Den här analysen har utförts i blindo, vilket innebär att analysmetoden har utformas till fullo innan den har använts på experimentell data insamlad med detektorn. På detta sätt kan vi utveckla analysen så opartiskt som möjligt, och utformar inte händelseurvalet specifikt med hänsyn till de individuella händelser som detekterats. Därmed vet vi heller inte på förhand vilket resultat som analysen kommer att ge, utan detta vet vi först i efterhand då analysen inte längre får redigeras. Däremot kan vi på förhand jämföra med resultaten från tidigare sökningar efter magnetiska monopoler inom samma hastighetsspann. Det har tidigare gjorts flera sökningar efter monopoler med hastigheter inom det intervall som den här analysen avser. Som bekant har inga magnet-iska monopoler hittats, utan alla har resulterat i en övre gräns på flödet. Det senaste resultatet inom detta intervall satte en övre gräns på flödet till färre än 3,46 × 10−18monopoler per kvadratcentimeter per sekund per steradian (en-heten för rymdvinkel). Den gränsen innebär att vårt händelseurval borde se färre än 33,2 detekterade monopoler under de åtta år som analysen behandlar. Utöver detta beräknade vi hur effektivt vårt händelseurval är på att avvisa astrofysikaliska neutrinhändelser. Händelseurvalet borde registrera i genom-snitt 0,256 neutriner under analysens åtta år, vilket innebär att vi skulle behöva observera nästan fyra gånger så lång tid för att detektera en enda neutrin.
När vi sedemera använde vår analysmetod på experimentell data visade det sig att ingen experimentell händelse uppfyllde urvalsvillkoren, alltså att ingen händelse bedömdes som monopol-lik. Den övre gräns som vi då kan sätta är att vi har observerat färre än 2,44 magnetiska monopoler under hela analysens åtta år, vilket motsvarar en övre gräns på flödet på färre än 2,54 × 10−19monopoler per kvadratcentimeter per sekund per steradian. Vårt resultat är alltså mer än 10 gånger bättre än det senaste motsvarande resultatet.
17. Acknowledgements
This thesis is dedicated to my children Olivia and Victor, who are all that is best in me. The five years that have led up to the writing of this thesis have been world-altering for me. Not only was I introduced to the role of a modern day re-searcher, and allowed to immerse myself in the international collaboration that is IceCube, but I also got married and had two children, as well as bought and sold two apartments and bought my first house, In addition to this, the final year of my Ph.D. period has been afflicted with a global pandemic, that has affected every aspect of our lives.
In this section I would like to highlight and thank some of the people who have contributed to my endeavor over the last five years.
To my main supervisor — Carlos Pérez de los Heros — thank you for your guidance over the last five years. Thank you indulging my unconventional ideas and discussions about all aspects of our work, from the scientific method to the nature of particle physics, from the state of Swedish particle physics to career advice, and personal topics such as vacations, children, Spain, etc. Your engagement and (figuratively) always open door is an inspiration for me.
To my former main supervisor, now co-supervisor — Allan Hallgren — thank you for brining me into the group and for your generous support over these years. I have met few people with such a high physics creativity as you have, and many a problem has been solved by your unprecedented “but have you tried this way?” or “have you checked this aspect?”. This boundless creativity is something that I continue to try to to internalize.
To my co-supervisor — Olga Botner — thank you for your inspiration and support over these years. Never have I met someone with such a piercing thought processes as yours. No matter what the issue is, you always find the core and twist and turn it until a solution can be found. You are the epitome of a physicist, with an unmatched physics intuition that I will always strive for.
To all of my supervisors, thank you for allowing me the freedom to trial different topics within our group, before finally selecting beyond the standard model astroparticle physics.
Thank you to Rickard and Henric for welcoming me to the group. And thank you to all of my previous and current colleagues at Uppsala University — Jim, Max, Mikael, Jan, Maja, Myrto, Olga S. G., Thomas, Venu, Walter, Elisabetta, Johan, Erin, Nora, Bo, and all others — for having made my time here very enjoyable through all of the lunches, fika and discussions. And thank you to Arnaud for your thorough feedback on this thesis. An additional thank
you to my colleagues in the Stockholm University IceCube group — Samuel, Jon, Martin, Marcel, Kunal, Matti, Maryon, Chad, Klas, Christian.
In the wider IceCube collaboration I would like to thank Anna P., who has grown into a close friend, for your mentorship and your patience with my endless questions about monopoles, about simulations, about weighting and upper limits, and for your support both in work and in life. And to Sophie — welcome to the world! Additionally, I also want to extend thanks to several colleagues within IceCube — Morten, Joakim, Mike, Liz, Ward, Christoph, Shivesh, Elim, Anna N, Michael, Justin, Frederik — for the good times we had in collaboration meetings and bootcamps.
Of all my colleagues I most want to send thanks to Lisa. You welcomed me with open arms for my very first job-interview with the group, and the time we shared as office mates will always shine bright in my memory. When you were there the office was large and warm and welcoming, and when you were out it was cold and small and unforgiving. Countless hours have we spent discussing, trouble-shooting and laughing, and you always provided support when needed. It was impossible to be unhappy when you were around. And thank you to Jerome for your endless patience, and to Jeli just for existing.
Thank you to my father, my mother and my brother — Douglas, Anne and Christian — for having been there through the good times and the bad, and for always believing in me. And thank you to my mother-in-law — Annette — for the numerous times you have helped us solve our life-puzzle over the last few years. Also thank you to my remaining family — Anneli, Pierre, Orvokki & Jari, Christian & Jenny, Linus, Hampus, Pontus, Linnea & Ted, Simon & Elin, Boel & Bosse, Janne & Lena, Anne-Lie, Kicki — for cheering me on and for providing support when needed.
A special thanks to my closest friends — Niklas, Camilla, Jonas — as well as Edda and Mira — for always being there, and for your patience with my work. An additional thank you to my friends — Martin, Marcus, Daniel, Filip, Douglas, Chuck, Alexandra, Veronica, Angelica & Marcus, Sofi & Simon.
I want to thank my children — Olivia and Victor — for bringing the biggest possible joy to my life. You are the reasons that I get up in the morning, and who I think about before falling asleep. Thank you for existing, for surprising me with your new capabilities, for your humor and for providing me with unconditional love and kindness.
Last but not least, as the cliché goes, I want to thank my loving wife — Angelica. Thank you for having put up with all of this. Thank you for taking on all of the roles that I needed in my Ph.D. endeavor — for cheering me on when I was out, for pushing me when I was lazy, for being my sounding board when I needed to vent and break things down, for strengthening me when I needed to stand up for myself and thank you for pulling me back up when I was down. Without your partnership and your support the last five years would not have been possible, thank you for making them the best years so far. I love you.
A. The IceCube EHE Analysis
Step I of the analysis that is presented in this thesis is formed by the event selection of another IceCube analysis — the Extremely High Energy (EHE) analysis. The purpose of the EHE analysis [46] is to discover a flux of cosmo-genic neutrinos with high energy (typically Eν & 108GeV) that was formed through the Greisen-Zatsepin-Kusmin (GZK) mechanism [81]. These neutri-nos are produced through the interaction between ultra high energy cosmic ray particles (protons or nuclei) and the cosmic microwave background, and are expected to have a different energy distribution than the diffuse astrophysical neutrino flux that is the background in the analysis presented in this thesis.
The EHE event selection is designed to accept as many neutrinos as possible with a high incident energy, while rejecting the majority of events with an atmospheric origin, and is described in Chapter 10.2. The event selection mainly selects based on the registered brightness of an event, which is highly correlated with the event deposited energy, and the cut value is determined by the reconstructed direction of the incident neutrino and its track fit quality. The selection variables in the EHE analysis are:
• The number of registered photo-electrons, nPE, and its base-10 loga-rithm, log10(nPE).
• The number of detector channels (DOMs) with registered charge, nCH. • The fit quality (the reduced χ2 parameter) of the EHE track
recon-struction, χred,EHE2 .
• The cosine of the zenith direction of the EHE reconstructed track, cos(θzen,EHE).
The selection criteria per analysis level are summarized below: The EHE filter Data reduction by selection on nPE:
nPE≥ 1000 (A.1)
The offline EHE cut Quality and data reduction cuts on nPE, nCH and χred,EHE2 separately:
nPE≥ 25 000 (A.2)
nCH≥ 100 χred,EHE2 ≥ 30
Figure A.1.Distributions of the signal (cosmogenic neutrinos) and background (atmo-spheric muons, conventional atmo(atmo-spheric neutrinos, prompt atmo(atmo-spheric neutrinos) of the EHE analysis, over event brightness, denoted by NPE, and fit quality, denoted by χ2/ndf, along with the track quality cut criterion (Equation A.3). Credit: Figure 1 from reference [46].
Figure A.2.Distributions of the signal (cosmogenic neutrinos) and background (atmo-spheric muons, conventional atmo(atmo-spheric neutrinos, prompt atmo(atmo-spheric neutrinos) of the EHE analysis, over event brightness, denoted by NPE, and fit quality, denoted by cos(θLF), along with the muon bundle cut criterion (Equation A.4). Credit: Figure 2 from reference [46].
The track quality cut Rejection of prompt atmospheric electron neutrinos: log10(nPE) ≥ 4.6 if χred,EHE2 < 80 4.6 + 0.015 × χ2 red,EHE− 80 if 80 ≤ χred,EHE2 < 120 5.2 if 120 ≤ χred,EHE2 (A.3) The muon bundle cut Rejection of atmospheric muon and muon neutrino
events from above.
log10(nPE) ≥ 4.6 if cos(θzen,EHE) < 0.06 4.6 + 1.85× r 1 − cos(θ zen,EHE)−1 0.94 2 if 0.06 ≤ cos (θzen,EHE) (A.4)
The surface veto Rejecting downwards directed events (θzen,EHE< 85°) in coincidence with two or more registered photons in the IceTop surface array. Simulated event distributions of the EHE analysis signal (cosmogenic trinos) and background (atmospheric muons, conventional atmospheric neu-trinos, prompt atmospheric neutrinos) are shown in Figures A.1 and A.2. Fig-ure A.1 shows the distributions over event brightness, here denoted by NPE, and fit quality, denoted by χ2/ndf, along with the applied selection criterion of the track quality cut. Correspondingly, Figure A.2 shows the distributions over event brightness and reconstructed zenith direction, here denoted by cos(θLF), along with the applied selection criterion of the muon bundle cut.
This results in a total rejection of all events with a brightness of log10(nPE) < 4.6 (i.e. nPE. 4.0 × 104) and full acceptance of all events with log10(nPE) ≥ 6.45 (i.e. nPE& 2.8 × 106). Between these values, the acceptance depends on the direction and fit quality of the event. The atmospheric muon and neu-trino event rates over each analysis level are displayed in Table A.1 along with the corresponding acceptance of cosmogenic neutrinos relative the EHE filter level.
Table A.1. The expected event rate of atmospheric muons and neutrinos, along with the acceptance of cosmogenic neutrinos relative the EHE filter level, for the EHE analysis levels [46].
Atmospheric Atmospheric Cosmogenic muon event neutrino event neutrino relative
Analysis level rate [Hz] rate [Hz] acceptance
EHE filter 0.8 7.6 × 10−6 1.00
Offline EHE cut 6.7 × 10−4 1.0 × 10−8 0.74
Track quality cut 1.6 × 10−4 6.1 × 10−10 0.61
Before applying the selection criteria, the selection variables in this analysis were validated against experimental data. This is described in Chapter 5.4.1.
The EHE analysis has been applied to 9 yr of experimental data, constituted by the detector seasons IceCube-40, -59, -79 and IceCube-86 I–VI. The EHE analysis was initially developed for the first four of these seasons, and the following seasons were added incrementally. One effect of this was that the full final season, IC86-VI, was designated as physics sample, as opposed to being divided into physics and burn samples.
Over the full 9 yr period, the EHE event selection was expected to accept an average of less than 0.085 events of atmospheric origin. The neutrino effective area of the event selection using the full detector configuration (IceCube-86) is shown in Figure 13.2.
The accepted neutrino events are expected to originate both from the dif-fuse astrophysical neutrino flux, measured by IceCube up to ∼ PeV ener-gies [73; 75; 79], and the GZK neutrino flux, which is not yet experimentally discovered. The diffuse astrophysical neutrino flux thus forms the dominant background for the EHE analysis. In the EHE analysis, the astrophysical flux is distinguished from the GZK neutrinos through statistical methods, as well as an event-by-event consideration. The result is an upper limit on the abundance of cosmogenic neutrinos.
B. Step I Observed Events over BDT Variables
The Step II BDT score and variable values of the Step I observed events A, B and C are displayed in Figures B.1, B.2, B.3 and B.4, and listed in Table B.1.
Figure B.1. The Step I observed events A, B and C over the Step II BDT score, along with the simulated magnetic monopole and astrophysical neutrino event distributions.
Table B.1. The values taken by the three Step I observed events A, B and C in the Step II BDT variables, as well as the BDT score.
Event A Event B Event C
BDT score −0.089 −0.742 −0.626
βBM 1.127 0.628 0.942
rsd(EMIL) 3.20 4.97 7.25
avg(dDOM,Q)CV-TrackChar 42.8 m 67.6 m 54.1 m
tFWHM,CV-TimeChar 2.76 µs 2.78 µs 2.56 µs LFRCV-TrackChar 0.615 0.362 0.344 RCOCV-HitStats 0.0458 0.434 0.0886 log10(nPE) 5.10 5.30 5.32 cos(θzen,BM) −0.203 0.0205 0.391 dC,BM 314 m 418 m 137 m
(a)The Step II speed variable,βBM.
(b)The Step II energy loss RSD variable, rsd(EMIL).
(c)The Step II average pulse distance variable,
avg(dDOM,Q)CV-TrackChar.
Figure B.2. The Step I observed events A, B and C over the Step II BDT variables, along with the simulated magnetic monopole and astrophysical neutrino event distri-butions.
(a)The Step II pulse-time FWHM variable,
tFWHM,CV-TimeChar.
(b)The Step II length fill ratio variable,
LFRCV-TrackChar.
(c)The Step II relative CoG offset variable,
RCOCV-HitStats.
Figure B.3. The Step I observed events A, B and C over the Step II BDT variables, along with the simulated magnetic monopole and astrophysical neutrino event distri-butions.
(a)The Step II
log-brightness variable, log10(nPE).
(b)The Step II cos-zenith variable, cos(θzen,BM).
(c)The Step II centrality variable, dC,BM.
Figure B.4. The Step I observed events A, B and C over the Step II BDT variables, along with the simulated magnetic monopole and astrophysical neutrino event distri-butions.
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