allow us to study the neutrino oscillations over the very long baseline and high energies never explored before. Tau neutrinos are also rarely directly observed, only 13 tau neutrino candidates have been observed by the human race and none at high energies [8] [9]. This thesis will explore my efforts and results of an analysis for first observation of tau neutrinos in the IceCube Neutrino Observatory. In Chapters 2, 3, and 4 I provide introductory material on neutrinos physics, neutrino fluxes, and IceCube. These chapters also provide motivation for a tau neutrino search in the context of particle physics research and astrophysical neutrino observations. The neutrino physics and fluxes section will cover neutrino interactions, oscillations, astrophysical and atmospheric neutrino production, neutrino flavor ratios, and the particle physics research potential via oscillations to tau neutrinos. Chapter 4 will introduce IceCube and how to observes neutrinos and other events with an emphasis on tau neutrino double pulse events. Chapter 5 will cover in depth the work done to improve on a previous double pulse selection conducted 2 with 3 years of IceCube data. One of the main improvements was the double pulse algorithm by adding a local coincidence double pulse that considers neighboring DOMs waveforms to lower the threshold. The selection improvements resulted in a factor of two increased effective area over the previous analysis which is an important improvement for this analysis as the expected number of tau neutrinos was 1 in 8 years of data. An additional improvement to this analysis was using a forward folding method to measure the astrophysical flux of tau neutrinos from this sample of data which is covered in Chapter 6. Along with a forward folded flux measurement this analysis reports a p-value per event and tau-ness score. The results of the selection applied and fit results using 8.5 years of data is shown in Chapter 7, and finally a conclusion in Chapter 8. This thesis only details my work on the tau neutrino search which was conducted over the last two years of my graduate studies. My other work focused on particle physics phenomenology for IceCube. This work includes ultra-high energy particle cross sections [2], exploration of the prompt atmospheric neutrino flux using forward charm production [10], comparison of double pulse methods for the search of tau neutrinos [11], and the self-veto effect of cosmic ray air showers in neutrino observatories [12]. 3

Chapter 2

Neutrino Physics

Neutrinos are a very special particle, they are the lightest known particle that have mass, only interact through the weak force, pass right through you without interacting, and change between the three types of neutrinos. The types of neutrinos are called ﬂavors, which there are three currently known, electron, muon,

and tau, represented symbolically as νe, νµ, and, ντ . Neutrino mass is one of the concrete pieces of evidence that shows the Standard Model of particle physics is incomplete, as there is no mechanism in the current model to provide mass to the neutrino. Neutrino physics is an area of particle physics that is rich for new research and potential discoveries, however it is difficult to conduct research on as they rarely interact and are difficult to observe. In this chapter we will discuss relevant neutrinos interactions for IceCube, their relation to charged leptons, and their oscillation between flavors.

2.1 Neutrino Interactions

Neutrinos only interact through the weak force, so all of the couplings involve either a W+,− or Z boson. The coupling constants for these bosons are very small compared to other boson coupling constants making the interaction cross section for neutrinos very small. When coupling with a W boson, the three point vertex includes the neutrino and a charged lepton. This charged lepton, electron, muon, or tau, must be the same as the flavor of the neutrino which gives rise to the concept and naming of the neutrino flavor. Neutrinos undergoing an interaction through a Z boson do not produce a charged lepton but instead a neutrino. The two couplings are called a a charged-current, CC, interaction and neutral-current, NC, interaction for W and Z bosons respectively. The interaction vertices are shown in Fig. 2.1. For high energy interactions above 10 GeV, the mediating boson couples with one of the quarks in the nuclei of an atom, depositing a large amount of energy that is enough to blow apart the nuclei. This type of interaction is a deep-inelastic scattering, or DIS. The resulting quarks from the now destroyed nuclei form many short lived hadrons. The cross section for CC and NC DIS interactions differ by a constant that comes from the weak angle phase. The cross section for DIS interactions on a proton are shown in Fig. 2.2. 1

1See the paper [2] for my research on ultra-high energy cross sections, including neutrino cross sections. 4

Figure 2.1: The Feynman diagrams for charged-current and neutral-current neutrino interactions with a nucleon. The diﬀerence between the two is the weak boson exchanged and the outgoing lepton.

30 10− PDF: CT10 NNLO νN X 32 → 10− ] 2 ) [cm

ν 34 10− E ( σ

36 Cooper-Sarkar (2011): CC This Work: NC 10− Cooper-Sarkar (2011): NC Block: CC This Work: CC Block: NC 102 104 106 108 1010 Eν [GeV]

Figure 2.2: The charged-current and neutral-current cross sections for neutrinos on a single nucleus. The cross section uses CT10 NNLO parton distribution functions [1]. The orange ”This Work” line refers to my work on high energy behavior of cross sections in the paper [2]. The modiﬁcation to the cross section is not important for this work as that is at much higher energies than IceCube can observe.

The total neutrino charge (neutral) current cross section for an incident neutrino energy Eν (i.e. s ≈ 2mpEν ) is given by the following expression

Z s Z 1 2 CC/NC 2 ∂ σνp σνp (Eν ) = dQ dx 2 (2.1) 2 2 ∂Q ∂x Qmin Q /s CC/NC 2 with Qmin = 1GeV, Q is the momentum transfer from the neutrino, s is the center of mass of energy, x is the fraction of energy the parton carries from the struck hadron, and 5

2 2 2 2 ∂ σνp GF Mi ν ν ν 2 = 2 2 [Y+FT + (1 y)FL Y−xF3 ] (2.2) ∂Q ∂x 2x Mi + Q − ± 2 2 where Y± = 1 (1 y) with y = Q /(xs), Mi = MW (MZ ) for charge (neutral) current interaction, ± − and “ + ” for neutrinos and “ ” for antineutrinos. In perturbative QCD, at leading order, F ν = 0 whereas − L ν 2 ν 2 the FT (x, Q ) and F3 (x, Q ) can be written as a function of the parton distribution functions, e.g. for a neutrino charge current interaction [13]

 ν ¯  FT = x(u +u ¯ + d + d + 2s + 2b + 2¯c) CC : , (2.3) xF ν = x(u u¯ + d d¯+ 2s + 2b 2¯c) 3 − − − and for a neutrino neutral current interaction

 ν 2 4 ¯  FT = x (1/2 sw + 10/9 sw)(u +u ¯ + d + d)  −  2 4  +(1/2 4/3 sw + 16/9 sw)(c +c ¯) NC : − , (2.4) 2 4 ¯  +(1/2 2/3 sw + 4/9 sw)(s + b +s ¯ + b)  −  xF ν = x (1/2 s2 )(u u¯ + d d¯) 3 − w − − where sw = sin(θw) is the sine of the weak mixing angle. Finally, the antineutrino structure functions for charge and neutral current are obtained by replacing q q¯ and F ν¯ F ν . → 3 → − 3 The variable y that appears in Eq. 2.2 is the inelasticity of the interaction, which is the ratio of the outgoing lepton’s energy to the incoming neutrino energy y = El/Eν . Generally the inelasticity of a neutrino interaction is (0.1). For tau neutrinos, the cross section probability peaks at y 0.66, this is however a O ≈ distribution, and can be any value from 0 to 1. This results in the hadronic interaction created by the struck nuclei and charged lepton to have roughly the same energy.

2.1.1 High Energy Lepton Interactions in Ice

The leptons produced in a charged-current neutrino interaction are called the daughter particle of the neutrino. The lepton produced is the same as the neutrino ﬂavor, so an electron neutrino would produce an electron. These leptons have similar energy loss mechanisms, but the energy at which the energy losses take place diﬀer, electrons experience radiative losses at a much lower energy than muons and taus, and the same for muons compared to taus [14]. This causes electrons to have rapid energy losses in ice and travel only a short distance of only a few meters. Muons are able to travel several kilometers at 100s of TeV, but will have several energy losses during the propagation some of which can happen randomly and be very large, these are called stochastic losses. Tau leptons at energies of 100s of TeV are minimum ionizing, undergoing only very minimal energy losses. However, they are unable to travel very far distances due to their short 6 livetimes. All of these leptons and any other charged particle produce cherenkov light when they travel above the speed of light in ice. This cherenkov light is the main source of light observable for these particles. How these particles are observed in IceCube will be discussed in detail in the next chapter.

2.2 Neutrino Oscillations

As discussed, neutrinos have flavors which are the eigenstates of the electro-weak interaction Hamiltonian. These eigenstates are not the eigenstates of the propagation or in other words, they are not the mass eigenstates. These two eigenstates are slightly misaligned as shown in Fig. 2.3. A neutrino is produced in a flavor eigenstate but propagates through the mass eigenstates. These mass eigenstates have different time evolution due to their differing energetics which causes the relative contributions from each mass state to change from the initial state. The differing mass eigenstate evolution lead to a changing projection back into the flavor eigenstates. In essence, a neutrino of one flavor can be produced, travel a distance and undergo an interaction as a different flavor. This process is called neutrino oscillation which is not a part of the standard model of particle physics and is an important unexplained phenomena.

Figure 2.3: A pictorial representation of the neutrino basis projection into the mass eigenstate basis. Where each color represents the ﬂavor contribution to each mass state. This is shown in normal mass ordering. Figure taken from [3].

The projection of the mass basis, νi into the ﬂavor basis, να , can represented by a unitary matrix U, | i | i X να = Uαk νk . (2.5) | i | i k

U here is represented with mixing angles, θij , and CP phases, δij which are all free parameters, { } { } 7

  −iδ13 c12c13 s12c13 s13e    iδ13 iδ13  U =  s12c23 c12s23s13e c12c23 s12s23s13e s23c13  , (2.6) − − −  iδ13 iδ13 s12s23 c12c23s13e c12s23 s12c23s13e c23c13 − − − where cij = cos θij and sij = sin θij. The full equation for a three ﬂavor, three mass state oscillation in vacuum is complicated and is not fully enlightening, however a simpliﬁed version with only two neutrino types is very enlightening. First we start with the mass eigenstate time evolution, a simple quantum mechanics equation,

−iEkt+ipkx νk(x, t) = e νk . (2.7) | i | i Applying Eq. 2.5 to this equation to we obtain the time evolution of the ﬂavor basis,

X ∗ −iEkt+ipkx να(x, t) = U e νk . (2.8) | i αk | i k

We can express the νk mass state as a ﬂavor state by the inverse of Eq. 2.5m, doing so we obtain, | i

X X ∗ −iEkt+ipkx να(x, t) = U e Uβk νβ . (2.9) | i αk | i β=e,µ,τ k Once here, we use the quantum mechanics method to ﬁnd the probability of one state given another, by multiplying the ket state by a bra state, in this case, we multiply Eq. 2.9 by the νβ state, h |

2 X ∗ −iEkt+ipkx 2 Pν →ν (x, t) = νβ να(x, t) = U e Uβk . (2.10) α β | h i | | αk | k The exponential term can be simpliﬁed by assuming the speed of the neutrino is light speed, and thus t x, ≈

2 2 2 2 Ek pk mk mk Ekt pkx (Ek pk)L = − L = L. (2.11) − ≈ − Ek + pk Ek + pk ≈ 2E Taking this simpliﬁcation and applying it to 2.10, and reorganizing terms we obtain,

which has two terms, the first a constant term, and the second a time evolving term. This second term is what causes neutrino oscillations. Taking a simplified version of Eq. 2.6 with only two neutrinos, this simplifies to, 8

2 2 2 ∆m L Pν →ν (L, E) = sin 2θ sin . (2.13) α β 4E where θ is the mixing angle between the two ﬂavor and mass eigenstates and ∆m2 is the square mass diﬀerence between the mass states. These mixing angles and mass states are free parameters and need to be experimentally found. In a vacuum, the oscillation probability is solely dependant on these free parameters, its energy, and distance traveled. 9

Chapter 3

Neutrino Fluxes and Flavor Ratio

3.1 Neutrino Production

Neutrinos can be produced in many different environments, deep in the Earth’s core, inside the Sun, high in the atmosphere above us, in the Big Bang, and in far away astronomical bodies. For this work, neutrinos above 100 TeV energy are of interest, so we will only discuss atmospheric neutrinos and astrophysical neutrinos. As discussed in Chapter 2, neutrinos only interact via the weak force. This also relates to their production, neutrinos can only be produced through the weak interaction limiting their possible parents to hadrons and heavy leptons. In this chapter, we will discuss the neutrino production via hadronic and lepton decays, their flavor ratio and how it changes from oscillations during propagation, and why tau neutrinos are a keystone to high energy astrophysical neutrino studies. The key ingredient to produce astrophysical and atmospheric neutrinos are high energy cosmic rays. Cosmic rays are nuclei that are accelerated by Galactic and Extragalactic astronomical bodies, and span several orders of magnitude in energy roughly following a power-law distribution as shown in Fig. 3.1 [4]. These cosmic rays form the grandparent particles of the neutrinos, they can interact to create hadronic secondary particles, which will in turn decay into neutrinos. These cosmic rays can interact during their acceleration, during their travel through space, and in the Earth’s atmosphere, we will refer to the first two as astrophysical sources, and the last as atmospheric. We won’t discuss the specific mechanics of the cosmic ray acceleration or their interactions other than how the different environments affect the resulting hadrons and the resulting neutrinos. Because the flux of cosmic rays is distributed according to a power law, the produced neutrinos will also follow a power-law distribution at a similar spectrum, φ E−γ . The × astrophysical neutrino spectral index, γ has been measured to be -2.19 to -2.9 with a normalization, φ (10−18)GeV−1cm−2s−1sr−1 [15, 16]. O For high energy neutrinos the most common parent particles, that is the particle that decayed to create the neutrino, are pions, kaons, and muons. This is due to a two fold effect, one, these particles are commonly created in high energy proton interactions, and two, they decay readily into neutrinos. Pions undergo a decay via a W boson between the u and d quark, which creates a muon and muon neutrino. Due to the 10

Figure 3.1: The all particle cosmic ray flux spanning many orders of magnitude in energy. The existence of hadronic cosmic rays guarantees the existence of astrophysical neutrinos. Plot taken from [4]. mass of the pion being similar to a muon, the muonic channel is the dominant one, occurring nearly 100% of the time [17]. Charged kaons can go through the same decay mechanism as the pion but is suppressed by the Cabibbo angle, resulting in a reduced rate decaying to only a muon and muon neutrino, about 65%, allowing for electron neutrinos to be produced through other decay channels. Neutral K-longs decay through a different process, resulting in a 40% rate to an electron and electron neutrino, and 27% to muon and muon neutrino. Finally, muons decay via a virtual W boson, producing a muon neutrino, a electron, and a electron neutrino. As you can see, the ratio of electron and muon neutrinos produced depends on which parent particles existed and decayed to create the neutrinos. This ratio is called the flavor ratio, and is denoted as νe : νµ : ντ . In low density environments, such as cosmic ray accelerators, all of the particles produced can readily decay. This leads to a 1:2:0 flavor ratio, pions are the most commonly produced parent particle, so their 11 decay chain dictates the flavor ratio. Fig. 3.2 illustrates the decay chain, first the pion decays to a muon and muon neutrino, then the muon decays to a muon neutrino and electron neutrino, resulting in one electron neutrino and two muon neutrinos, thus the 1:2:0 flavor ratio. In higher density cosmic ray accelerators, pions can readily decay, but muons will interact before decaying due to their longer life time. This suppresses the electron component of the neutrino flux, resulting in a ratio close to 0:1:0.

p p ⇡ X

µ ⌫µ

e ⌫e ⌫¯µ

Figure 3.2: The decay change of a pion produced by cosmic ray interaction, note this can also be a p γ interaction. The pion decays to a muon and muon neutrino, this muon further decays into an electron, electron neutrino, and muon neutrino. The resulting ﬂavor ratio is 1:2:0.

For very high density environments, such as the Earth atmosphere, muons, pions, and kaons will interact prior to decaying depending on their energy. Fig. 3.3 shows how the dominant parent particle changes as a function of energy for cosmic rays interacting in the Earth’s atmosphere [5]. The life time of the parent particles dictate this dependence, longer lived particles will interact and lose energy before decaying and at higher energies those particles life time increase in the the lab frame. This energy dependent parent particle gives an energy dependent flavor ratio, going from 1:10:0 at (1 GeV) to 1:1:0 at (1 PeV) and higher. At O O energies above 100 GeV, muons are so long lived that they can reach several kilometers deep into the Earth surface, giving rise to an atmospheric muon flux that is the same magnitude as the atmospheric neutrino flux. The atmospheric fluxes for the three neutrino flavors and muons broken down by parent particles are shown in Fig. 3.4 [6]. At even higher energies, (1 PeV) and higher, pions and kaons live so long that they O cannot decay fast enough before interacting with the Earth’s atmosphere, reducing the flux of neutrinos from those particles significantly. At this energy, a rare class of hadrons that contain a charm quark become the dominant neutrino and muon parent, as seen in Fig. 3.4 due to those charmed hadrons having very prompt decay times. To simplify the discussion of atmospheric neutrinos and muons, those produced by pions and kaons are referred as conventional and those produced by charm hadrons are called prompt. 1

1See the paper [10] for my work on prompt neutrinos.

1 12

Figure 3.3: The fraction of the atmospheric neutrino ﬂux produced by pions, kaons, and charm particles as a function of energy. As the energy increases the parent particles start to interact with the environment, losing energy, before decaying, reducing the ﬂux of neutrinos from that parent at those energies. Plot from [5].

3.2 Tau Neutrinos and ﬂavor ratio

An important aspect of the flavor ratio at production of the atmospheric and astrophysical neutrinos is the lack of tau neutrinos. Tau neutrinos are only produced through the exceedingly rare strange D meson decay resulting in orders of magnitude lower flux for tau neutrinos compared to electron or muon neutrinos. This leads to a very small flux of atmospheric tau neutrinos at energies of hundreds of TeV and higher, as shown in Fig 3.4. Increasing the distance the neutrino travels, to Galactic and intergalactic distances, neutrino oscillations can significantly change the flavor ratio of the flux. As we discussed in the previous chapter, neutrinos have a chance to oscillate from one flavor to another given by a probability dependent on the neutrino energy and distance propagated. For one neutrino source, the flavor ratio at Earth of neutrinos from that source is specified by the oscillation probabilities and the flavor ratio at production. However, the flux of astrophysical neutrinos is not from a single source, but from a large sample of sources, all at different distances, and thus different flavor ratios arriving at Earth. Under the standard model of neutrino oscillations this ensemble of neutrino flavor ratios, regardless of the flavor ratio at creation, tends towards a total neutrino flavor ratio of approximately 1:1:1 [7]. The region the expected flavor ratio at Earth lies, assuming current measured errors of neutrino oscillation parameters with four different flavor ratios at production, is shown in Fig. 3.5 [7]. Observing a flux of tau neutrinos would be an incredibly significant discovery for two reasons; it would be an additional confirmation of astrophysical neutrinos that is independent of the modeling of background atmospheric neutrinos and it would shed light on the neutrino flavor ratio at Earth. As we discussed there 13

Figure 3.4: Atmospheric muon and neutrino flux as a function of energy broken down by their parent particle. These fluxes are calculated with SIBYLL 2.3 RC-1 and TIG cosmic ray model. Plots from [6]. are practically zero atmospheric tau neutrinos and so any observed tau neutrino most likely came from an astrophysical source as shown in Fig 3.6. This is unlike the observed astrophysical electron or muon neutrino flux that has an atmospheric neutrino background on top of it requiring a statistical ensemble of events to confirm the observation. While an additional confirmation of astrophysical neutrinos is not necessary, the existing observations have reached 5 σ, it would be the final puzzle piece for astrophysical neutrinos and a background independent observation is very compelling. Measuring the astrophysical flavor ratio at Earth allows us to explore new regions of particle physics and create possibilities to study beyond standard model physics. The longest baseline of neutrino oscillations that have been studied so far is from the Sun to the Earth, increasing this distance to Galactic and Extragalactic scales allows for very minuscule effects to accumulate that would otherwise be un-observable. These minuscule effects could come from things such as non-unitarity neutrino mixing matrices, Lorentz violation, additional neutrino flavors, non-standard model particle interactions, and many more exotic new physics phenomena [7]. In addition to the cumulative effect over a long baseline, there exists a possibility of energy dependent 14

0.0 1.0 (1 :2 :0) (1 :0 :0) 0.2 0.8 (0 :1 :0) (0 :0 :1)

⊕ 0.4 0.6 α τ α µ ⊕

0.6 0.4

0.8 0.2

1.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0

αe⊕

Figure 3.5: The flavor ratio of astrophysical neutrinos at Earth. The plot shows the regions of flavor ratio assuming four different flavor ratios at production with current oscillation parameters uncertainties. Regardless of the production flavor ratio the flavor ratio at Earth is close to 1:1:1. Plot from [7]. new physics affecting the neutrino oscillations. These astrophysical neutrinos extend to considerably higher energies than any previous oscillation study, allowing us to probe these possible energy dependent propagation terms. These new physics can effect the neutrino oscillations by driving the overall flavor ratio away from 1:1:1, as shown in Fig. 3.7. If the measured flavor ratio is not near 1:1:1 this would provide a hint for exciting new physics that could break down the door for a new era of particle physics. However, a flavor ratio near 1:1:1 would exclude certain models of new physics, and help push the physics community in other directions that are more promising. While this thesis work does not aim to measure the astrophysical flavor ratio, an important first step to measure it is observing tau neutrinos. 15

10 7

10 8

10 9

10 10

Atmospheric Tau Neutrino Astrophysical Neutrino E^2 dN/dE (10^-18 GeV^-1 cm^-2 s^-1 sr^-1) 10 11 104 105 106 107 Neutrino Energy (GeV)

Figure 3.6: The flux of astrophysical tau neutrinos assuming a 1:1:1 flavor ratio compared to the atmospheric tau neutrino flux [6]. The astrophysical flux is about at least 1.5 orders of magnitude larger than the atmospheric neutrino flux in the region of interest, > 100 TeV. 16

Figure 3.7: Four plots that show the regions of flavor ratio when including possible beyond standard model physics mechanisms to the oscillation mechanics. Each plot assumes a differing production flavor ratio, the most probable two are 1:2:0 or 0:1:0. Note that the allowed regions include flavor ratios that are far from 1:1:1. Plot taken from [7] 17

Chapter 4

The IceCube Neutrino Observatory

As established in the previous chapter, observing astrophysical tau neutrinos can have provide important measurements of physics that impacts not only astrophysics studies, but also beyond standard model particle physics. Neutrinos, though difficult to detect as we discussed in Chap. 2, only interact through the weak force and require a very large detector to observe any appreciable amount. In addition neutrinos can only be observed indirectly through the secondary particles they produce in an interaction. In this chapter I will discuss the IceCube neutrino observatory, a particle detector specifically constructed to detect high energy astrophysical neutrinos. In addition, I will discuss how tau neutrinos interactions appear in the IceCube detector and different ways of identifying them. The IceCube detector is a 1 km3 volume of ice that is instrumented by 5,160 Digital Optical Modules, DOMs. Each DOM consists of a photomultiper tube, PMT, electronics to digitize the waveform the PMT outputs, and other elements. The ATWD waveform recorded is the voltage output of the PMT in 3.3 ns time bins, which corresponds to the amount of light striking the PMT as a function of time. The DOMs are placed on strings which are vertical cables providing power and communication to the surface for the DOMs. Each string holds 60 DOMs spaced 17 m apart, except for 8 strings which have a shorter spacing of 7 m for the bottom 50 DOMs and 10 m for the other 10 DOMs. The strings with shorter spacing comprise a denser instrumented section at the bottom middle part of IceCube called DeepCore. The 78 strings with 17 m spacing are spaced 125 m apart in a hexagonal pattern. These 78 strings comprise the majority of the IceCube detector volume. The detector is located near the geographical South Pole where the ice is very clear with long absorption lengths. The instrumented volume is between 1450 m and 2450 m below the surface of the glacial ice. The structure of IceCube in the glacial ice is shown in Fig. 4.1. The sparse nature of IceCube limits it’s ability to observe lower energy neutrinos but excels at higher energy neutrinos, sensitive to neutrinos of energies (5 GeV) to (10 PeV). O O The large volume of IceCube increases the number of neutrinos interacting inside it allowing for the study of astrophysical neutrinos. These neutrinos are observable by the secondary particles produced in their interaction with the ice. These observable secondary particles include the daughter charged lepton of 18

Figure 4.1: The IceCube detector near the geographic south pole buried in the glacial ice. The grey dots between 1450 m and 2450 m are the DOMs that measure and record the light produced by particles interacting in the ice. the neutrino, electrons, muons, photons, and hadrons. Other than the daughter lepton, these secondary particles are produced by the struck ice nuclei breaking apart or the charged daughter lepton. These charged particles travel faster than the speed of light in ice causing cherenkov light to be produced which can be observed by the DOMs. The cherenkov light can travel a considerable distance, up to a few 100 meters in the clearest ice, allowing multiple DOMs to observe the light produced from a single point [18]. The topology of the event observed depends on which daughter lepton is produced. As discussed in chapter 2 the leptons in the range of a few 100 Tev to 1 PeV can travel varying distances, electrons travel short distances of a few meters, muons travel hundreds of meters, and taus travel a few meters to 10s of meters before decaying. Muons and long lived taus travel an appreciable distance away from the neutrino interaction vertex. These leptons can produce other particles or light which create spatially elongated events compared to single point-like events that do not contain muon or tau leptons. The elongated events are referred to tracks or double cascades. For leptons that travel shorter distances, such as electrons and low energy taus, they will have a single point-like event. We can classify these topologies into three catagories, tracks, cascades and double cascades. Track events are produced by muons and muon neutrino undergoing charged-current interactions. Cascades are produced by electron neutrinos, short lived tau leptons, and all three neutrinos undergoing neutral-current interactions. Double cascades are produced by very high energy tau neutrinos undergoing charged-current interactions and the subsequent tau lepton decaying via hadrons or electron, creating two distinct, separate cascades. The distance between these two cascades are set by the 19

(a) Single Cascade (b) Track (c) Double Cascade

Figure 4.2: Event view of the three event topologies in IceCube. The single cascade is a spherically symmetric event with a single point light source. The track event is elongated due to the long lived and traveling muon. The double cascade has two spherically symmetric light source, one from the hadronic interaction and the other from the tau decay. tau lifetime, which is variable and correlated to the tau lepton energy. Event views of these topologies are shown in Fig. 4.2. Event views in IceCube are shown in colored bubbles per DOM, the size of the bubble is proportional to the charge observed by the DOM and the color relates to when the DOM first saw light, red being early, blue late. Besides neutrinos, IceCube observes atmospheric muons, that is muons that are created in cosmic ray interactions in the atmosphere. The flux of atmospheric muons is not substantially higher than that of neutrinos, but are observed at a rate several orders of magnitude higher than neutrinos due to a cross section being several orders of magnitude larger. Atmospheric muons create track events in IceCube with an additional constraint, they only enter from above as the Earth shields the detector from the other directions. In addition, the atmospheric muons produce light as they enter the detector, so the events are first observed near the edge of the detector as opposed to neutrinos which can be first observed in any part of the detector volume. 1 Thankfully, tau neutrinos have a distinct interaction in the IceCube, so observing them becomes a task of searching for their unique topology. This topology is called a double bang event, which is where a tau neutrino undergoes a charged-current interaction and they produced tau lepton decays hadronically or through an electron, which produces exactly two large energy losses. The first from the initial hadronic interaction with a nuclei of an ice molecules and the second from the tau lepton decaying. As discussed in chapter 2 tau leptons have a low interaction cross section and can travel freely through the ice without losing

1See the paper [12] for my research on atmospheric muons in IceCube. 20

energy, but their livetime is very short, they decay rapidly not far from their creation point. These traits of the tau lepton make the tau neutrino interaction unique, no other neutrino has an interaction resulting in a localized interaction with two losses. The distance that a tau lepton travels is directly related to its energy. The average distance traveled as a function of energy can be found by time dilation δt0 = γ δt, energy × E = γ mτ , and distance traveled d = v t. Combining these along with the tau lepton mass and lifetime, × × −13 mτ = 1776.82 MeV, ττ = 2.906 10 s, you obtain Eq. 4.1, ×

E 4.909 m d(E) = × . (4.1) 100 TeV The ﬂux of astrophysical tau neutrinos is a falling spectrum, meaning there are considerably more low energy neutrinos than high energy neutrinos, a factor of 10−2 per energy decade. This results in far more low energy events and thus, tau neutrino events with tau leptons that travel on the order of 10s of meters are far more common than tau lengths of 100s of meters. When a tau lepton travels only a few 10s of meters IceCube is unable to easily resolve the position of the two energy depositions due to the sparse nature of the detector, making an event that looks like a single cascade. However, a single DOM can easily detect the light arriving from the initial interaction and tau lepton decay. When the two light pulses are well separated, they appear as two bumps in the waveform, as shown in Fig. 4.3. For a DOM to observe this type of waveform it needs to be near the interaction point, otherwise the light pulses can start to merge and wash out due to travel time and scattering in the ice. This type of waveform is referred to as a a double pulse, and can be used to detect tau neutrino events with short lived tau leptons.

Figure 4.3: The waveform of a double pulse event created by a charged-current tau neutrino interacting in IceCube. This is compared to a single pulse waveform created by an electron neutrino interaction.

This work focuses on finding these lower length and energy tau double pulse events by using a specialized algorithm which will be discussed in the next chapter. It leverages the differences in the event topologies 21 discussed in this chapter, first, looking for double pulse waveforms in individual DOMs to separate double pulse events from single cascades. And next, measuring how track-like or cascade-like the event is to remove atmospheric muon and muon neutrino events from the cascade-like double pulse event. 22

Chapter 5

Tau Neutrino event Selection

5.1 General overview and motivation

As we have established in chapter 4, IceCube can detect tau neutrinos. However, as discussed in 2, tau neutrinos are rare particles can be difficult to distinguish from other neutrino flavors. In order to observe a tau neutrino in the IceCube data, we need to apply significant cuts to reduce the background events, non-double pulse tau neutrinos, electron neutrinos, muon neutrinos, and atmospheric muons. We target to remove these backgrounds in three different steps, called cut levels. The first level is a double pulse algorithm, DPA, which focuses on selecting double pulse tau neutrinos and rejecting single cascade events and tau neutrinos that do not produce a double pulse. The second is a topology cut, where we select cascade- like events and reject longer, track-like events created by muons and muon neutrinos. Finally, we have a containment cut that selects only events that start inside the detector, which excludes the last remaining atmospheric muons. This analysis improves on a previously performed IceCube NuTau double pulse analysis [19]. This previous analysis, which will be referred to as PRD, constructed the general event selection framework to select double pulse Tau Neutrino events. The PRD analysis used 3 years of IceCube data and observed zero double pulse events, which was not unexpected as the expected number of signal events was 0.45 events, assuming an 1 10−18E−2GeV −1cm−2sr−1s−1 astrophysical neutrino flux. If this analysis was performed × using the full 8 years of IceCube data the expected signal rate, assuming a more realistic neutrino flux, would still be below 1 event. This low rate of signal events along with better understanding of the IceCube detector and more available monte carlo statistics, motivated me to take the PRD analysis and improve the event selection by modifying all of the cut levels to increase the signal efficiency. Overall the improvements that I implemented increased the signal rate by roughly a factor of 2, increasing the expected signal events to be 1.8 in 8 years of IceCube data. In this chapter I will discuss in detail the various cuts used to create the double pulse selection along with the improvements of the cuts from the previous PRD analysis. I will also discuss the physical motivation of each cut and what new information or technique allowed me to create the improvements. 23

To optimize the cuts presented here, I used monte carlo simulated events. This monte carlo simulation was split into the different particle types: electron, muon, and tau neutrino along with atmospheric muons. This split allows to examine the performance of the cut as it’s being created to maximize efficiency and purity of the final sample. The neutrino simulation has events randomly injected from all directions and over an energy range of 5 TeV to 100 PeV with an E−1.5 spectrum. The neutrinos were weighted by the interaction and Earth propagation probabilities along with re-weighting to a astrophysical flux of 0.9 × 10−18E−2.13GeV −1cm−2sr−1s−1 in addition to an atmospheric flux. Each neutrino flavor had a total of 500,000,000 events simulated. The muon simulated events will be discussed later in this chapter.

5.2 Double Pulse Algorithm and Local Coincidence

To begin the selection process, we apply two pre-cuts to significantly reduce the amount of events. As discussed in 4, double pulse events are only observable in energetic, bright events, and in DOMs near the interaction vertex. The energy threshold for a double pulse event in IceCube is roughly 100 TeV, below this energy, the secondary tau lepton tends to decay too rapidly to produce a pulse that is clearly separate from the initial neutrino interaction pulse. Therefore, events with less than 2000 total detected photoelectrons (PE) are rejected, which corresponds to roughly 10 TeV neutrino energy. We place the pre-cut below the tau neutrino double pulse energy threshold due to it not being a hard threshold and to ensure no events are lost. Next we apply a cut to individual DOM waveform charge, the double pulse signal is only observable to DOMs very close to the neutrino interaction point, so we apply a cut of 432 PE to remove DOMs far from the event vertex. The light from the neutrino interaction and tau decay become scrambled together at long distances due to the scattering effect of ice, thus only DOMs near the event vertex can distinguish the two pulses. These two pre-cuts dramatically reduce the amount of data that is processed, the 2000 PE total charge cut reduces the event stream by about 99.999% or 5 orders of magnitude. The individual DOM charge cut reduces the data analyzed per event by 90% to 99.94%, as on average only 3 DOMs pass this charge cut per event compared to the 5160 DOMs in the entire IceCube array. The original double pulse algorithm (DPA) was designed to find double pulse waveforms in individual DOMs while rejecting single pulse waveforms. The necessary features to identify a double pulse are the rising and falling edge of the first pulse and the rising edge of the second pulse. A second pulse falling edge is not necessary to search for as it is a guaranteed feature and offers no discriminating power. An example double pulse waveform is shown in Fig. 5.1. First a sliding time window is used to find the start of the waveform pulse. Then the rising and falling edges are found by calculating the time derivative of the waveform averaged over 4 ATWD time bins, a 13.2 ns period. Once the necessary edges are found, their duration and steepness are determined and used to decide if the waveform is a double pulse. Though these 24 features themselves are obvious, at what threshold should a rising edge and falling edge be called a pulse is not. One of the issues is the size of the two pulses is variable, a lower energy interaction near a DOM can look the same as a higher energy pulse far from a DOM, and the ratio between the first and second pulse is a distribution. In addition, the timing structure between the two pulses is a distribution according to the tau lifetime, as discussed in 2. Due to the lack of constraints on these features, a general minimum threshold for all the features is the most efficient for selection.

Figure 5.1: A double pulse waveform from a tau neutrino charged-current interaction is shown, it shows the ﬁrst pulse rising and fall edge along with the second pulse falling edge. A comparison is a single pulse from a electron neutrino interaction with only one pulse.

In the original PRD analysis, two thresholds were created, one which was optimized to select all pre- hand selected double pulse events, the second to maximize the number of double pulse events with a low background event rate. The two thresholds had an expected signal rate of 0.72 and 0.29 tau neutrino events per year respectively. The issue with the former selection was a substantial electron neutrino single cascade background rate. Electron neutrinos and neutral current neutrino interactions can create a fake double pulse due to noisy waveforms, prepulsing, and late scattered light. To reduce this background, the second threshold increased the the minimum steepness and duration of the trailing and 2nd rising edge pulses. However, this more than halved the rate of signal tau neutrino events. The PRD analysis used the 2nd threshold configuration to ensure high sample purity. With this established method, it was clear that there is a significant optimization possible that can increase the number of tau neutrino events that potentially can be observed. One of the features that the original method failed to use was that a double bang can create double pulse features that appear in multiple DOMs near the event vertex. This is contrast to a single cascade event which generally only makes a double pulse-like feature in a single DOM, due to the statistical fluctuation nature of the fake double pulse. We 25 can take advantage of this feature by looking at pairs of neighboring DOMs to see if they both have double pulse-like waveforms, in which case a lower threshold can be used without increasing the background rate.

5.2.1 The Local Coincidence DPA

The main enhancement my work focused on for the DPA was incorporating the neighboring DOM double pulse feature and optimizing the thresholds for these neighboring DOMs. This additional requirement is referred to as local coincidence (LC). The local coincidence requires two DOMs that are nearest neighbors or next-to-nearest neighbors on the same string to have both passed the LC DPA threshold. The threshold for both neighboring DOMs is the same in order to reduce the complexity of the threshold. The choice to allow nearest and next-to-nearest DOMs was to ensure the largest flexibility of the LC DPA, IceCube contains DOMs that are non-functioning and to not punish the region around those DOMs next-to-nearest local coincidence was chosen. The difficulty with optimizing the LC DPA threshold is there are 6 independent parameters, the 1st, 2nd and falling edge steepness and duration, that makeup the threshold to declare a waveform a double pulse. To optimize the thresholds, I first extracted the DPA features for both signal tau neutrinos and background electron neutrino monte carlo events that passed a very minimal threshold using the original DPA code. I then scanned over the 6 DPA parameters to create 14,000 LC DPA thresholds each with a unique set of parameters. These 14,000 LC DPA thresholds were then applied to the extracted DPA features of the tau and electron monte carlo events, recording the event rates for each threshold, shown in Fig. 5.2.

9 1.0 8

0.8 7

6 0.6

5 Amp2

0.4 4

Double Pulse Events/year 3 0.2 2

0.0 1 0 1 2 3 4 5 6 7 Single Cascade Background events/year, NuTau NC

Figure 5.2: The tau neutrino charged-current event rate versus electron charged current plus all ﬂavor neutral current event rate as a function of LC DPA parameter set thresholds are shown. Each dot is a diﬀerent parameter set, the color represents one the Amp2 parameter in that parameter set. 26

After these 14,000 DPA thresholds, another scan was performed in the promising region threshold region. It was chosen that the signal to single cascade background rate should be at least 10:1 to ensure a good event selection purity. The LC DPA threshold was picked that resulted in the highest signal event rate that passed this signal to background rate of 9:1, this can be seen in Fig. 5.3, the second scan, over a promising region, is shown in Fig. 5.2. The threshold is shown in Table 5.1 and compared to the original DPA threshold.

18.0 0.6 16.5

0.5 90% Purity 15.0

13.5 0.4 12.0

0.3 Amp2 10.5

0.2 9.0 Double Pulse Events/year 7.5 0.1 6.0 0.0 0.00 0.05 0.10 0.15 0.20 0.25 Single Cascade Background events/year, NuE + NC

Figure 5.3: A scan of a promising region from Fig. 5.2, showing the 9:1 signal to single cascade background rate ratio line. Each dot is a diﬀerent parameter set, the color represents one the Amp2 parameter in that parameter set. The parameter set that obtained the highest double pulse signal rate while reaching the (:1 signal to single cascade event rate was chosen.

As seen in Table 5.1, the LC DPA threshold allows for smaller and shorter duration pulses than the PRD DPA algorithm. One of the largest differences is the first rising edge and following trailing edge thresholds being significantly smaller. A first rising edge is a feature in both single cascade and double cascade events and so is not a good discriminator between background and signal. However, in the original method the first rising edge threshold was large to reduce prepulsing single cascade events. Prepulsing is a process in which incoming light excites electrons that skip the dynodes of the PMT and are received in the anode prior to the electrons coming from the dynodes. In the improved method this background is not a concern because prepulsing is a random process and rarely occurring in multiple DOMs in an event.

ντ interactions tend to have low inelasticity because of mass threshold effects of τ production, which manifests in IceCube as a small first energy deposition and more energetic second deposition. Decreasing the first pulse threshold makes this low inelastic phase space observable. Additionally the overall decrease in the double pulse thresholds makes lower energy ντ events observable. Both of these effects increase the effective area, as shown in Fig. 5.4. Overall the LC technique has a 50% increase in signal rate over the 27

LC Method PRD 93.022001 1st Rising Edge Steepness >1 mV/ns >10 mV/ns 1st Rising Edge Duration >13.2 ns >26.4 ns Falling Edge Steepness <-0.5 mV/ns <-17 mV/ns Falling Edge Duration >26.4 ns >26.4 ns 2nd Rising Edge Steepness >12 mV/ns >18 mV/ns 2nd Rising Edge Duration >39.6 ns >39.6 ns

Table 5.1: Comparison of the threshold values from the improved local coincidence method to the method used in the previous analysis. These are threshold values for declaring a waveform with two rising edges and a falling edge a double pulse. 28 previous technique while maintaining a similar signal purity. A Monte Carlo event that passes the improved selection that would have been previously rejected is shown in Fig. 5.5. With the LC DPA the duration of the first rising edge is reduced, while this at first glance might just appear to allow smaller first pulses to pass the DPA threshold, the shorter pulse duration also allows for events with shorter tau livetimes to pass the threshold. In a hypothetical situation of a ντ interacting very close to a DOM, the shortest lived tau that could pass the LC DPA is 17.14 ns, which corresponds to the tau traveling 5.14 meters. This is in comparison to the PRD DPA which could only observe taus living longer than 22.86 ns, or taus that traveled further than 8.86 meters. Also investigated for this analysis was multi-neighboring DOM DPA. It was found that a LC DPA that considered three neighboring DOMs to all observe double pulse waveforms did not significantly reduce the thresholds or increase the expected event rate. For this reason, the analysis only considered pairs of DOMs for the local coincidence. For the event selection of the tau neutrino analysis, a combination of the LC DPA and PRD DPA was used. It was found that some events only passed the original single DOM PRD DPA selection, specifically very high energy events. To ensure the largest effective area, the combination of allowing events to pass either the LC DPA or the PRD DPA was used. These two along with the pre-cuts formed the Level 4 selection of the analysis which was then passed to the next level of cuts. In Fig. 5.6 the energy of the tau neutrinos that pass the double pulse cut is shown. There is a clear minimum energy around 100 TeV required for a tau neutrino to create a double pulse.

5.2.2 Local Coincidence Double Pulse Algorithm Veriﬁcation

With the established DPA that is a combination the PRD DPA and LC DPA, the next step is to verify its operation with real world data. However, this analysis is designed to be a blind analysis, that is, an analysis that does not look to optimize itself using real world data, and minimizes the amount of real world data seen during development. This blind analysis policy is put into place to minimize bias from the scientist constructing the analysis. For this analysis, only 10% of the data collected by IceCube was used to verify the data selection, this data is called the burn sample. As discussed in chapter 3, atmospheric muons are a dominant background for IceCube, and after the DPA cut, they make up the vast majority of the data selected. In order to verify the DPA cut with the burn sample, a monte carlo sample of simulated atmospheric muons is needed. This monte carlo simulation is created by the program Corsika, which simulates cosmic rays interacting in the Earth atmosphere and the produced muons from these interactions [20]. One of the largest difficulties with the atmospheric muon background simulation is obtaining enough statistics, as shown in Fig. 5.7 the effective livetime is only sufficient above 5 PeV, however a saving grace is the muon energy is usually at least a factor of 10 to 100 29

102 Local Coincidence method Single DOM (PRD.93.022001) SD + LC Level 4 101 ) 2 m (

e 0 r 10 A

e v i t c e f f 10 1 E

10 2

102 103 104 Tau Neutrino Energy (TeV)

Figure 5.4: The eﬀective area of the Local Coincidence DPA compared to the previous single DOM DPA used in PRD 93.022001. This analysis uses both, shown by the blue line. 30

Figure 5.5: A monte carlo simulation tau neutrino event view is shown. This event passed the LC DPA but not the single DOM DPA, showing what potentially new events can be seen with this analysis. The two grey spheres are the two main losses, the initial neutrino interaction and hadronic decay of the tau lepton, which are 12 m apart. Inset are the two double pulse waveforms that were selected by the LC DPA. 31

0.025 Level 4

0.020

0.015

0.010

0.005 Tau Neutrinos in 235 days

0.000 104 105 106 107 108 True Neutrino Energy

Figure 5.6: The distribution of simulated tau neutrinos binned by their true energy. This plot shows the double pulse starts being observable above 100 TeV. less than the cosmic ray primary energy.. This issue will be discussed in greater detail in section 5.4. To verify the DPA cut, we compare the six DPA variables between the Corsika simulation and the burn sample for any event that passes the DPA cut. One note, a single event can have multiple double pulse waveforms that contribute to this comparison. For the Corsika simulation we give each waveform parameter a weight equal to the event weight they came from. This possibly introduces a bias to the Corsika waveform parameters as the data was simulated at a hard spectrum and high energy events tend to have higher number of double pulse waveforms, thus increasing the rate of Corsika waveforms. We however have not determined a better way of handling the weight in a manner that guarantees no bias. The six different DPA variables for the Corsika, burn sample, and the three neutrino flavors are shown in Figs. 5.8. These plots illustrate a general agreement between the real data burn sample and simulated Corsika sample. However, there is a disagreement, this in part is due to the weighting bias discussed earlier, and in part due to imperfect Corsika simulation. The shape of the corsika curves can vary depending on the chosen model for the cosmic ray flux. In addition, the corsika simulation is using an older interaction model, which can change the shape of these histograms. We can also compare event-wise data to verify the DPA cut. One general quantity that is often compared is the total charge, QTot, seen by the IceCube detector during the event. This quantity is relatively low level and doesn’t depend on any reconstruction. The comparison between burn sample and simulated Corsika is shown in Fig. 5.9. In addition, we can compare the QTot for events that only pass the LC DPA cut, this is 32

104 Protons 3 Helium 10 Nitrogen Aluminum 102 Iron

101

100

10-1

-2 Livetime (Years) 10

10-3

10-4 103 104 105 106 107 108 109 Primary Energy (GeV)

Figure 5.7: The total eﬀective livetime of the Corsika monte carlo atmospheric muon sample shown per cosmic ray primary particle. At low energies the statistics are lacking, ideally this would be greater than the livetime considered in the experiment. A saving grace is the muon energy is usually at least a factor of 10 to 100 less than the cosmic ray primary energy. shown in Fig. 5.10. These two comparisons agree quite well and show that the DPA cut is not acting oddly between the simulated data and real data.

5.3 Topology Cuts

As seen in Fig. 5.9, the number of muon and muon neutrino events dominate the selection after the DPA cut, the next cut in this event selection is designed to remove the vast majority of these two types of background events. Muon related background events can pass the DPA cut easily because muons can have multiple energy losses close in time, which create a multiple pulse signature that the DPA selects for. The ﬂux of muons and muon neutrinos is considerably higher than tau neutrinos and so they dominate the selection. However, muons are also long lived compared to the tau lepton, and so can travel several kilometers through the ice. These long muons create events, called track events, that extend through the detector which are distinct from the very localized tau neutrino events, called cascade events. We can leverage this topological diﬀerence between the event types to create a cut that predominantly removes the muon related backgrounds while keeping the majority of tau neutrino events. To classify an event as either cascade or track we can apply reconstructions that assumes the event is 33

105 105 105 4 Astro. NuTau CC 4 Astro. NuTau CC 4 Astro. NuTau CC 10 Astro. NuMu CC 10 Astro. NuMu CC 10 Astro. NuMu CC 103 Astro. NuE CC 103 Astro. NuE CC 103 Astro. NuE CC 2 Corsika 2 Corsika 2 Corsika 10 Burn Sample 10 Burn Sample 10 Burn Sample 101 101 101 100 100 100 10-1 10-1 10-1 10-2 10-2 10-2 10-3 10-3 10-3 10-4 10-4 10-4 10-5 10-5 10-5 -6 -6 -6

Double Pulse Waveforms in 235.0 Days 10 Double Pulse Waveforms in 235.0 Days 10 Double Pulse Waveforms in 235.0 Days 10 0 100 200 300 400 500 0 50 100 150 200 250 300 0 100 200 300 400 500 2.0 2.0 2.0 1.8 1.8 1.8 1.6 1.6 1.6 1.4 1.4 1.4 1.2 1.2 1.2 1.0 1.0 1.0 0.8 0.8 0.8

Data/Corsika 0.6 Data/Corsika 0.6 Data/Corsika 0.6 0 100 200 300 400 500 0 50 100 150 200 250 300 0 100 200 300 400 500 1st Rising Edge Steepness (dV/dt) 1st Rising Edge Duration (ns) Falling Edge Steepness (dV/dt)

(a) Amp1 (b) ToT1 (c) AmpT

Double Pulse Waveforms in 235.0 Days 10 Double Pulse Waveforms in 235.0 Days 10 Double Pulse Waveforms in 235.0 Days 10 0 50 100 150 200 250 300 0 100 200 300 400 500 0 50 100 150 200 250 300 2.0 2.0 2.0 1.8 1.8 1.8 1.6 1.6 1.6 1.4 1.4 1.4 1.2 1.2 1.2 1.0 1.0 1.0 0.8 0.8 0.8

Data/Corsika 0.6 Data/Corsika 0.6 Data/Corsika 0.6 0 50 100 150 200 250 300 0 50 100 150 200 250 300 350 400 450 0 50 100 150 200 250 300 Falling Edge Duration (ns) 2nd Rising Edge Steepness (dV/dt) 2nd Rising Edge Duration (ns)

(d) TbT (e) Amp2 (f) ToT2

Figure 5.8: The comparison between the burn sample and Corsika simulated events using the six DPA parameters corresponding the the rising and falling edge slope and duration of the double pulses observed. 34

103 102 101 100 10-1 10-2 10-3 -4 10 Astro. NuTau CC -5 Astro. NuMu CC 10 Astro. NuE CC 10-6 Corsika

Double Pulse Events in 235.0 Days Burn Sample 10-7 104 105 106

1.4 1.2 1.0 0.8 0.6 Data/Corsika 103 104 105 106 107 QTot

Figure 5.9: The monte carlo expected event rate binned by the charge observed by IceCube compared to the 10% burn sample at level 4. The lower plot shows a ratio of the burn sample data to the simulated atmospheric muons. This level is dominated by atmospheric muons. a cascade and another that assumes the event is a track. The likelihood value of the resulting cascade and track best fits are a measure of how well each the event topology fits with the two different assume event types. A single value to cut on for this topology difference can be constructed by taking the difference between the reduced log likelihoods of the two fits. The reduced log likelihood is the log of a the likelihood divided by the number of struck DOMs of the event. This is to normalize the likelihoods between events, as events with large numbers of struck DOMs results in a larger likelihood than one with small number of struck DOMs. Due to the high volume of events at this stage of selection, the techniques used to separate the muon events need to be computationally-efficient and fast. In general, one could implement a very sophisticated reconstruction technique to remove the background events, though this method would take a very long time to calculate and cut events, several months potentially. In an effort to reduce computational time simple 35

5 Level 4 - Only LC Double Pulse 10 Burn Sample Corsika 104 103 102 101 100 10-1 10-2 10-3 10-4

Double Pulse Events in 235.0 Days 10-5 103 104 105 106 107 2.0 1.8 1.6 1.4 1.2 1.0 0.8

Data/Corsika 0.6 103 104 105 106 107 QTot

Figure 5.10: The monte carlo expected event rate binned by the charge observed by IceCube compared to the 10% burn sample when only applying the pre-cuts and LC DPA. The lower plot shows a ratio of the burn sample data to the simulated atmospheric muons. reconstruction techniques are preferred. However, too simple of a reconstruction may be easily confused by complicated events and fail to perform well at separating the signal from the background. This issue will be discussed later in the chapter. The two reconstructions chosen for this cut are SPEFit32 and CscdLLh, with an underlying assumption of track and cascade events respectively. Both of these reconstructions assume a fairly simple approximation for the event structure. SPEFit32 assumes an infinitely long muon on a straight line that is emitting a cherenkov lightcone. This muon line is moved around in both direction and position such that the timing profile of the light observed by the DOMs most closely matches the expected light from the muon. The fitter iterates this process 32 times to find the maximal likelihood for muon track given the data. CscdLLh assumes a single point of spherically symmetric light emission. This fitter moves the position of the light emission point and also the amount of light emitted to match the observed light in the DOMs. CscdLLh maximizes 36 the likelihood of the model to find the best fit point. These two reconstructions are computationally efficient due to the simple approximations of the neutrino interactions and detector configuration. To combine these two reconstructions and determine which of the two topologies an event most likely falls under, the difference between the reduced log likelihood of the reconstructions is taken. A cascade event will have a large likelihood for the CscdLLh reconstruction and small likelihood for the SPEFit32 and vice-versa for a track event. The distribution of the differences between CscdLLh and SPEFit32 reduced log likelihood is shown in Fig. 5.11. You can see the cascade events of tau neutrino and electron neutrinos group near positive difference values, cutting at -0.5 retains most of the tau neutrino signal events while rejecting the vast majority of background. There is an approximate 27% reduction of signal tau neutrino events after this cut, this is due to two physical processes. The tau lepton has a 17% chance of decaying into a muon, creating a track event. Second, at very high energies the tau lepton is long lived and creates an elongated event that straddles the single cascade and track event topology. These two processes are the main contributions to the 27% tau neutrino event rate reduction after this cut. The very high energy reduction in the tau neutrino effect can be seen Fig. 5.12, where the events above 1 PeV neutrino energy are reduced compared to the Level 4 events. One additional cut is applied to further reduce the atmospheric muon background, this is primarily to remove low energy muons that do not produce long tracks in the detector. Atmospheric muons only come from above the detector and so generally are first seen at the top of the detector. Whereas neutrinos interactions are evenly distributed throughout the detector volume. By removing events that have their first observed light at the top of the detector, a large number of atmospheric muons are removed with only a small reduction of signal tau neutrinos, as shown in Fig. 5.13. Specifically the variable used for this cut is first hit z, which records the height of the DOM that is first hit by light by an event. The topology cut and first hit z variable reduces the atmospheric muon background by 99.5% and the muon neutrino background by 88% while only reducing the signal tau neutrino event rate by 27%. These two cuts together form the Level 5 cut, event rates for all event types are shown in Table 5.2. The level 5 selection reduces the background to nearly the same rate as the signal events, however for the discovery of tau neutrinos, a higher purity is still necessary. The remaining background muon events are trickier to remove and will require additional simulation and study of their topology, this will discussed in the next section.

5.4 Geometric Containment Cut

With only 16 burn sample events we can visually inspect them to understand why they were not removed with the level 5 cut. Two of the remaining burn sample events are shown in Fig. 5.14, they represent two muon topologies that the level 5 failed to remove. The ﬁrst are corner-clippers, these are muon events that 37

105 Burn Sample Astro. NuE CC 4 10 Astro. NuTau CC Corsika 103 Astro. NuMu CC 102 101 100 10-1 10-2 10-3 10-4

Double Pulse Events in 235.0 Days 10-5 15 10 5 0 5 2.0 1.8 1.6 1.4 1.2 1.0 0.8

Data/Corsika 0.6 14 12 10 8 6 4 2 0 2 Delta rLogL

Figure 5.11: The event rate of all simulated particles considered binned by the rLogL difference between the CscdLLh and SPEFit32 fits compared to the burn sample. The majority of atmospheric muons have negative values whereas the majority of tau neutrinos have positive values. A cut is applied at -0.5, removing any events below this value. only passed through a small portion of the detector near a corner. The second are muon events that pass through Deepcore, a densely instrumented portion of Icecube. In this section, we will discuss why these two topologies passed the level 5 cut and how to remove these events. Before any cut can be created, sufficient simulation statistics are needed to understand the behavior of the events and verify the cut. After the level 5 cuts, the Corsika muon background simulation has poor statistics and is dominated by a handful of events. Thankfully these handful of events have a unique characteristic, they are individual high energy muon events, as shown in Fig. 5.15. Rµ is the ratio of the highest energy muon to the total muon energy in an event is a proxy to if an event is a single muon or multiple muons. This characteristic, while rare, makes the event very simple to simulate using a dedicated program called MuonGun. We combine the MuonGun simulation with Corsika simulation by removing all the Corsika events 38

0.025 Level 4 Level 5

0.020

0.015

0.010

0.005 Tau Neutrinos in 235 days

0.000 104 105 106 107 108 True Neutrino Energy

Figure 5.12: Distribution of simulated tau neutrinos after the level 5 cuts compared to the level 4 cuts. Overall the rate is reduced due to removing the muon decay mode of the tau lepton. In addition, the high energy tail above 3 PeV is reduced due to the elongation of the events at these energies.

with Rµ values larger than 0.9 and add the MuonGun events into the simulation sample. This is done to ensure the single muon event type is not double counted. The new combined muon background sample agrees better with the burn sample than Corsika alone as shown in Fig. 5.16. I’ll use this combined simulation set for creating the cuts we discuss in this section. The DeepCore events are fairly straightforward to remove. Because the SPEFit32 and CscdLLh reconstructions are simple, they are confused by the higher density of Deepcore and prefer a single cascade event reconstruction located in Deepcore. Telling the reconstructions to ignore the Deepcore DOMs during the fitting procedure removes the confusion and more accurately reconstructs the events. The rLogL distribution of the Deepcore removed reconstructions is shown in Fig. 5.17. Due to the better single muon statistics, the Corsika + MuonGun simulation extends further into positive rLogL values compared to Corsika alone in 5.11. This prompts a harder cut at -0.15, compared to -0.5 at Level 5, on the rLogL value to remove more of this background. After the second topology cut there remains a small, but not insignificant, muon background which consists of corner clipping muons and single muons. Corner clipping events only pass through a small portion of the detector, either the top or bottom corners, resulting in a very short track which appear as cascade-like. High energy muons primary energy losses are random stochastic losses, such as pair production. It is possible that a single muon only has one stochastic loss and otherwise only insignificant small energy 39

105 Astro. NuTau CC 4 10 Astro. NuMu CC 103 Astro. NuE CC Corsika 102 Burn Sample 101 100 10-1 10-2 10-3 10-4 Double Pulse Events in 235.0 Days 10-5 600 400 200 0 200 400 600 2.0 1.8 1.6 1.4 1.2 1.0 0.8

Data/Corsika 0.6 600 400 200 0 200 400 600 First Hit Z (m)

Figure 5.13: The event rate of all simulated particles considered binned by the ﬁrst hit z variable. The majority of atmospheric muons interact at the top of the detector whereas the neutrinos have no dependence of the ﬁrst hit z. A cut is applied at 475, removing any events below this value.

losses, which makes the event appear to be more cascade-like than track-like. Because of the cascade-like topologies of these two muon event conﬁgurations, they can potentially pass the topology cut. But we can leverage the geometric information that muon events start outside of the detector volume to remove them. To use the geometric information, we can create a containment cut, which requires the events to start inside the IceCube detector and not the edge, which rejects these last muon events and keeps a large fraction

of tau neutrino events. The containment cut uses a single variable, R250PE, the ﬁrst 250 photoelectron center of gravity, 1 P R250PE = ri Ci, 250PE i=1 ∗ where ri is the position of the ith DOM and Ci is the charge that DOM observed until 250 PE total charge was observed in an event. This R250PE provides the information where the very beginning of an event is, and thus shows if an event was starting inside the detector or near an edge. We distill the three 40

(a) DeepCore Event

(b) Corner Clipping Event

Figure 5.14: Two event views of burn sample events that represent the remaining atmospheric muon background. (a) is a muon event that passes through DeepCore, skewing the level 5 reconstructions. (b) is a muon event that clips a top corner of IceCube, making it appear cascade like, a muon event can also clip a bottom corner of IceCube. 41

Level 5 Event Rate in 235 Days NuTau CC 0.234 0.0024 ± NuMu Astro. + Atmo. 0.16 0.013 ± NuE Astro. + Atmo. 0.046 0.002 ± Burn Sample 16 Corsika 10.5 1.3 ±

Table 5.2: The expected rate of events in the 235 burn sample period.

Figure 5.15: The Corsika atmospheric muon sample binned by the muon ratio, Rµ, and the L5 delta rLogL value. At large Rµ values, the event is dominated by a single muon. This plot shows that the sample is dominated by single muon events at level 5 that are cascade like.

dimensional center of gravity into two variables, distance to closest edge, Eveto, and height, Zveto, in the detector which allows for a simpler cut as the detector is not cylindrically symmetric. The distribution of these two variables for the muon background, burn sample, and signal tau neutrino events are shown in Fig. 5.18. The red shaded areas denote the three regions that are removed by the containment cut, the top corner, bottom corner, and edge of the detector. There regions deﬁned as,

Top Corner: Zveto + 1/3 Eveto > 400 m × Bottom Corner: Eveto < 75 m and Zveto < 200m − Edge Region: Eveto < 10m. While the containment cut successfully removes the vast majority of the muon background, it does reduce 42

Figure 5.16: The distribution of the combined Corsika and Muongun sample as described in the text compared to a Corsika only sample and burn sample at level 5. The combined Corsika and Muongun sample agree with the burn sample better than the Corsika only sample.

Figure 5.17: The level 5 no DeepCore ∆rLogL distribution of tau neutrinos, atmospheric muon simulated events, and burn sample events. A cut is applied at -0.15, removing all events below this value. the eﬀective volume of the detector. A neutrino interacting at the edge of the detector will be removed by this cut, reducing the volume the neutrino can interact and successfully pass into the ﬁnal sample. The total 43 volume reduction is around 40%, reducing the total event rate by about 40%. The overall decrease in event rate can be seen in Fig. 5.19.

Figure 5.18: The distribution of events in the detector using the R250PE CoG position. The atmospheric muons cluster near the edge, top and bottom corners. The pink shaded area are the regions that are removed by the containment cut.

The two cuts, the DeepCore removed topology and containment cut, together form the last level of cut, level 6. At this stage there are no remaining burn sample events so there is no ability to verify the cut against burn sample other than the expected rate for all events in the burn sample is below zero. The expected rate of all event types after is shown in Fig. 5.20. This ﬁgure shows the signal tau neutrinos dominates over all of the other background events in a large energy range. The expected rate for all particles is shown in Table 5.3.

5.5 Final Sample

After the three cut levels presented here, level 4 through 6, we have created a sample of events where tau neutrinos are the dominant event type. An overview of the rates for the different event types are shown in Table. 5.4. In summary, for 8 years of livetime this selection expects to find a total of 3.13 events, 1.71 of which are signal tau neutrinos. One of the main purposes of this selection is the first observation of tau neutrinos in IceCube, so we created a scoring evaluation to highlight specific events in the sample. This tau-ness score uses two variables, maxToT1 and Ereco, and compares the rate of signal to total events binned in these two variables. The Ereco is the reconstructed energy from a cascade reconstruction, Monopod, and maxToT1 is the maximum first pulse duration observed in the double pulse waveforms of an event. The tau-ness score is defined as,

Score = Rateντ ,i/(Rateντ ,i + RateBG,i),

where i represents the 2D bin the event falls into, Rateντ ,i is the expected rate of tau neutrinos from simulation in the ith bin, and RateBG,i is the expected rate of all simulated background events in the ith bin. The bins are deﬁned in Fig. 5.21, and are set to have good statistics in the majority of the bins. 44

Event Rate in 235 Days NuTau CC 0.143 0.0019 ± NuMu Astro. + Atmo. 0.074 0.0081 ± NuE Astro. + Atmo. 0.025 0.0014 ± Burn Sample 0 Corsika 0 MuonGun 0.02 0.011 ±

Table 5.3: The Level 6 ﬁnal sample expected rate of events in the 235 burn sample period.

Event Rate in 8 years NuTau CC 1.72 0.023 ± NuMu Astro. + Atmo. 0.95 0.048 ± NuE Astro. + Atmo. 0.26 0.010 ± Atmospheric Muons 0.2 0.14 ±

Table 5.4: The ﬁnal sample expected rate of events in the 8 years of data. 45

0.025 Level 4 Level 5 Level 6 0.020

0.015

0.010

0.005 Tau Neutrinos in 235 days

0.000 104 105 106 107 108 True Neutrino Energy

Figure 5.19: The expected rate of tau neutrino events as a function of true neutrino energy compared after the level 6 cuts. The overall rate is decreased by about 40% for all energies due to the reduced ﬁdicual volume of the containment cut.

The distribution of scores for the signal and background simulated events is shown in Fig. 5.22. Tau neutrinos group towards larger values and the background events towards smaller values showing good performance of this tau-ness scoring. During the unblinding of the 8.5 years of IceCube data, all events found will be given a tau-ness score which will highlight which of the events are most likely to be tau neutrinos. One of the goals of this work was to improve upon the previous analysis, a metric to compare two analyses against each other is the effective area. This quantity is the cross section for tau neutrinos in the detector including selection efficiency as a function of energy. A larger effective volume results in a higher event rate in the final sample. A comparison of the legacy PRD analysis and this new analysis is shown in Fig. 46

Figure 5.20: The charge distribution of the ﬁnal sample after all cuts are applied. Above 104 PE the sample is dominated by tau neutrino events.

Figure 5.21: The distribution of the signal tau neutrino, background neutrinos, and their ratio binned in MaxToT1 and Monopod reconstructed energy. Most of the tau neutrinos have reconstructed energies of a few 100 TeV to 1 PeV with at least 26.3 ns long MaxToT1. This can be seen especially in the right most plot, the ratio between the signal tau neutrino event rate to the total event rate is high in these regions.

5.23. The effective area of the new analysis presented here is roughly a factor of 2 larger than the previous analysis this was based on, showing the efforts to improve upon the previous analysis was successful. With this sample the flux of tau neutrinos can be measured using statistical methods detailed in the next chapter. 47

Figure 5.22: The tau-ness score distribution of the ﬁnal sample for the signal tau neutrino events and the background neutrinos. The tau neutrinos generally have large tau-ness scores, showing the tau-ness score does have an ability to show how signal-like the event is. 48

Figure 5.23: The effective area for the three neutrino flavors at the final level of the analysis compared to the previous double pulse analysis this is based on. This analysis has an effective area a factor of 2 larger than the previous analysis, showing the improvements discussed in this section were effective. 49

Chapter 6

Forward Folding

6.1 Forward Folding

With an established event selection we can start extract relevant physical information by using statistical fitting techniques. For this analysis I choose to use a binned forward folding method which will be explained in this chapter. Forward folding is useful as it fits many different parameters simultaneously which returns the fitted physical value, such as astrophysical tau neutrino normalization. In addition it is a framework to create confidence intervals of these physical parameters using a Feldman-Cousins scan which ensures proper coverage for limited statistic folding. A third benefit of forward folding is the ability to study systematic errors and their affect on the resulting fit. For these reasons forward folding was chosen to fit the final sample of the event selection to extract the physical information. Forward folding is based on a likelihood, , technique which is a fairly simple formula with some subtleties, L Q (µ) = P (xi µ), where µ is any number of parameters to be fit and xi is the data being fit. The value L i | of µ that maximizes the likelihood is the best fit value of µ for the data. The data can be either unbinned or binned, for this analysis the data will be binned to simplify the construction of the probability function. x i −λi λi e For a binned data likelihood the probability will be a poisson probability, P (xi, λi) = , where λi is xi!

the number of expected events in ith bin and depends on µ and xi is the number of events observed in the ith bin. To reduce the computational difficulty of the likelihood, a logarithm is applied and the negative P is taken which turns the likelihood into log( (µ)) = log(P (xi µ)). The value µ that minimizes this − L − i | log-likelihood is the best fit value. Forward folding is the method of fitting using the likelihood and modifying the weights of simulated monte carlo events to recalculate the λi for each µ being considered. To apply the forward folding method to this analysis a few decisions need to be made. First, what observables the data will be binned by and how many bins should be used. Next, what parameters of µ will be fit. I choose to use the same observables used for the tau-ness score and p-value, Monopod reconstructed energy and MaxToT1. When binning the final monte carlo sample, these two observables showed the best separation between background neutrinos and tau neutrinos. We choose a fairly course binning to ensure the relative monte carlo statistical error per bin is small, as shown in Fig. 6.1. A course binning is necessary due 50 to the limited monte carlo statistics. Specifically, Monopod reconstructed energy is binned with logarithmic bins with 5 bins per decade, and MaxToT1 has linear bins, each 26.4 nanoseconds wide.

Figure 6.1: The neutrino monte carlo statistical error per bin relative to the events expected per bin for the chosen binning of the forward folding.

Choosing which parameters to fit is a more difficult decision to be made. With a final sample size of only a few events, any shape related parameter becomes very difficult to fit well. The astrophysical flux being fit γ is assumed to be a simple powerlaw, Φν E , where Φν is the normalization and γ is the spectral index. For × the astrophysical flux, the spectral index is determined by fitting the energy distribution shape of the events observed, causing exactly the issue of fitting with only a few events. For this reason, we choose to fix the astrophysical spectrum to spectral indexes that have been fit by previous IceCube experiments, γ = -2.19, -2.5, and -2.9, the through-going muon neutrino, global fit, and HESE best fit spectral indexes respectively [15] [21] [16]. The astrophysical neutrino flux normalization on the other hand is, as the name describes, it is just a normalization, an easier quantity to fit. Because of reasons described in 3, all three neutrino normalizations are free to float, allowing the flavor ratio to be any value. With these choices of parameters, the tau neutrino normalization becomes the main result of this analysis. In addition to the astrophysical neutrino flux parameters, the atmospheric neutrino flux has parameters to be fit. The atmospheric neutrino flux only has background neutrinos, no tau neutrinos. Just like the astrophysical flux, the atmospheric has a normalization and spectral index parameter that can be fit though they are represented slightly differently. For the normalization there are two parameters, conventional and prompt normalization, taken as a modification of the SIBYLL 2.1 and ERS conventional and prompt fluxes [22, 23]. In addition to the normalization there is a parameter, called K/Pi ratio, which acts as a modification 51 of the hadronic interaction model that manifests itself in changing the zenith distribution of the atmospheric neutrino flux. There is also a parameter relating to the spectrum, it is a modification of the cosmic ray spectrum, ∆CR/gamma, which in turn modifies the atmospheric neutrino spectrum. For the forward folding I choose to let all of these parameters to float. These are all related to background and so are not the main results of the analysis. Additionally, allowing all of the atmospheric parameters to float can absorb any of background fluctuations and not affect the signal region. The nominal values for the parameters are: conventional and prompt normalization: 1, K/Pi ratio: 1, ∆CR/gamma: 0. With all of the parameters chosen for the likelihood fitting all that remains is putting the data into the forward folding software. The forward folding software I’m using was written by Chris Weaver, which I have modified for use with this analysis. The forward folding handles the expected number of events per bin, λi, in the poisson probability function. The forward folding software first bins all of the monte carlo events that remain after the data selection cuts discussed in the previous chapter and keeps track of the meta-data needed to weight the events. The meta data includes information relating to the monte carlo simulation, simulation energy, zenith, and azimuth range, true neutrino energy, direction and interaction probability. For each set of parameters the expected number of events per bin is calculated by the forward folding software using the meta-data of the binned data. The set of λi are then passed to the likelihood function that calculates the log-likelihood of that set of µ. A minimizer function is used to find the set of µs that corresponds to the minimum log-likelihood. The minimizer scans over the astrophysical and atmospheric µ’s chosen to be fit, passing each to the forward folding software to calculate the λi, which then passes those to the likelihood to calculate the log-likelihood, passing that value back to the minimizer. This process is repeated by the minimizer until a minimum log-likelihood is found which is determined to be the best-fit parameters.

6.2 Sensitivity

The forward folding method can be used to find an analysis’ sensitivity to a parameter, a measure of the minimum value of that parameter that the average realization of an experiment can observe. To find this average realization the forward folding software can conduct thousands of fake experiments called data challenges. To create a data challenge random events need to be selected from the monte carlo sample, how many is determined by a random integer number with a probability given by a poisson distribution with the total number of expected events for that monte carlo set as the mean. Each neutrino monte carlo set follows the same process separately. Once the number of events for a data challenge is chosen, random events are selected out of the monte carlo set to form this data challenge. The probability of an event being selected is given by its event weight divided by the number of expected events for that flavor. This process of selecting events is called injecting events and needs a pre-selected flux. These events are then passed into the forward folding software as if they were real data events to find the best fit parameters for the data challenge. In 52 addition, a scan of the likelihood space is done to find the 90% confidence interval for the tau neutrino normalization, which is defined as the value at which the log-likelihood increases by 1.355 over the best fit log-likelihood. To measure the sensitivity, I inject monte carlo events at three different astrophysical fluxes, 1.01 10−18 × × E−2.19, 2.2 10−18 E−2.5, and 2.02 10−18 E−2.9 GeV−1cm−2s−1sr−1 at a flavor ratio of 1:1:0, that × × × × is no tau neutrino events. For each data challenge trial the best fit tau neutrino normalization and 90% confidence interval are recorded. For each spectrum 1,000 data challenge trials are conducted. The 90% tau neutrino normalization upper limit of these 1,000 data challenges are shown in Figs. 6.2. As discussed earlier, the sensitivity is the minimum value observable by an average realization of the experiment, so taking the median value of the 90% upper limits we find the sensitivity. The sensitivities are 1.16 10−18 E−2.19, × × 2.28 10−18 E−2.5 , and 4.32 10−18 E−2.9 GeV−1cm−2s−1sr−1. These values are slightly higher than × × × × the best fit per flavor astrophysical neutrino normalization of the analyses the spectrums are obtained from.

0.6 E^-2.19 E^-2.5 E^-2.9 0.5 Median 0.4 Median Median 0.3 Relative Rate 0.2

0.1

0.0

0 2 4 6 8 10 90% upper limits (10^-18 GeV^-1 cm^-2 s^-1 sr^-1)

Figure 6.2: The distribution of the tau neutrino normalization 90% upper limit for 1,000 data challenges for each assumed spectrum. The median upper limit value is shown for each spectrum as a vertical line.

An important consideration for experiments is the systematic errors coming from mismodeling or mis- understanding the experimental device. For IceCube, the primary systematic errors that are of concern relate to the ice and DOM efficiency. The method to find the sensitivity can be used to estimate the affect these systematic errors have on the analysis by comparing the upper limit distribution with a systematic error applied. Each systematic error had a monte carlo simulation set created by varying that systematic in the simulation of events. The systematic variations considered are: bulk ice scattering +10%, bulk ice absorption +10%, bulk ice scattering and absorption -7%, optical properties of hole ice p2 = -1, 1, 3, and DOM efficiency 0.81, 0.90, 0.95, 1.08, and 1.17. The nominal values for the hole ice optical property p2 53 is 0, this value controls the angular photon acceptance of the DOM. The DOM efficiency nominal value is 0.99 which is relative to an lab measured efficiency of the DOMs before deployment. Each systematic was simulated over an energy range of 5 TeV to 10 PeV with a spectrum of -1.5 for 70,000,000 events. For each systematic error 1,000 data challenge trials were created using the systematic set and then fit with the forward folding software using the baseline set that was specially made with the same energy range and spectrum as the systematic sets. The distribution of each systematic set’s data challenge trials 90% tau neutrino normalization upper limit along with the baseline set is shown in Fig. 6.3. The averages for all of these systematic sets are shown in the blue band, the specific average 90% upper limits are shown in Table 6.1. The distribution of the averages all cluster around the baseline upper limit average, most within 5% of the baseline. When you compare this distribution to the statistical 1 σ variability of the baseline upper limits from the data challenge trials, it becomes clear that the variation of the systematic averages is far below that of the statistical variation. This is due to the very small expected sample size of the final sample, observing 1 event is as likely as 4 events, which compared to the change of any one of the systematic errors, is vastly larger. This shows the analysis is not sensitive to any of the systematic errors nor do any of them affect the outcome of the analysis to the same extent as the statistical variability. This can be understood by a simple explanation; if an event is observed at a reconstructed energy of 305 TeV, this analysis is unable to say if this event should be 300 TeV because of a systematic error or if the event is there due to the realization of the experiment. This study shows that the more likely reason is the statistical variability of the experimental realization. For this reason, no systematic errors are considered for the forward folding analysis.

Systematic Data Challenges, 1000 Trials 700 Scattering + Absorption -3% Holeice p2 = 1.0 600 DOM Efficency 1.08 DOM Efficency 1.17 500 DOM Efficency 0.90 Baseline 1 Sigma Absorption +5% 400 DOM Efficency 0.95 Holeice p2 = -3.0 Holeice p2 = -1.0 300 Scattering +5% DOM Efficency 0.81 Baseline 1 Sigma 200 Average Upper limits Data Challenge Trials Baseline

100

0 0 1 2 3 4 5 90% upper limits (10^-18 GeV^-1 cm^-2 s^-1 sr^-1)

Figure 6.3: The distribution of the tau neutrino normalization 90% upper limit for 1,000 data challenges for each systematic error. The averages of each systematic is shown in the blue band. The 1 σ deviation of the baseline upper limits are shown as the vertical red lines. All of the systematic error averages are within the 1 σ band. 54

Another check to perform of the systematic error is the confidence interval coverage. A confidence interval is defined as to contain the true value of the parameter at the interval specified. Such as, a 68% confidence interval of a parameter will contain the true value of that parameter 68% of the time. If in reality, the parameter is contained more or less often than that the confidence interval is said to have over- and under- coverage respectively. The coverage can be tested by data challenges, this time by injecting an astrophysical flux with a flavor ratio of 1:1:1 and recording the tau neutrino normalization 68% confidence interval. With a collection of data challenge trials the percentage of trials that contain the injected tau neutrino normalization can be determined and the if reported 68% confidence interval has correct coverage. 1,000 data challenge trials were conducted for each systematic along with the baseline set and the tau neutrino normalization containment of the 68% confidence interval for each systematic is shown in Table 6.2. All the systematic errors and baseline confidence intervals have under-coverage, this is expected for two reasons detailed in [24], very small expected event sample size and the fit occurring near a boundary of the parameter, the fit does not allow the tau neutrino normalization to become negative. However, none of the systematic errors vary far from the baseline coverage, showing that the systematic error is not a concern for the coverage. However, this study does show that the confidence interval construction needs careful consideration and construction, which will be detailed in the next section.

6.2.1 Feldman-Counsins Conﬁdence Interval

As discussed in the previous section, this analysis shows an under-coverage issue with its confidence interval. This under-coverage can be remedied by the procedure described in [24], a process that uses data challenges to construct a parameter dependant log likelihood difference, ∆-LLh, value to determine the confidence interval instead of a constant 1.355 ∆-LLh value. We will create a tau neutrino normalization dependent ∆-LLh value to create a proper coverage confidence interval for the tau neutrino normalization. Each data challenge trial is fit twice, once with the same parameters floating as the normal forward folding fit and another time with all of the same parameters floating except for the tau normalization fixed to the value being injected. The difference between the log-likelihood of these two fits is recorded for each data challenge trial. To scan over the parameter space of the tau neutrino normalization, the injected parameters are kept at their nominal values and the tau neutrino normalization is injected from 0 to 10 10−18GeV−1cm−2s−1sr−1 × in steps of 0.1. Each normalization has 10,000 data challenge trials and this is repeated for each astrophysical spectrum considered. The sample of data challenge at a specific normalization and spectrum is binned by the difference between the two fits likelihood and the value at which 90% of the trials are below, is determined to be the ∆-LLh value to determine the 90% confidence interval for the normalization and spectrum. An example of this distribution is shown in Fig. 6.4 This value is determined for all normalizations and spectrums considered, 55

Systematic Average Upper limit Baseline 1.23 10−18 Scattering +10% 1.16 10−18 Absorption +10% 1.15 10−18 Scattering & Absorption -5% 1.19 10−18 P2 = -1 1.25 10−18 P2 = 1 1.25 10−18 P2 = 3 1.26 10−18 DOM Eff = 0.81 1.17 10−18 DOM Eff = 0.90 1.23 10−18 DOM Eff = 0.95 1.26 10−18 DOM Eff = 1.08 1.30 10−18 DOM Eff = 1.17 1.24 10−18

Table 6.1: The average upper limits from 1000 data challenge trials when using a systematic set to create the trial and ﬁtting with the baseline set. All of the systematic sets are close to the baseline set and within the 1 σ variablility of the baseline upper limit. The average upper limit are in units of GeV−1cm−2s−1sr−1. 56

Systematic % of time 1 σ CI includes injected flux Baseline 61.9 % Scattering +10% 55.1 % Absorption +10% 57.9 % Scattering & Absorption -5% 57.8 % P2 = -1 58.6 % P2 = 1 60.0 % P2 = 3 58.6 % DOM Eff = 0.81 56.8 % DOM Eff = 0.90 57.9 % DOM Eff = 0.95 58.1 % DOM Eff = 1.08 59.3 % DOM Eff = 1.17 61.1 %

Table 6.2: The 68% confidence actual coverage when considering the baseline set and systematic sets. All sets have under coverage, though none are significantly different than the baseline coverage. The under coverage issue will be solved by a Feldman Cousins scan, presented in the next section. 57 which are shown in Fig. 6.5. Once the analysis has been performed on the experimental sample, the ∆-LLh profile of the tau neutrino normalization will be scanned and the points at which the profile crosses over the ∆-LLh value shown in Fig. 6.5 will create the 90% confidence interval.

0.40 = 0.1 0.35 = 2.0 = 5.0 0.30

0.25

0.20

Probability 0.15

0.10

0.05

0.00 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 TS

Figure 6.4: The distribution of the TS values fo 10,000 Feldman Cousin trials using three diﬀerent example normalizations, 0.1, 1.0, and 5.0. The vertical lines are the point of 90% containment of the trials, those values are the critical values for determining the 90% conﬁdence interval when conducting the likelihood scan.

6.3 Event P-Values

An informative piece of information for any event observed in the data selection is the signiﬁcance of that event being a signal event or background event, a p-value. The p-value of an event can be obtained by the relative position of the event in comparison to background only distribution of a test statistic, TS, value. This TS value does not have a speciﬁc construction and is analysis dependent. For this analysis the event TS value is,

TS = Log( (λ)/ (λ = 0)). (6.1) L L 58

5 E 2.5 E 2.9 E 2.19 4

Delta LLH 2

0 0 2 4 6 8 10 10 18GeV 1cm 2s 1sr 1

Figure 6.5: The ∆ Log likelihood values found by the Feldman Cousins procedure to determine the 90% conﬁdence interval of the unblinding data. The values are shown for the three spectrums that will be used for the forward folding.

where is the per bin likelihood with a fitted parameter λ. The likelihood is maximized by fitting λ for the L bin an event lies in. The likelihood is defined as,

(λ) = (Pi,j + λ Pi,j)/(λ + 1), (6.2) L B × S

i,j where PB,S are the background, signal probability density function for the i,jth bin the event lies in, nor- malized as i,j i,j NB,S PB,S = RR , (6.3) NB,SdEdt i,j NB,S is the number of background, signal events observed in the i,jth bin which is dependant on the assumed astrophysical flux. The bins are set to the same as forward folding, Monopod reconstructed energy binned with logarithmic bins with 5 bins per decade, and MaxToT1 with linear bins, each 26.4 nanoseconds wide. The TS distribution of background only events will then be used to determine the p-value of an event observed in the final sample. The assumed spectrums for the TS distributions are 1.01 E−2.19, 2.2 E−2.5 × × , and 2.02 E−2.9 10−18GeV−1cm−2s−1sr−1, which are the best fit astrophysical from previous IceCube × 59 analyses. These TS distributions are shown in Fig. 6.6 for the three spectrums used in the forward folding, three p-values will be presented for each final sample event, each for the different spectrums. Each observed event will have its TS value calculated and compared to the background TS distribution, the percentage of the distribution above the events TS value is the event p-value. If an event has a TS score of 0, the p-value will be 1, or background like. 60

(a) E−2.19 (b) E−2.5

Figure 6.6: The TS distribution of background neutrino events for the three diﬀerent spectrums used in this analysis. These distributions will be used to determine the p-value of any events found during the unblinding. 61

Chapter 7

Results

7.1 Data Sample

The event selection detailed in Chapter 5 was applied to 2759.66 cumulative days of data in a period between May 2010 and December 2018. Data during periods where more than 2 strings in IceCube were not functioning correctly, if there was a noted issue with IceCube data taking, a test was being performed, or data from the burn sample were discarded. In this data analyzed a total of three events were observed, one in 2014, 2015, and 2017. Each event will be discussed in detail in the next three sections. The energy distribution of the events along with the expected event rate for an 1.01 10−18 E−2.19 GeV−1cm−2s−1sr−1 × × 1:1:1 astrophysical plus nominal atmospheric neutrinos are shown in Fig. 7.1.

Final Level, E^-2.19 Background Neutrinos Tau Neutrinos 100 Total Data

10 1 Events in 2759.66 days 10 2

10 3 104 105 106 107 Monopod Reconstructed Energy

Figure 7.1: The distribution of the ﬁnal level expected events compared to the three events observed after unblinding. The expected events assume an 1.01 10−18 E−2.19 GeV−1cm−2s−1sr−1 1:1:1 astrophysical × × ﬂux. 62

7.1.1 2014 Event

The event observed in 2014 is the most interesting event of the sample from the perspective of it having the highest probability of being a signal tau neutrino. It has a tau-ness score of 0.60, hinting towards this event being slightly more signal like than background like. The event passed both the single DOM and local coincidence double pulse algorithm, the waveforms that passed the DPA are shown in Fig. 7.2. The waveform parameter, MaxToT1 used in the forward folding is 26.4 ns, suggesting a signal like double pulse waveform. The Monopod, single cascade dedicated, reconstructed energy is 93 TeV which is on the tail of the expected event energy. Inspecting the event view, shown in Fig. 7.3, we see this event occurred in the middle of the detector suggesting this event is likely a neutrino. However, the position of the event is slightly unfortunate it is just above the dust-layer, a region of ice that has very high absorption properties due to contaminants. This region obscures the light produced by particles in it. Because of this, it is diﬃcult to assess if there is any outgoing muon that would be produced in a background muon neutrino interaction.

2014 Event 1750 OMKey(20,26,0) OMKey(20,27,0) 1500

1250

1000

750 Voltage (mV) 500

250

9900 10000 10100 10200 10300 Time (ns)

Figure 7.2: The two waveforms selected by the double pulse algoritm are shown. These waveforms are on neighboring DOMs and so pass the new local coincidence double pulse selection. The waveform recorded on DOM 20, 27 also passed the previous single DOM double pulse algorithm. The longer duration ﬁrst rising edge hints towards a signal tau neutrino event.

Due to the lower energy, 93 TeV, the p-values of this event are not signiﬁcant, 0.29, 0.196, and 1.0 for E−2.19,E−2.5, andE−2.9 respectively. In addition, the unfortunate interaction vertex of the event limits our ability to inspect the event for any outgoing muon tracks. At this lower energy the primary background are muon neutrino CC events with outgoing muons. Because of these limitations, there are no conclusions about the source of this event beyond that is most likely a neutrino. 63

Pop Pop

Figure 7.3: Event view of the 2014 event, ”Pop Pop”. The interaction point is directly above the dust layer of IceCube that can potentially obscure an outgoing muon. The interaction appears to start inside of the detector volume, so a neutrino event is highly likely.

A note of interest for this event, another tau neutrino analysis that uses a reconstruction method to identify double cascade events found this event as a tau neutrino candidate. Further work is needed to address the source of this event, the two analyses ﬁnding this event hints towards this event being a tau neutrino as both analyses have diﬀerent dominant backgrounds.

7.1.2 2015 Event

The event observed in 2015 is a less significant event with a tau-ness score of 0.32, showing this event is more background like than signal like. This event passed only the single DOM DPA configuration, the waveform that passed the cut is shown in Fig. 7.4. One of the characteristics that shows this event is background like is the sharp, short duration first pulse with a maxToT1 of 13.2 ns. The reconstructed energy is 117 TeV, once again reducing the likelihood this event is a signal tau neutrino as most of the expected signal events are higher in energy. The p-values for this event is 1.0 for all three assumed spectrums, suggesting a background event. The event view of this event, see Fig. 7.5, shows this event is likely a background muon neutrino. First, the event starts inside the detector volume with a horizontal development direction, pointing towards a neutrino event. Second, the horizontal development, seen especially on the left most strings in the event view, is an indication of a muon traveling out of the initial cascade and creating additionally light in a track. The best fit event direction suggests that this muon leaves the detector volume soon after being produced, which creates an event that appears somewhat cascade like with a very short observable track. 64

2015 Event

600 OMKey(10,44,0)

500

400

300

Voltage (mV) 200

100

9900 10000 10100 10200 10300 Time (ns)

Figure 7.4: The double pulse waveform recorded for this event. Only one DOM recorded a double pulse, the neighboring DOMs have no evident double pulse signature. The first pulse is sharp with a short duration first rising edge and falling edge, suggestive of a muon cherenkov light producing the first pulse. This would be inline with the track like event topology.

Britta

Figure 7.5: The event view of the 2015 event, ”Britta”. This event starts inside of the detector going in a horizontal direction. There are a few hits on the left side of the detector that hint towards this event containing a muon that leaves the detector. This is in agreement with the p-value and tau-ness score suggesting this is a background event.

The double pulse waveform can be explained by a muon track, the best ﬁt muon direction shows the muon passing close, 10 m, to the DOM that observes the double pulse. This muon would be producing cherenkov 65 light, which the DOM would observe as a short duration pulse just like the ﬁrst pulse seen in the waveform. The muon can reach the DOM prior to the initial hadronic cascade due to the muon traveling faster than the speed of light in ice, so the DOM can observe the muon cherenkov light prior to the initial hadronic cascade, creating a double pulse waveform. From the tau-ness score, p-values, and visual inspection, this event appears to be a neutrino event with a muon, most likely a muon neutrino. This is inline with the expected number of events, 1 muon neutrino events in 8 years.

7.1.3 2017 Event

The ﬁnal event was observed in 2017, and is the least signal like of the three with a tau-ness score of 0.06. The reconstructed energy is 14 TeV, far below any expected signal event energy, along with a short maxToT1 of 13.2 ns. The event passed only the single DOM DPA, the double pulse waveform is shown in Fig. 7.6. The p-values for this event are all 1.0 for all three assumed spectrums.

2017 Event

700 OMKey(12,15,0) OMKey(12,15,0) 600

500

400

300 Voltage (mV) 200

100

10200 10300 10400 10500 10600 Time (ns)

Figure 7.6: The single waveform picked by the DPA to be classified as a double pulse. Similar to the 2015 event, this waveform has a sharp first peak characteristic of cherenkov light. The first pulse has a short duration first rising edge that tends to be associated with background events.

The event view of this event, shown in Fig. 7.7, is very enlightening as to what the event is. The event is two atmospheric muons that pass through the top of the detector one after the other, otherwise known as coincident muons. A coincident muon occur in 10% of the events in IceCube. The two muon tracks confuse the cascade and track reconstructions, both fitting the event poorly but the cascade reconstruction performs slightly better which allows this event to pass the topology cut. The containment cut was optimized to remove high energy muons, not low energy muons such as the two in this event. This analysis uses a standard event splitting algorithm meant to remove coincident muons by looking for DOM hits that are 66 not causally connected and separating them into two different events. However, this event was not split by this splitting algorithm, possibly due to noise hits bridging the two muons. The failure rate of the splitting algorithm has not been studied in depth, though an estimate puts it at 10%. When a different splitting algorithm is applied, specifically HiveSplitter, this event is split into two events, one for each of the muon tracks. These two split events are passed back through the event selection and are both rejected by the charge cut threshold. The original event passed this charge cut threshold by 1 PE.

Star-Burns

Figure 7.7: The event view of the 2017 event, ”Star-Burns”. From this view it is clear the event is comprised of two atmospheric muons, arriving one after the other. The event on the right side arrives ﬁrst and contains the double pulse waveform, the event on the left arrives after the ﬁrst muon has left the detector.

This event poses an issue for the forward folding method, there are no simulated events that represent it at the final level meaning that the forward folding method cannot find an appropriate type of event to attribute it to. That is not to say there are no monte carlo events that represent it, just that all were removed by the event selection. If this event, along with the two others, is included in the forward folding fit, the fit will be rather poor with unrealistic parameters as the fitter attempts to fit this event with an incorrect event type. For this reason, I will exclude this event from the fit as it is an obvious background event with no representative background monte carlo event. This lack of any monte carlo events at the final level is not entirely surprising, the atmospheric muon simulation, corsika, has only 1 year of equivalent livetime at the relevant energy range, compared to 8.5 years of analyzed data.

7.2 Forward Folding Results

The forward folding ﬁt was applied to the 2014 and 2015 event, excluding the 2017 event, using the method described in chapter 6. The results of the ﬁt for the three astrophysical spectrums are shown in 67

E−2.19 E−2.5 E−2.9

ντ Norm. 0.0 0.0 0.0

νe Norm. 0.0 1.76 0.0

νµ Norm. 0.0 1.93 1.81 Pi/K Ratio 0.0 0.0 0.0 Conv. Norm. 0.64 0.91 0.59 Prompt Norm. 0.0 0.0 0.0

∆CRγ -0.97 -0.83 -0.97

Table 7.1: The best fit values of the floating parameters for the three different assumed astrophysical flux spectrums. All astrophysical normalizations are in units of 10−18GeV−1cm−2s−1sr−1.

Table 7.1. The major take away from the fit results is the zero astrophysical tau neutrino flux normalization. The analysis prefers zero signal events and attributes the two observed events to background events. This is most likely due to no events in the region of a few 100 TeV where the majority of the signal events are expected. Taking the best fit values in Table 7.1, the tau neutrino astrophysical flux normalization are varied, keeping all other parameters the same as their best fit value and record the likelihood value for each variation. The difference between these log-likelihood values and the best fit log-likelihood value for each spectrum are shown in Fig. 7.8 for each different spectrum. The point at which the ∆ log-likelihood crosses the Feldman Cousin’s confidence interval value determines the 90% confidence interval. Reading the values off these plots those upper limits are, 1.1 10−18 E−2.19, 2.5 10−18 E−2.5, and 6.0−18 E−2.9GeV−1cm−2s−1sr−1. × × × × × 7.3 Results Discussion

The final sample and forward folding best fit did not have a significant observation of tau neutrinos, the p-values of the 2014 event are only about 1 σ and the best fit tau neutrino flux is zero. However, this is not in conflict with previous IceCube results which all report a best fit astrophysical below the upper limits of this analysis, if a 1:1:1 flavor ratio is assumed. One issue that appeared during the fitting is parameters best fit being far from their nominal value, specifically ∆γCR, and the astrophysical normalization for the spectrum E−2.19. If I were to reconduct the forward folding fit, I would choose to apply priors to the atmospheric parameters and electron and muon neutrino astrophysical neutrinos. These priors would penalize the likelihood value if it strays far from the nominal values by using an additional gaussian function using information from previous experiments to determine the width and nominal value. These priors would add additional information to the forward folding fit so that it can better fit the data using reasonable 68

E^-2.19 5 E^-2.5 5 Feldman Cousin Forward Folding Scan Upper Limit 4 4

3 3 Delta LLH Delta LLH 2 2

1 1 Feldman Cousin Forward Folding Scan Upper Limit 0 0 0 2 4 6 8 10 0 2 4 6 8 10 18 1 2 1 1 10 GeV cm s sr 10 18GeV 1cm 2s 1sr 1

(a) E−2.19 (b) E−2.5

E^-2.9 5 Feldman Cousins Forward Folding Scan Upper Limit 4

3 Delta LLH 2

0 0 2 4 6 8 10 10 18GeV 1cm 2s 1sr 1

Figure 7.8: The likelihood scan of the tau neutrino astrophysical normalization plotted against the Feldman Cousins scan performed in Chapter 6. The point at which the likelihood curve crosses the critical value determines the 90% upper limit of the tau neutrino ﬂux, this point is denoted with a vertical red line. 69 parameters. 70

Chapter 8

Conclusions

The field of astrophysical tau neutrinos is rich with with new particle physics with the study of astrophysical flavor ratio. It can reach into new energy and distance frontiers of neutrino oscillations not yet explored. This analysis was not designed to measure the flavor ratio of the astrophysical neutrino flux, instead it was meant to be a stepping stone on the way to measure it. IceCube has not yet conclusively observed a tau neutrino, which is a necessary first step to measure the flavor ratio. A large emphasis of this work was to improve the data selection process of double pulse tau neutrino events, increasing the expected event rate keeping the same purity as a previous search. This selection process increased the expected event rate by nearly a factor of two over the previous one. In addition, a new analysis method based on forward folding was used to better fit the astrophysical tau neutrino flux. The analysis method was applied to 2759.66 cumulative days of data taken by IceCube which had three events that passed the data selection process. The best fit flux from this analysis was zero tau neutrino astrophysical flux but the upper limit is not in conflict with previous astrophysical flux measurements. The sample of three events included one possible signal event, and two probable background events. The event observed in 2014 had a slight indication of signal-like with p-values of 0.29, 0.196, and 1.0 for E−2.19, E−2.5, and E−2.9 spectrums respectively. The other two events have p-values of 1.0 for all spectrums and their event views show topologies of background events. While the 2014 event is inconclusive if it is a tau neutrino event, further work by other analyzers is being performed on this event. Three upper limits were constructed, 1.1 10−18 E−2.19, 2.5 10−18 E−2.5, and 6.0−18 E−2.9GeV−1cm−2s−1sr−1. These are not in conflict × × × × × with a 1:1:1 flavor ratio, as the measured normalization for these three spectrums are below the upper limits. While this analysis did not observe a conclusive tau neutrino event, one event has some hints towards an interesting event. The 2014 event was observed by a separate analysis that uses reconstruction techniques to classify double cascade events. This event is under more review by the other analyzers and is potentially more interesting as this analysis and the reconstruction analysis have dis-similar dominant backgrounds. In the future, a more sophisticated analysis of double pulse waveforms will most likely necessary to observe any significant number of tau neutrinos by lowering the threshold even more. This potentially could involve 71 convolution neural networks or double bang reconstruction techniques applied to waveforms to find double pulses. In addition an upgraded, IceCube-Gen2, plans to significantly increase the detector volume, increasing the number of neutrino events interacting inside the volume. However the plans currently have an even sparser instrumentation than IceCube, which may limit the ability to observe double pulse waveforms, as the interaction vertex needs to be very close to a DOM for a double pulse to be observable. This thesis covered the work I performed over the last two years of my graduate work, it does not include my work on particle physics phenomenology, though throughout this document I added foot notes with citations to my work when relavent to the discussion. This work included ultra-high energy particle cross sections [2], limits of prompt neutrino production [10], the self-veto effect in IceCube [12], and double pulse identification techniques [11]. 72

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