B.S.E., University of Michigan (2019) Department of Physics

Doctor of Philosophy

June 2023 May 23, 2023

© 2023 Nicholas Kamp. All rights reserved.

The author hereby grants to MIT a nonexclusive, worldwide, irrevocable,
royalty-free license to exercise any and all rights under copyright, including
to reproduce, preserve, distribute and publicly display copies of the thesis,
or release the thesis under an open-access license.

Janet M. ConradProfessor

Lindley WinslowAssociate Department Head of Physics

# Experimental and Phenomenological Investigations of the MiniBooNE Anomaly

Nicholas Kamp

The $4.8\sigma$ excess of electron neutrino-like events reported by the
MiniBooNE experiment at Fermilab’s Booster Neutrino Beam (BNB) is one of the
most significant and longest standing anomalies in particle physics. This
thesis covers a range of experimental and theoretical efforts to elucidate the
origin of the MiniBooNE low energy excess (LEE). We begin with the follow-up
MicroBooNE experiment, which took data along the BNB from 2016 to 2021. The
detailed images produced by the MicroBooNE liquid argon time projection
chamber enable a suite of measurements that each test a different potential
source of the MiniBooNE anomaly. This thesis specifically presents
MicroBooNE’s search for $\nu_{e}$ charged-current quasi-elastic (CCQE)
interactions consistent with two-body scattering. The two-body CCQE analysis
uses a novel reconstruction process, including a number of deep-learning based
algorithms, to isolate a sample of $\nu_{e}$ CCQE interaction candidates with
$75\%$ purity. The analysis rules out an entirely $\nu_{e}$-based explanation
of the MiniBooNE excess at the $2.4\sigma$ confidence level. We next perform a
combined fit of MicroBooNE and MiniBooNE data to the popular $3+1$ model; even
after the MicroBooNE results, allowed regions in $\Delta
m^{2}$-$\sin^{2}2_{\theta_{\mu e}}$ parameter space exist at the $3\sigma$
confidence level. This thesis also demonstrates that, due to nuclear effects
in the low-energy cross section behavior, the MicroBooNE data are consistent
with a $\overline{\nu}_{e}$-based explanation of the MiniBooNE LEE at the
$<2\sigma$ confidence level. Next, we investigate a phenomenological
explanation of the MiniBooNE excess involving both an eV-scale sterile
neutrino and a dipole-coupled MeV-scale heavy neutral lepton (HNL). It is
shown that a 500 MeV HNL can accommodate the energy and angular distributions
of the LEE at the $2\sigma$ confidence level while avoiding stringent
constraints derived from MINER$\nu$A elastic scattering data. Finally, we
discuss the Coherent CAPTAIN-Mills (CCM) experiment–a 10-ton light-based
liquid argon detector at Los Alamos National Laboratory. The background
rejection achieved from a novel Cherenkov-based reconstruction algorithm will
give CCM world-leading sensitivity to a number of beyond-the-Standard Model
physics scenarios, including dipole-coupled HNLs.

### Acknowledgments

Development from a starry-eyed first year graduate student into a competent
researcher is like the MSW effect: it doesn’t happen in a vacuum. There are
many people who have helped me along the way in both physics and life, without
whom I would never have gotten to the point of writing this thesis.

First and foremost, I owe an immense debt of gratitude to Janet Conrad. Janet
has been an incredible mentor to me during my time as a graduate student; her
advice and wisdom have helped me become the scientist I wanted to be when I
came to MIT four years ago. I’d like to specifically thank Janet for taking my
interests seriously and working with me to develop research projects that
matched them. Creativity, ingenuity, enthusiasm, and kindness run rampant in
the Conrad group–I will always be grateful for being offered a spot in it. I
look forward to many years of fruitful collaboration to come.

To my partner, Wenzer: thank you for the love, support, and patience over the
last two years. Life is not so hard when we can act as a restoring force for
one another–I am grateful for having been able to rely on it while writing
this thesis. I look forward with great excitement to our future adventures
together.

Thank you to my past mentors: Christine Aidala for introducing me to particle
physics through POLARIS, Robert Cooper for asking me about my research at APS
DNP 2016, Bill Louis for answering my many questions about neutrino physics in
my first summer at LANL, Richard Van de Water for teaching me to follow the
data (which greatly influenced my choice of graduate research), and Josh Spitz
for helping develop confidence as a neutrino physicist on JSNS2. I’d also like
to thank Christopher Mauger and the rest of the Mini-CAPTAIN team for an
introduction to what it takes to run a particle physics experiment at an
accelerator.

Thank you to members of the Conrad group past and present: those I worked
with, Lauren Yates, Adrian Hourlier, Jarrett Moon, Austin Schneider, Darcy
Newmark, Alejandro Diaz, and John Hardin, for being fantastic collaborators,
and those I did not, Loyd Waits, Joe Smolsky, Daniel Winklehner, Philip
Weigel, and Josh Villareal, for making MIT a brighter place. Thank you
especially to Austin for your infinite patience in answering my many questions
on statistics and software–each of our projects has been a great pleasure.

To my MicroBooNE collaborators not mentioned above, Taritree Wongjirad, Katie
Mason, Joshua Mills, Polina Abratenko, Ran Itay, Mike Shaevitz, Georgia
Karagiorgi, Davio Cianci, Rui An, and everyone else: thank you for your
excellent teamwork in putting together the Deep Learning analysis.

To my CCM collaborators not mentioned above, Edward Dunton, Mayank Tripathi,
Adrian Thompson, Will Thopmson, Marisol Chávez Estrada, and everyone else:
thank you for the invigorating research and discussion over the last couple of
years, and best of luck with CCM200!

Thank you to Carlos Argüelles, Mike Shaevitz, Matheus Hostert, Stefano
Vergani, and Melissa Uchida for your excellent mentorship and collaboration in
our phenomenological endeavors together. Thank you specifically to Carlos for
giving me a welcome introduction to neutrino phenomenology, Mike for ensuring
the robustness of each analysis, and Matheus for patiently answering my many
model-building questions.

To all of my friends not mentioned above; Jack, Ryan, Alexis, Melissa, Ben,
Bhaamati, Charlie, Vincent, Patrick, Caolan, Ouail, Artur, Sam, Zhiquan,
Rebecca, Felix, Lila, Rahul, Brandon, Field, Kelsey, Woody, Joey, Rory,
Cooper, Daniel, Kaliroë, Elena, and everyone else: thank you for all of the
great memories–climbing, hiking, skiing, playing music, eating, drinking,
commiserating, and laughing–over the past four years. Thank you especially to
the last three for making preparation for the oral exam significantly more
enjoyable.

Thank you to the MIT administrative staff, including (but not limited to)
Lauren Saragosa, Karen Dow, Catherine Modica, Sydney Miller, Alisa Cabral, and
Elsye Luc, for helping make graduate school a more manageable endeavor. Thank
you also to the rest of my thesis committee, Joseph Formaggio and Washington
Taylor, for helping me get through the final part of graduate school.

Finally, thank you to my parents, Jim and Carla, my siblings, Serafina and
Daniel, and the rest of my family. From elementary school science fairs to
Saturday Morning Physics to today, none of this would have been possible
without your love and support.

###### Contents

  1. 1 Introduction
    1. 1.1 A Brief History of the Neutrino
    2. 1.2 Neutrinos in the Standard Model
    3. 1.3 Massive Neutrinos
    4. 1.4 Anomalies in the Neutrino Sector
  2. 2 The MiniBooNE Experiment
    1. 2.1 Overview of MiniBooNE
      1. 2.1.1 The Booster Neutrino Beam
      2. 2.1.2 The MiniBooNE Detector
    2. 2.2 The MiniBooNE Low Energy Electron-Like Excess
  3. 3 The MicroBooNE Detector
    1. 3.1 Liquid Argon Time Projection Chamber
      1. 3.1.1 Cryogenics
      2. 3.1.2 LArTPC Drift System
      3. 3.1.3 Light Collection System
    2. 3.2 TPC Signal Processing
      1. 3.2.1 Noise Filtering
      2. 3.2.2 Deconvolution
  4. 4 The MicroBooNE Electron Neutrino Analysis: Overview and Selection
    1. 4.1 Dataset and Simulation
    2. 4.2 The Electron Low Energy Excess Template
    3. 4.3 Philosophy Behind the Two-Body CCQE Analysis
    4. 4.4 Reconstruction
      1. 4.4.1 Convolutional Neural Networks in LArTPCs
      2. 4.4.2 Vertex and Track Reconstruction
      3. 4.4.3 Publication: Electromagnetic shower reconstruction and energy validation with Michel electrons and $\pi^{0}$ samples for the deep-learning-based analyses in MicroBooNE
    5. 4.5 $1e1p$ Event Selection
      1. 4.5.1 Basic Data Selection Criteria
      2. 4.5.2 Boosted Decision Tree Ensemble
      3. 4.5.3 Particle Identification Cuts
      4. 4.5.4 The Final $1e1p$ Sample
  5. 5 The MicroBooNE Electron Neutrino Analysis: Results and Discussion
    1. 5.1 First Results from the Two-Body CCQE Analysis
      1. 5.1.1 Background Estimation
      2. 5.1.2 Evaluation of Systematic Uncertainties
      3. 5.1.3 Constraint from the $1\mu 1p$ Sample
      4. 5.1.4 Blinded Analysis Approach
    2. 5.2 Statistical Interpretation
      1. 5.2.1 Goodness of Fit
      2. 5.2.2 Two Hypothesis Test
      3. 5.2.3 Signal Strength Scaling Test
    3. 5.3 Discussion and Outlook
      1. 5.3.1 Publication: MiniBooNE and MicroBooNE Combined Fit to a $3+1$ Sterile Neutrino Scenario
      2. 5.3.2 Publication: Implications of MicroBooNE’s low sensitivity to electron antineutrino interactions in the search for the MiniBooNE excess
  6. 6 Neutrissimos: Heavy Neutral Leptons with a Dipole Moment
    1. 6.1 Dipole-Portal Neutrissimos
    2. 6.2 Overview of the Mixed Model
    3. 6.3 Neutrissimos in MiniBooNE
      1. 6.3.1 Simulation in LeptonInjector
      2. 6.3.2 Fits to the MiniBooNE Excess
    4. 6.4 Publication: Dipole-coupled neutrissimo explanations of the MiniBooNE excess including constraints from MINERvA data
  7. 7 The Coherent CAPTAIN-Mills Experiment
    1. 7.1 The CCM Beamline and Detector
    2. 7.2 Cherenkov Light Reconstruction
      1. 7.2.1 Simulation-Based Sensitivity Estimation
      2. 7.2.2 Identifying Cherenkov Light in Data
    3. 7.3 Neutrissimos in CCM
  8. 8 Conclusions and Future Prospects
  9. A Publication: Convolutional neural networks for shower energy prediction in liquid argon time projection chambers
  10. B Signal Event Displays from the Two-Body CCQE Analysis

###### List of Figures

  1. 1.1 Telegram from Fred Reines and Clyde Cowan informing Wolfgang Pauli of their detection of neutrinos from a nuclear reactor.
  2. 1.2 The deficit of the observed solar $\nu_{e}$ flux compared with the theoretical expectation. The Homestake experiment is shown on the far left; follow-up solar neutrino measurements confirming the deficit are also shown, including the 2002 SNO result which brought forth a solution to the solar neutrino problem. Figure from Ref. [1].
  3. 1.3 The up-down asymmetry measured in SuperK as a function of lepton momentum, separated into $e$-like and $\mu$-like events as well as fully-contained (FC) and partially-contained (PC) events. The dashed line indicates the best fit to $\nu_{\mu}\to\nu_{\tau}$ oscillations. Figure from Ref. [2].
  4. 1.4 Measurement of the solar 8B flux from the SNO collaboration, broken down into the $\nu_{e}$ and $\nu_{\mu,\tau}$ sub-components. Measurement of the CC, NC, and ES channels show up as slices in the two-dimensional flux parameter space. Figure from Ref. [3].
  5. 1.5  Diagrams contributing to $\nu e^{-}$ elastic scattering
  6. 1.6  Diagrams contributing to $\overline{\nu}e^{-}$ elastic scattering
  7. 1.7  Diagrams contributing to neutrino-nucleon charged-current quasielastic scattering
  8. 1.8 CC inclusive neutrino and antineutrino nucleon scattering cross sections as a function of neutrino energy. Figure from Ref. [4].
  9. 1.9 The LSND excess of $\overline{\nu}_{e}$ events on top of the predicted SM background (green and red regions). The blue region indicates the best fit to $\overline{\nu}_{\mu}\to\overline{\nu}_{e}$ oscillations via a sterile neutrino state. Figure from Ref. [5]
  10. 1.10 The MiniBooNE electron-like channel data and SM background prediction for the entire neutrino mode dataset, as a function of the reconstructed neutrino energy.
  11. 1.11 Data contributing to the reactor antineutrino anomaly, indicating the $\sim 5\%$ flux deficit observed by short-baseline reactor neutrino experiments. The red line indicates the prediction incorporating SM neutrino oscillations only, while the blue line shows an example prediction including a sterile neutrino. Figure from Ref. [6].
  12. 1.12 Data contributing to the gallium anomaly, indicating the $\sim 20\%$ deficit in the 71Ge production rate observed by SAGE, GALLEX, and BEST. Figure from Ref. [7].
  13. 1.13 Preferred regions in $\sin^{2}2\theta_{ee}$–$\Delta m^{2}$ parameter space to explain the RAA [8] (green contour) and gallium anomaly [9] (blue regions). The total excluded region from other experiments (grey region) is also shown. Figure from Ref. [9].
  14. 1.14 Preferred regions in $\sin^{2}2\theta_{\mu e}$–$\Delta m^{2}$ parameter space to explain the LSND anomaly [5] (filled contours) and MiniBooNE anomaly [10] (open contours). Figure from Ref. [10].
  15. 1.15 Graphical representation of the tension observed in 3+1 global fits between different subsets of the experimental landscape. Figure 1.15(a) shows the tension between $\nu_{e}$ appearance experiments and $\nu_{e}$/$\nu_{\mu}$ disappearance experiments observed in Ref. [11]. Figure 1.15(b) shows the tension between allowed regions from $\nu_{e}$ appearance (lower right), $\nu_{e}$ disappearance (upper right), and $\nu_{\mu}$ disappearance (upper left) experiments observed in Ref. [12], which includes the latest results from the BEST experiment.
  16. (a) From Ref. [11]
  17. (b) From Ref. [12]
  18. 2.1 A schematic depiction of the BNB at Fermilab, including the downstream MiniBooNE detector. Figure from Ref. [13].
  19. 2.2 Breakdown of the neutrino flux at the BNB in neutrino (left) and antineutrino (right) mode. Figure from Ref. [14]
  20. 2.3 The MiniBooNE detector situated in the cylindrical detector hall (left) and an image of the interior of the MiniBooNE detector (right), showing the PMTs in both the signal and veto regions. Figure from Ref. [15].
  21. 2.4 Visual representations of particle identification in MiniBooNE. Figure 2.4(a) shows a schematic representation of the detector signature from the three main particle classes in MiniBooNE: muons, electrons, and neutral pions. Figure 2.4(b) shows the MiniBooNE log-likelihood-ratio between the $e$-like and $\mu$-like hypothesis as a function of reconstructed neutrino energy, considering both simulated $\nu_{e}$ CCQE (top) and $\nu_{\mu}$ CCQE (bottom) interactions.
  22. (a) From Ref. [76]
  23. (b) From Ref. [77]
  24. 2.5 The $E_{\nu}^{\rm QE}$ distribution of the MiniBooNE $e$-like excess in the total neutrino mode (figure 2.5(a)) and antineutrino mode (figure 2.5(b)) datasets. The observation and SM prediction in each bin are shown by the data points and colored histograms, respectively.
  25. (a) $\nu_{e}$ sample, from Ref. [10]
  26. (b) $\overline{\nu}_{e}$ sample, from Ref. [79]
  27. 2.6 The lepton visible energy (figure 2.6(a)) and $\cos\theta$ (figure 2.6(b)) distributions of the MiniBooNE $e$-like excess in the total neutrino mode dataset. The observation and SM prediction in each bin are shown by the data points and colored histograms, respectively. Figures from Ref. [10].
  28. (a) Lepton $E_{\rm vis}$ distribution
  29. (b) Lepton $\cos\theta$ distribution
  30. 2.7 The MiniBooNE and LSND excesses as a function of the ratio $L/E$. The MiniBooNE data is separated into neutrino and antineutrino mode. Figure from Ref. [10].
  31. 3.1 Schematic depictions of the MicroBooNE LArTPC. Figure 3.1(a) shows the detection process for charged particles from a neutrino interaction in a MicroBooNE-like LArTPC. Figure 3.1(b) shows a cross-sectional view of the MicroBooNE detector along the $-\hat{z}$ direction. Figures from Ref. [16].
  32. (a)
  33. (b)
  34. 3.2 Figure 3.2(a) shows a close-up image of the cathode plane of the MicroBooNE LArTPC. The stainless steel field cage tubes can also be seen surrounding the active volume. Figure 3.2(b) shows a cross-sectional map of the electric field at the edge of the active volume, considering a cathode plane voltage of -128 kV. The legend shows the field strength in units of V/m. Figures from Ref. [16].
  35. (a)
  36. (b)
  37. 3.3 Figure 3.3(a) shows a photograph of a single wire carrier board with 32 mounted wires. Figure 3.3(b) shows the fully-assembled MicroBooNE LarTPC, highlighting the anode plane mounted on the stainless steel frame. Figures from Ref. [16].
  38. (a)
  39. (b)
  40. 3.4 The LAr scintillation light spectrum, TPB ultra-violet absorption spectrum, TPB emission spectrum, PMT quantum efficiency, and PMT surface transmission efficiency as a function of photon wavelength. Figure from Ref. [17].
  41. 3.5 Figure 3.5(a) shows a photograph of a single PMT system used in the MicroBooNE detector. The acrylic window here has not yet been coated with TPB. Figure 3.5(b) shows the PMT signal from a stopped cosmic muon (top) that decays to a Michel (bottom). Figures from Ref. [16].
  42. (a)
  43. (b)
  44. 3.6 2D displays of the signal from wires in one of the induction planes in a single data event, before and after the application of the offline noise filters. Figure from Ref. [18].
  45. 3.7 A U plane event display of a candidate neutrino interaction in the MicroBooNE data. The impact of the 1D and 2D deconvolution algorithms on the post-noise-filtering signal is shown. Figure from Ref. [19].
  46. 4.1 Figure 4.1(a) shows the unfolded $\nu_{e}$ prediction in MiniBooNE calculated using the first $6.46\times 10^{20}$ POT of neutrino mode data [20]. Figure 4.1(b) shows the unfolded eLEE model weights derived from the first $12.84\times 10^{20}$ POT of MiniBooNE neutrino mode data, which constitute the MicroBooNE eLEE model.
  47. (a) From Ref. [20]
  48. (b)
  49. 4.2 The expected distribution of $\nu_{e}$ interactions in MicroBooNE as a function of the true $\nu_{e}$ energy. The dotted line shows the expectation from the MicroBooNE eLEE model of the MiniBooNE excess discussed in section 4.2.
  50. 4.3 An example candidate $1e1p$ data event in MicroBooNE, including the raw LArTPC collection plane image (left) and the pixel labels assigned from SparseSSNet (right).
  51. 4.4 The relationship between the final state lepton (left) and proton (right) energy and scattering angle, for different neutrino energies, in $\nu_{\mu}$ (top) and $\nu_{e}$ (bottom) CCQE scattering.
  52. 4.5 Figure 4.5(a) shows a diagram of the SparseSSNet U-ResNet architecture. Figure 4.5(b) shows the SparseSSNet pixel labels on a simulated image in the training dataset. Figures from Ref. [21].
  53. (a)
  54. (b)
  55. 4.6 Figure 4.6(a) shows a diagram of the MPID architecture. Figure 4.6(b) shows the MPID image scores on an example simulated event. Figures from Ref. [22].
  56. (a)
  57. (b)
  58. 4.7 The fraction of EM showers reconstructed to within 5% of the true deposited energy as a function of the fraction of unresponsive wires in the LArTPC collection plane, considering three different methods. The ResNet and Inception network significantly outperform the traditional linear calibration between charge and energy. Figure from Ref. [23].
  59. 4.8 Figure 4.8(a) shows the angular metric that is minimized to find a 3D neutrino vertex candidate. Figure 4.8(b) shows the iterative track reconstruction algorithm, which relies on calculating distances (L1 and L2) and angles ($\theta$ and $\phi$) with respect to the previous point and the end of the track. Figures from Ref. [24].
  60. (a)
  61. (b)
  62. 4.9 An example of an event that fails the shower energy consistency cut, because the EM shower passes through an unresponsive region of the collection plane.
  63. 4.10 Figure 4.10(a) shows the distribution of the fractional shower energy consistency variable for events with an old $1e1p$ BDT score above/below 0.7. Figure 4.10(b) shows the efficiency with which events above/below the old $1e1p$ BDT cutoff pass the fractional consistency cut as a function of the chosen upper bound.
  64. (a)
  65. (b)
  66. 4.11 The F score of each variable for one of the $1e1p$ BDTs in the ensemble from run 1, run2, and run 3.
  67. (a) Run 1
  68. (b) Run 2
  69. (c) Run 3
  70. 4.12 Figure 4.12(a) and figure 4.12(b) show the MC distribution of the $1e1p$ BDT ensemble average score over all three run periods for the full [0,1] range and zoomed in to the [0.95,1] range, respectively.
  71. (a)
  72. (b)
  73. 4.13 Figure 4.13(a) and figure 4.13(b) show the predicted $\nu_{e}$ event rate in run period 2 and run period 3, respectively, using both the run period 2 ensemble and the run period 3 ensemble.
  74. (a)
  75. (b)
  76. 4.14 Figure 4.14(a) and figure 4.14(b) show the fractional difference in average BDT score $(S_{n}-S_{0})/S_{0}$ as a function of the number of omitted BDTs $n$ over the simulation from run period 2 and run period 3, respectively. The red histogram shows the actual distribution of the number of omitted BDTs over the run period 2 and run period 3 simulation samples, respectively. Scores are calculated using the run period 3 and run period 2 BDT ensemble, respectively.
  77. (a)
  78. (b)
  79. 4.15 Figure 4.15(a) and figure 4.15(b) show the MPID electron and muon score, respectively, as a function of the reconstructed electron energy in intrinsic $\nu_{e}$ MC events.
  80. (a)
  81. (b)
  82. 4.16 The $E_{\nu}^{\rm range}$ distribution for the $1e1p$ signal sample, showing only the predicted event rate from the MC. The prediction from the eLEE model is shown in the dashed blue line.
  83. 4.17 Figure 4.17(a) shows the distribution of the fractional error on the neutrino energy for MC events in the $1e1p$ signal sample, restricted to $200<E_{\nu}^{\rm Range}\;[{\rm MeV}]<1200$. Figure 4.17(b) shows the 2D distribution of fractional error as a function of the true neutrino energy.
  84. (a)
  85. (b)
  86. 4.18 Figure 4.18(a) shows the post-vertex-identification efficiency of true $\nu_{e}$ CCQE selection for subsequent stages of the $1e1p$ cuts. Figure 4.18(b) shows the true $\nu_{e}$ CCQE event rates over the full run 1-3 dataset after subsequent stages of the $1e1p$ cuts.
  87. (a)
  88. (b)
  89. 5.1 Top: pixel intensity (color scale is in PIU as defined in section 4.4); Bottom: SparseSSNet labels; Left to Right: U, V, Y, planes. The white circle indicates the reconstructed vertex. The horizontal axis corresponds to the wire plane direction and the vertical axis corresponds to the electron drift direction, which is measured using the arrival time of charge on the wires.
  90. 5.2 The $1e1p$ sample $E_{\nu}$ distribution, comparing data (black points) to the unconstrained prediction (stacked histogram) in the $200<E_{\nu}<1200$ MeV region. The eLEE model prediction is represented by the dashed blue line. The prediction is presented in terms of both interaction type (figure 5.2(a)) and final state topology (figure 5.2(b)).
  91. (a)
  92. (b)
  93. 5.3 Average $1e1p$ BDT ensemble score distribution comparing data to the unconstrained prediction.
  94. 5.4 Comparison between data and unconstrained prediction in the $E_{e}$ (figure 5.4(a)), $E_{p}$ (figure 5.4(b)), $\theta_{e}$ (figure 5.4(c)), and $E_{\nu}^{QE-\ell}$ (figure 5.4(d)) distributions of the $1e1p$ sample.
  95. (a)
  96. (b)
  97. (c)
  98. (d)
  99. 5.5 The fit to the $\nu_{\mu}$ background distribution to the $1e1p$ analysis. The shape fit is performed at a loose BDT score cutoff of 0.7 (figure 5.5(a)) and scaled to the signal cutoff of 0.95 (figure 5.5(b)). Blue points represent the prediction from the simulation, with error bars representing the Gaussian approximation of the statistical error (quadrature sum of event weights). The orange line and corresponding shaded region represent prediction and uncertainty, respectively, coming from the Landau+linear fit.
  100. (a)
  101. (b)
  102. 5.6 The data and MC prediction for events with a $1e1p$ BDT score inside $[0.7,0.95]$. Good agreement is observed between data and prediction. The prediction incorporating the Landau+linear background fit is shown by the red line.
  103. 5.7 The uncertainty in each bin of the $E_{\nu}^{\rm range}$ distribution of the $1e1p$ (figure 5.7(a)) and $1\mu 1p$ (figure 5.7(b)) samples.
  104. (a)
  105. (b)
  106. 5.8 The joint covariance (figure 5.8(a)) and correlation (figure 5.8(b)) matrices for the $E_{\nu}^{\rm range}$ distribution of the $1e1p$ and $1\mu 1p$ samples.
  107. (a)
  108. (b)
  109. 5.9 The $E_{\nu}^{\rm range}$ distribution in the $1\mu 1p$ channel, comparing data to the MC prediction.
  110. 5.10 Fractional systematic uncertainty in the $1e1p$ $E_{\nu}^{\rm range}$ distribution before and after the $1\mu 1p$ constraint.
  111. 5.11 Comparison between data and prediction in the $1e1p$ $E_{\nu}^{\rm range}$ distribution after applying the $1\mu 1p$ constraint procedure.
  112. 5.12 Comparison between data and prediction in the $1e1p$ BDT ensemble average score distribution within the range $[0.7,0.95]$.
  113. 5.13 Distributions of the $\Delta\chi^{2}$ test statistic defined in equation 5.7 for $H_{0}$ (red) and $H_{1}$ (blue), calculated by generating $10^{5}$ pseudo-experiments under each hypothesis. The $\Delta\chi^{2}$ value of the data is also shown.
  114. 5.14 Confidence intervals on $x_{\rm LEE}$ calculating using the Feldman-Cousins procedure. The solid and dotted lines indicate the confidence level with which a given $x_{\rm LEE}$ is disfavored, calculated using the Feldman-Cousins method [25] and Wilks theorem [26], respectively. The MiniBooNE statistical and systematic errors are shown as a band around $x_{\rm LEE}=1$.
  115. 5.15 Figure 5.15(a) shows the observation compared to the nominal ($H_{0}$) prediction in all four signal channels from the three MicroBooNE $\nu_{e}$ analyses, including statistical errors on the data points and systematic errors on the prediction. The eLEE prediction ($H_{1}$) is also indicated by the red line. Figure 5.15(b) shows the observed $1\sigma$ and $2\sigma$ confidence intervals on $x_{\rm LEE}$ from all four signal channels. The $2\sigma$ expected sensitivity of each channel is shown in red.
  116. (a)
  117. (b)
  118. 6.1  Feynman diagram depicting the effective dipole operator of equation 6.1.
  119. 6.2 New interactions involving the neutrissimo that are enabled by the dipole operator in equation 6.1, including three-body $\pi^{0}$ decay (figure 6.2(a)), Primakoff-like upscattering (figure 6.2(b)), and neutrissimo decay (figure 6.2(c)).
  120. (a)
  121. (b)
  122. (c)
  123. 6.3 $3+1$ global fits including MiniBooNE, considering global (left), appearance-only (middle), and disappearance-only (right) experiments. The allowed regions in $3+1$ parameter space at the 90%, 95%, and 99% confidence levels are shown by the red, green, and blue points, respectively. The best-fit point is indicated by the star.
  124. 6.4 $3+1$ global fits without MiniBooNE, considering global (left), appearance-only (middle), and disappearance-only (right) experiments. The allowed regions in $3+1$ parameter space at the 90%, 95%, and 99% confidence levels are shown by the red, green, and blue points, respectively. The best-fit point is indicated by the star.
  125. 6.5 Schematic depiction of the neutrissimo model in MiniBooNE as simulated using LeptonInjector. Figure 6.5(a) shows the simulation of Primkaoff upscattering along the beamline, and figure 6.5(b) shows an example of upscattering, neutrissimo decay and pair-production within the MiniBooNE detector.
  126. (a)
  127. (b)
  128. 6.6 Allowed regions at the 95% and $3\sigma$ confidence level in $d_{\mu\mathcal{N}}$-$m_{\mathcal{N}}$ obtained through fits to the MiniBooNE excess in the $E_{\nu}^{\rm QE}$ and $\cos\theta$ distributions. Existing $2\sigma$ constraints on this model are indicated by the grey regions.
  129. 6.7 Figure 6.7(a) and figure 6.7(b) show the $E_{\nu}^{\rm QE}$ and $\cos\theta$ distributions of the MiniBooNE excess, respectively, compared with the prediction from the neutrissimo model indicated by the black star in figure 6.6. The oscillation contribution from the $3+1$ global fit without MiniBooNE is also shown.
  130. (a)
  131. (b)
  132. 6.8 The added time delay in MiniBooNE for a neutrissimo with the indicated parameters, as calculated in Ref. [27].
  133. 7.1 Schematic depiction of the Lujan TMRS Figure from Ref. [28].
  134. 7.2 Figure 7.3(a), from Ref. [29], shows the energy distribution of $\pi^{+}$ decay-at-rest neutrinos from the Lujan beam dump source. Figure 7.2(b), from Ref. [30], shows the timing distribution of particles produced in the Lujan beam dump source after traveling through the TMRS.
  135. (a)
  136. (b)
  137. 7.3 Figure 7.3(a) shows a schematic 3D rendering of the CCM200 detector. Figure 7.3(b) shows an image of the interior of the CCM200 detector.
  138. (a)
  139. (b)
  140. 7.4 Two of the veto PMT assemblies constructed at MIT, including the 1-inch PMT, base circuit board, and TPB-coated acrylic window.
  141. 7.5 Figure 7.5 shows one of the veto PMTs across from the LED in the light-tight box. Figure 7.5 shows the average response of the 20 veto PMTs to 1 V (top) and 2 V (bottom) LED pulses.
  142. 7.6 The timing distribution of photons from the Lujan source (solid black line) compared with that of neutrons measured in CCM120 (dashed red line). Figure from Ref. [30].
  143. 7.7 Figure 7.7(a) shows the integration in equation 7.1 as a function of $\lambda_{1}$ for $\lambda_{2}=700~{}{\rm nm}$ and $z=1$. Figure 7.7(b) shows the Cherenkov cone angle $\cos\theta_{C}$ for an electron as a function of the photon wavelength and the electron kinetic energy.
  144. (a)
  145. (b)
  146. 7.8 Templates of the average number of p.e. detected in each CCM PMT within the first 8 ns of an electron event. Different templates are shown for electron kinetic energies of $T_{e^{-}}=1~{}{\rm MeV}$ and $T_{e^{-}}=5~{}{\rm MeV}$, both with and without Cherenkov photons. Coated (uncoated) PMTs are indicated by the solid (dashed) circles. Grey PMTs indicate those which registered no hits within the first 8 ns across all simulations. The dimensions on each axis are in units of cm.
  147. (a) With Cherenkov photons; $T_{e^{-}}=1~{}{\rm MeV}$
  148. (b) Without Cherenkov photons; $T_{e^{-}}=1~{}{\rm MeV}$
  149. (c) With Cherenkov photons; $T_{e^{-}}=5~{}{\rm MeV}$
  150. (d) Without Cherenkov photons; $T_{e^{-}}=5~{}{\rm MeV}$
  151. 7.9 Example event displays showing the total number of p.e. detected in each CCM PMT within the first 8 ns of a single simulated electron event. Displays are shown for electron kinetic energies of $T_{e^{-}}=1~{}{\rm MeV}$ and $T_{e^{-}}=5~{}{\rm MeV}$. Coated (uncoated) PMTs are indicated by the solid (dashed) circles. Grey PMTs indicate those which registered no hits in the first 8 ns of this specific simulation.
  152. (a) $T_{e^{-}}=1~{}{\rm MeV}$
  153. (b) $T_{e^{-}}=5~{}{\rm MeV}$
  154. 7.10 Distributions of the test statistic in equation 7.6 over all $10^{4}$ simulations, considering either all photons or scintillation photons only. Distributions are shown for $T_{e^{-}}=1~{}{\rm MeV}$ and $T_{e^{-}}=5~{}{\rm MeV}$. The vertical line indicates the lower bound requirement which can reject 99% of scintillation-only backgrounds.
  155. (a) $T_{e^{-}}=1~{}{\rm MeV}$
  156. (b) $T_{e^{-}}=5~{}{\rm MeV}$
  157. 7.11 Curves of the efficiency to retain events with Cherenkov light (“Ring efficiency”) v.s. the fraction of events without Cherenkov light that can be rejected (“No-Ring Rejection Factor”), generated by considering successively larger lower bounds on $\Delta\log\mathcal{L}$. Different curves are shown for $T_{e^{-}}\in\\{1,2,3,4,5\\}~{}{\rm MeV}$.
  158. 7.12 Figure 7.12(a) shows a schematic depiction of the derivative-based pulse definition in the current CCM reconstruction. Figure 7.12(b) shows an example of this pulse finder in a data event, from Ref. [30].
  159. (a)
  160. (b)
  161. 7.13 Two example waveforms from CCM200 beam data. The regions identified by the derivative filter are indicated in red and the result of the fit to equation 7.7 is indicated by the purple curves.
  162. 7.14 Figure 7.14(a) shows an image of the six CosmicWatch pairs on top of the CCM detector. Figure 7.14 shows a schematic diagram of the cosmic muon trigger in CCM200.
  163. (a)
  164. 7.15 Figure 7.15(a) shows the summed waveform across all PMTs in CCM for a single example cosmic muon trigger. The delayed signal from a Michel electron can also be seen. Figure 7.15 shows the difference in rise times between coated and uncoated PMT signals in the top and bottom halves of the barrel of the detector (labeled “sides-top” and “sides-bottom”, respectively), as described in the text.
  165. (a)
  166. 7.16 Schematic depiction of prompt $\nu_{\mu}$ from $\pi^{+}$ decay in the Lujan target upscattering to neutrissimos within shielding along the path to CCM200 and decaying to photons in the detector. The pink circle represents the TMRS shown in figure 7.1.
  167. 7.17 Figure 7.17(a) shows the distribution of background and signal prediction in CCM200 for $m_{\mathcal{N}}=20.35~{}{\rm MeV}$ and $d_{\mu{\mathcal{N}}}=3\times 10^{-7}~{}{\rm GeV}^{-1}$, considering a background reduction factor of $10^{-3}$ compared to CCM120. Figure 7.17 shows the background-subtracted plot, with a red band indicating the expected statistical uncertainty on the background.
  168. (a)
  169. 7.18 Figure 7.18(a) shows the expected sensitivity of CCM200 to the neutrissimo model, where the blue band corresponds to a background reduction factor between $10^{-4}$ (“CCM200 Low Background”) and $10^{-2}$ (“CCM200 High Background”). The MiniBooNE $E_{\nu}^{\rm QE}$ allowed region (pink) and existing constraints (grey) come from Ref [31]. Figure 7.18(b) shows the same plot, but considering $\mathcal{N}\to\nu_{\tau}\gamma$ decays with $d_{\tau{\mathcal{N}}}=d_{\mu{\mathcal{N}}}m_{\tau}/m_{\mu}$.
  170. (a)
  171. (b)
  172. 7.19 The time delay of neutrissimo single photon decays with the CCM detector for the indicated mass and coupling, as calculated using LeptonInjector.
  173. B.1 Top: pixel intensity; Bottom: SparseSSNet labels; Left to right: U, V, Y, planes. The white circle indicates the reconstructed vertex.
  174. B.2 Top: pixel intensity; Bottom: SparseSSNet labels; Left to right: U, V, Y, planes. The white circle indicates the reconstructed vertex.
  175. B.3 Top: pixel intensity; Bottom: SparseSSNet labels; Left to right: U, V, Y, planes. The white circle indicates the reconstructed vertex.
  176. B.4 Top: pixel intensity; Bottom: SparseSSNet labels; Left to right: U, V, Y, planes. The white circle indicates the reconstructed vertex.
  177. B.5 Top: pixel intensity; Bottom: SparseSSNet labels; Left to right: U, V, Y, planes. The white circle indicates the reconstructed vertex.
  178. B.6 Top: pixel intensity; Bottom: SparseSSNet labels; Left to right: U, V, Y, planes. The white circle indicates the reconstructed vertex.
  179. B.7 Top: pixel intensity; Bottom: SparseSSNet labels; Left to right: U, V, Y, planes. The white circle indicates the reconstructed vertex.
  180. B.8 Top: pixel intensity; Bottom: SparseSSNet labels; Left to right: U, V, Y, planes. The white circle indicates the reconstructed vertex.
  181. B.9 Top: pixel intensity; Bottom: SparseSSNet labels; Left to right: U, V, Y, planes. The white circle indicates the reconstructed vertex.
  182. B.10 Top: pixel intensity; Bottom: SparseSSNet labels; Left to right: U, V, Y, planes. The white circle indicates the reconstructed vertex.
  183. B.11 Top: pixel intensity; Bottom: SparseSSNet labels; Left to right: U, V, Y, planes. The white circle indicates the reconstructed vertex.
  184. B.12 Top: pixel intensity; Bottom: SparseSSNet labels; Left to right: U, V, Y, planes. The white circle indicates the reconstructed vertex.
  185. B.13 Top: pixel intensity; Bottom: SparseSSNet labels; Left to right: U, V, Y, planes. The white circle indicates the reconstructed vertex.
  186. B.14 Top: pixel intensity; Bottom: SparseSSNet labels; Left to right: U, V, Y, planes. The white circle indicates the reconstructed vertex.
  187. B.15 Top: pixel intensity; Bottom: SparseSSNet labels; Left to right: U, V, Y, planes. The white circle indicates the reconstructed vertex.
  188. B.16 Top: pixel intensity; Bottom: SparseSSNet labels; Left to right: U, V, Y, planes. The white circle indicates the reconstructed vertex.
  189. B.17 Top: pixel intensity; Bottom: SparseSSNet labels; Left to right: U, V, Y, planes. The white circle indicates the reconstructed vertex.
  190. B.18 Top: pixel intensity; Bottom: SparseSSNet labels; Left to right: U, V, Y, planes. The white circle indicates the reconstructed vertex.
  191. B.19 Top: pixel intensity; Bottom: SparseSSNet labels; Left to right: U, V, Y, planes. The white circle indicates the reconstructed vertex.
  192. B.20 Top: pixel intensity; Bottom: SparseSSNet labels; Left to right: U, V, Y, planes. The white circle indicates the reconstructed vertex.
  193. B.21 Top: pixel intensity; Bottom: SparseSSNet labels; Left to right: U, V, Y, planes. The white circle indicates the reconstructed vertex.
  194. B.22 Top: pixel intensity; Bottom: SparseSSNet labels; Left to right: U, V, Y, planes. The white circle indicates the reconstructed vertex.
  195. B.23 Top: pixel intensity; Bottom: SparseSSNet labels; Left to right: U, V, Y, planes. The white circle indicates the reconstructed vertex.
  196. B.24 Top: pixel intensity; Bottom: SparseSSNet labels; Left to right: U, V, Y, planes. The white circle indicates the reconstructed vertex.

###### List of Tables

  1. 4.1 The definition of kinematic variables used throughout the two-body CCQE analysis.
  2. 4.2 The suite of variables used to isolate and analyze the $1e1p$ and $1\mu 1p$ samples. Variables used in the BDT ensemble for each sample are specified. The “$*$” character indicates that the variable is calculated in the rest frame of the struck nucleon. The mathematical definitions of many of these variables appear in Table 4.1.
  3. 4.3 The specific used to define the $1\mu 1p$ and $1e1p$ samples. For definitions of kinematic variables, see Table 4.1.
  4. 5.1 Breakdown of MC events in the “background” category of figures 5.3 and 5.4 over the range $200<E_{\nu}<1200$ MeV. The events are partitioned both by the interaction channel and the event topology.
  5. 5.2 Results from goodness-of-fit tests comparing observed $1e1p$ data to the $H_{0}$ and $H_{1}$ predictions, reported via the $\chi^{2}_{\text{CNP}}$ test statistic and the frequentist $p$-value. The top half of the table considers the nominal prediction and uncertainties before the $1\mu 1p$ constraint described in section 5.1.3, while the bottom half considers the post-constraint prediction and uncertainties.
  6. 6.1 Relevant parameters of the ten most abundant nuclei in the Earth’s upper crust according to [32]

##  Chapter 1 Introduction

We begin with a brief primer on neutrinos, the surprises they have given
physicists throughout recent history, and the mysteries that remain today.
Readers already familiar with the mathematical details of massive neutrinos
and the Standard Model may wish to read only section 1.1 and section 1.4
before continuing.

###  1.1 A Brief History of the Neutrino

Figure 1.1: Telegram from Fred Reines and Clyde Cowan informing Wolfgang Pauli
of their detection of neutrinos from a nuclear reactor.

The first indication of what would come to be known as the neutrino came from
Wolfgang Pauli in 1930 [33]. Addressing the “radioactive ladies and gentlemen”
of Tübingen, Germany, he appealed to the existence of new electrically neutral
particles to save the law of energy conservation in nuclear beta decays. This
idea was developed further by Enrico Fermi in 1934, who calculated the
transition probability for $\beta$-decay with a neutrino in the final state
[34]. Fermi’s theory represents the first study of the weak interaction–the
only Standard Model gauge group under which neutrinos are charged.

As the name “weak interaction” suggests, neutrinos interact very feebly with
particles in the Standard Model. Thus, it wasn’t until 1956 that the neutrino
was observed in an experimental setting for the first time. A team of
scientists from Los Alamos Scientific Laboratory, led by Frederick Reines and
Clyde Cowan, detected a free neutrino from a nuclear reactor via the inverse
beta decay interaction ($\bar{\nu}_{e}p\to e^{+}n$) [35, 36]. Though it was
not known at the time, they had detected electron antineutrinos
($\bar{\nu}_{e}$). Electron (anti)neutrinos represent one of the three weak-
flavor eigenstates neutrinos can occupy in the Standard Model–specifically,
the eigenstate that couples to the $e^{\pm}$ charged leptons through the
charged-current weak interaction. Upon confirmation of their discovery, Reines
and Cowan sent the telegram shown in figure 1.1 to Pauli, alerting him of the
definitive existence of the neutral particles he proposed in Tübingen.

Shortly after this, the phenomenon of neutrino oscillations–periodic
transitions between different types of neutrinos–started to appear in the
literature. In 1958, Bruno Pontecorvo discussed the possibility of mixing
between right-handed antineutrinos $\bar{\nu}_{R}$ and “sterile” right-handed
neutrinos $\nu_{R}$, in analogy with $K^{0}$–$\bar{K}^{0}$ mixing observed in
the quark sector [37]. A second possible source of neutrino oscillations came
following the 1962 experimental discovery of a second neutrino weak-flavor
eigenstate–the muon neutrino ($\nu_{\mu}$) [38]. After this, the notion of
mixing between neutrino flavor and mass eigenstates was introduced by Ziro
Maki, Masami Nakagawa, and Shoichi Sakata [39]. In a 1967 paper [40],
Pontecorvo introduced the possibility of vacuum $\nu_{e}$–$\nu_{\mu}$
oscillations, even predicting a factor of two suppression in the total solar
neutrino flux before such a deficit would actually be observed [41].

The aforementioned deficit, known as the “solar neutrino problem”, was
established in 1968 through a now-famous experiment at the Homestake Mine in
South Dakota led by Raymond Davis [42]. Davis and his colleagues detected the
capture of electron neutrinos from the sun on 37Cl nuclei, allowing a
measurement of the solar $\nu_{e}$ flux. Their result was about a factor of
$\sim 1/3$ lower than the leading prediction from John Bachall [43]. This is
shown in figure 1.2, including confirmations of the deficit following the
Homestake experiment. The solution was not a mistake in the experimental
measurement or theoretical prediction, as physicists expected at the time;
rather, it was a deficiency in our understanding of neutrinos. This was the
first piece of the puzzle that would eventually lead to the discovery of
neutrino oscillations and nonzero neutrino masses.

Figure 1.2: The deficit of the observed solar $\nu_{e}$ flux compared with the
theoretical expectation. The Homestake experiment is shown on the far left;
follow-up solar neutrino measurements confirming the deficit are also shown,
including the 2002 SNO result which brought forth a solution to the solar
neutrino problem. Figure from Ref. [1].

The next piece of the puzzle came from atmospheric neutrinos, i.e. neutrinos
coming from the decay of mesons created from the interactions of primary
cosmic rays in the atmosphere. Around the mid-1980s, two water Cherenkov
detectors, IMB-3 [44] and Kamiokande [45], began to measure the interactions
of atmospheric $\nu_{\mu}$ and $\nu_{e}$ events (initially just as a
background for their main physics goal, the search for nucleon decay). The
ratio of $\nu_{\mu}:\nu_{e}$ interactions was found to be lower than the
theoretical expectation by a factor of $\sim 2/3$ [46]. This was known as the
“atmospheric neutrino anomaly”. The source of this anomaly was not clear at
the time; it could have been a deficit of muon neutrinos, an excess of
electron neutrinos, or some of both. Systematic issues in the flux prediction
or muon identification were also suggested [46]. It was far from clear that
neutrino oscillations could be responsible for the observed deficit.

The solution to the atmospheric neutrino anomaly came from the Super-
Kamiokande (SuperK) experiment [47]. SuperK was a much larger version of the
Kamiokande detector, allowing the detection of higher energy muons (up to
$E_{\mu}\sim 5\;{\rm GeV}$). SuperK also measured the up-down asymmetry of
muon-like and electron-like events in their detector, $(N_{\rm up}-N_{\rm
down})/(N_{\rm up}+N_{\rm down})$. Upward-going events have traveled a much
longer distance than downward-going events before reaching the SuperK
detector–thus positive detection of an asymmetry would be smoking-gun evidence
for a baseline-dependent effect like neutrino oscillations. This is precisely
what SuperK observed [2]. As shown in figure 1.3, an up-down asymmetry is
observed in the muon-like channel, the magnitude of which increases with the
observed muon momentum. Such behavior is consistent with muon neutrino
oscillations to a third flavor eigenstate, $\nu_{\tau}$ (the mathematical
details of neutrino oscillations will be described in section 1.3). No such
effect was observed in the electron-like channel. Thus, the atmospheric
neutrino anomaly is a result of muon neutrino disappearance, specifically
coming from $\nu_{\mu}\to\nu_{\tau}$ oscillations.

The solution to the solar neutrino problem came in 2002 from the Sudbury
Neutrino Observatory (SNO) [48]. The SNO experiment used a heavy water
Cherenkov detector, specifically relying on the use of deuterium target nuclei
to be sensitive to three different neutrino interactions,

$\begin{split}&\nu_{e}+d\to p+p+e^{-}~{}~{}~{}(\rm{CC}),\\\ &\nu_{x}+d\to
p+n+\nu_{x}~{}~{}~{}(\rm{NC}),\\\
&\nu_{x}+e^{-}\to\nu_{x}+e^{-}~{}~{}~{}~{}~{}(\rm{ES}).\end{split}$ (1.1)

Charged-current (CC), neutral-current (NC), and elastic scattering (ES)
interactions were separated based on the visible energy and scattering angle
of the final state particles. NC events were further separated by tagging the
6.25 MeV photon released from neutron capture on deuterium. By measuring all
three channels, SNO was able to measure the 8B solar neutrino flux broken down
into the $\nu_{e}$ and $\nu_{\mu,\tau}$ components. SNO’s 2002 result showed
that the missing neutrinos from the Homestake experiment were in fact showing
up in the $\nu_{\mu,\tau}$ component [3]. Figure 1.4 shows the flux of each
component as constrained by the measured CC, NC, and ES interaction rate. The
flavor transitions here come not from vacuum oscillations but rather from
matter-enhanced resonant behavior as neutrinos travel through the dense solar
medium–a phenomenon known as the Mikheyev–Smirnov–Wolfenstein (MSW) effect
[49, 50]. The MSW effect still, however, requires mixing between the neutrino
flavor and mass eigenstate as well as non-zero squared differences between the
mass eigenstates. It is worth noting here that the KamLAND reactor neutrino
experiment was essential in determining the oscillation parameters which led
to the SNO observation [51]. Thus, the SNO solution to the solar neutrino
problem and the SuperK solution to the atmospheric neutrino anomaly were both
evidence for the existence of neutrino oscillations and thus non-zero neutrino
masses. The collaborations shared the 2015 Nobel Prize in physics for this
discovery [52, 53].

Since SuperK and SNO, neutrino oscillations have been measured extensively by
a global program of reactor, accelerator, atmospheric, and solar neutrino
experiments. The mixing angle and mass-squared splittings of the three
Standard Model neutrinos have been measured to few-percent-level precision in
most cases [54, 55, 56]. There are a number of open questions in the standard
three-neutrino mixing paradigm, including the ordering of the three mass
eigenstates and the value of the charge-parity-violating complex phase
$\delta_{CP}$. Though preliminary results exist on both fronts [57, 58, 55,
54, 56], definitive answers to each will come from next-generation neutrino
experiments, including Hyper-K [59], DUNE [60] and JUNO [61].

Figure 1.3: The up-down asymmetry measured in SuperK as a function of lepton
momentum, separated into $e$-like and $\mu$-like events as well as fully-
contained (FC) and partially-contained (PC) events. The dashed line indicates
the best fit to $\nu_{\mu}\to\nu_{\tau}$ oscillations. Figure from Ref. [2].
Figure 1.4: Measurement of the solar 8B flux from the SNO collaboration,
broken down into the $\nu_{e}$ and $\nu_{\mu,\tau}$ sub-components.
Measurement of the CC, NC, and ES channels show up as slices in the two-
dimensional flux parameter space. Figure from Ref. [3].

###  1.2 Neutrinos in the Standard Model

The arguments and notation presented in this section follow closely from
chapter 2 of Ref. [62].

The interactions of the known fundamental particles of our Universe are
described by a specific quantum field theory known as the Standard Model (SM).
Above the electroweak scale, there are three gauge groups contained within the
SM:

  * •

$SU(3)_{c}$, which governs the gluon-mediated “strong interactions” of color-
charged fields.

  * •

$SU(2)_{L}$, one part of the “electro-weak interaction”, mediated by the
$W^{\pm}_{\mu}$ and $W^{0}_{\mu}$ vector bosons.

  * •

$U(1)_{Y}$, the other part of the “electro-weak interaction”, mediated by the
$B_{\mu}$ gauge boson.

After electro-weak symmetry breaking (EWSB) via the Higgs mechanism, the
$SU(2)_{L}\times U(1)_{Y}$ subgroup breaks down to $U(1)_{Q}$, which describes
the electromagnetic (EM) interactions of charged fields mediated by the
$A_{\mu}$ gauge boson, also known as the photon.

Of the three fundamental interactions of the SM, neutrinos are only charged
under the weak $SU(2)_{L}$ gauge group–they are singlets under the $SU(3)_{c}$
and $U(1)_{Q}$ gauge groups. Thus, neutrinos only appear in the electro-weak
part of the SM Lagrangian, which is given by

$\mathcal{L}=\frac{g}{\sqrt{2}}(J^{\mu}W^{+}_{\mu}+J^{\mu\dagger}W^{-}_{\mu})+\frac{g}{\cos\theta_{W}}K^{\mu}Z_{\mu},$
(1.2)

where $g=e/\cos\theta_{W}$ is the $SU(2)_{L}$ gauge coupling of $W_{\mu}$ and
Higgs field, $\theta_{W}$ is the Weinberg angle describing the rotation that
occurs during EWSB between the neutral parts of the $SU(2)_{L}$ and $U(1)_{Y}$
gauge boson fields, and $W^{\pm}_{\mu}$ ($Z_{\mu}$) is the charged (neutral)
piece of $SU(2)_{L}$ after EWSB. The currents coupled to $W^{\pm}_{\mu}$ and
$Z_{\mu}$ bosons are given by

$\begin{split}J^{\mu}&=\begin{pmatrix}\overline{u}^{0}&\overline{c}^{0}&\overline{t}^{0}\end{pmatrix}\gamma^{\mu}P_{L}\begin{pmatrix}d^{0}\\\
s^{0}\\\
b^{0}\end{pmatrix}+\begin{pmatrix}\overline{\nu_{e}}&\overline{\nu_{\mu}}&\overline{\nu_{\tau}}\end{pmatrix}\gamma^{\mu}P_{L}\begin{pmatrix}e\\\
\mu\\\ \tau\end{pmatrix}\\\
K^{\mu}&=\sum_{f}\overline{f}\gamma^{\mu}[I_{3L}P_{L}-\sin^{2}\theta_{W}Q_{f}]f\\\
&=\sum_{q}[\epsilon_{L}(q)\overline{q}\gamma_{\mu}P_{L}q+\epsilon_{R}(q)\overline{q}\gamma_{\mu}P_{R}q]\\\
&+\frac{1}{2}\sum_{\alpha\in\\{e,\mu,\tau\\}}[\overline{\nu_{\alpha}}\gamma^{\mu}P_{L}\nu_{\alpha}+\overline{\ell}_{\alpha}\gamma_{\mu}(g_{V}^{\alpha}-\gamma_{5}g_{A}^{\alpha})\ell_{\alpha}],\end{split}$
(1.3)

where $P_{R}(P_{L})=(1\pm\gamma^{5})/2$ is the projection operator onto the
right-handed (left-handed) chiral state, and the subscript $0$ on the quark
fields indicates that these are the weak flavor eigenstates rather than the
mass eigenstates. The first generation coupling constants in $K^{\mu}$, which
derive from the specified EM charge and $SU(2)_{L}$ representation of each
field, are given by

$\begin{split}&\epsilon_{L}(u)=\frac{1}{2}-\frac{2}{3}\sin^{2}\theta_{W}~{}~{}~{}~{}~{}\epsilon_{R}(u)=-\frac{2}{3}\sin^{2}\theta_{W}\\\
&\epsilon_{L}(d)=-\frac{1}{2}+\frac{1}{3}\sin^{2}\theta_{W}~{}~{}~{}\epsilon_{R}(d)=\frac{1}{3}\sin^{2}\theta_{W}\\\
&g_{V}^{e}=-\frac{1}{2}+2\sin^{2}\theta_{W}~{}~{}~{}~{}~{}~{}~{}g_{A}^{e}=-\frac{1}{2}.\end{split}$
(1.4)

The Lagrangian in equation 1.2 can be used to calculate cross sections for the
various SM interactions of the neutrino. The first term describes the charged-
current interactions of neutrinos such as nuclear beta decay, while the second
term describes neutral current interactions such as $\nu_{\mu}e^{-}$ elastic
scattering. At energy scales below the electro-weak scale, one can integrate
out the $W_{\mu}$ and $Z_{\mu}$ gauge bosons and describe interactions in
terms of the dimensional Fermi constant

$G_{F}=\frac{g^{2}}{4\sqrt{2}M_{W}^{2}}=1.166\times 10^{-5}\;\rm{GeV}^{-2}.$
(1.5)

The low-energy Lagrangian describing 4-fermion interactions can be derived
from equation 1.2 as

$\mathcal{L}_{4f}=\frac{-4G_{F}}{\sqrt{2}}[J_{\mu}J^{\mu\dagger}+K_{\mu}K^{\mu}].$
(1.6)

As an example, we consider low-energy neutrino electron elastic scattering
(ES) ($\nu e^{-}\to\nu e^{-}$). This is a purely leptonic process and is
therefore relatively clean; specifically, ES models do not need to account for
the complex dynamics of the nuclear medium. The Feynman diagrams for the
contributing interactions are shown in figure 1.5. Both the charged-current
(CC) and neutral-current (NC) diagrams contribute to $\nu_{e}e^{-}$
scattering, while only the NC diagram contributes to $\nu_{\mu,\tau}e^{-}$
scattering. Using the Feynman rules associated with equation 1.6, one can
calculate the cross sections to be [62]

$\begin{split}\sigma_{\nu_{e}e^{-}\to\nu_{e}e^{-}}(E_{\nu})&=\frac{G_{F}^{2}m_{e}E_{\nu}}{2\pi}\bigg{[}(2\sin^{2}\theta_{W}+1)^{2}+\frac{4}{3}\sin^{4}\theta_{W}\bigg{]}\\\
&\approx 0.9\times 10^{-43}\bigg{(}\frac{E_{\nu}}{10\;{\rm MeV}}\bigg{)}{\rm
cm}^{2}\\\
\sigma_{\nu_{\mu,\tau}e^{-}\to\nu_{\mu,\tau}e^{-}}(E_{\nu})&=\frac{G_{F}^{2}m_{e}E_{\nu}}{2\pi}\bigg{[}(2\sin^{2}\theta_{W}-1)^{2}+\frac{4}{3}\sin^{4}\theta_{W}\bigg{]}\\\
&\approx 0.15\times 10^{-43}\bigg{(}\frac{E_{\nu}}{10\;{\rm MeV}}\bigg{)}{\rm
cm}^{2},\end{split}$ (1.7)

which is valid for $E_{\nu}>>m_{e}$. Similarly, one can calculate the cross
section for antineutrino electron ES
($\overline{\nu}e^{-}\to\overline{\nu}e^{-}$). The diagrams contributing for
this process are shown in figure 1.6, and the cross section is given by [62]

$\begin{split}\sigma_{\overline{\nu}_{e}e^{-}\to\overline{\nu}_{e}e^{-}}(E_{\nu})&=\frac{G_{F}^{2}m_{e}E_{\nu}}{2\pi}\bigg{[}\frac{1}{3}(2\sin^{2}\theta_{W}+1)^{2}+4\sin^{4}\theta_{W}\bigg{]}\\\
&\approx 0.378\times 10^{-43}\bigg{(}\frac{E_{\nu}}{10\;{\rm MeV}}\bigg{)}{\rm
cm}^{2}\\\
\sigma_{\overline{\nu}_{\mu,\tau}e^{-}\to\overline{\nu}_{\mu,\tau}e^{-}}(E_{\nu})&=\frac{G_{F}^{2}m_{e}E_{\nu}}{2\pi}\bigg{[}\frac{1}{3}(2\sin^{2}\theta_{W}-1)^{2}+4\sin^{4}\theta_{W}\bigg{]}\\\
&\approx 0.14\times 10^{-43}\bigg{(}\frac{E_{\nu}}{10\;{\rm MeV}}\bigg{)}{\rm
cm}^{2}.\end{split}$ (1.8)

We now turn to the interaction at the core of this thesis: neutrino-nucleon
charged-current quasi-elastic (CCQE) scattering. The relevant Feynman diagrams
for this process are shown in figure 1.7. Unlike ES, models of CCQE do need to
account for the nuclear environment surrounding the target nucleon. As the
final state nucleon travels through the nuclear medium, it may scatter off of
other nucleons and/or produce additional mesons through a process known as
final state interactions (FSIs). As shown in figure 1.8, CCQE is dominant for
$E_{\nu}\lesssim 1\;{\rm GeV}$. Above this energy, nucleon resonance processes
start to take over, in which Delta resonances decay to final state mesons. In
the regime $E_{\nu}\gtrsim 10\;{\rm GeV}$, neutrinos start to undergo deep
inelastic scattering (DIS) off of the constituent quarks within the nucleon.

In order to calculate the CCQE cross section, one considers a theory
containing nucleon degrees of freedom. The original calculation for free
nucleons (i.e., not bound within a nucleus) was carried out by Llewellyn-Smith
in 1972; the differential cross section as a function of the squared four-
momentum transfer $Q^{2}$ is given by [4, 63]

$\begin{split}\frac{d\sigma}{dQ^{2}}=\frac{G_{F}^{2}M^{2}|V_{ud}|^{2}}{8\pi
E_{\nu}^{2}}\bigg{[}A\pm\frac{s-u}{M^{2}}B+\frac{(s-u)^{2}}{M^{4}}C\bigg{]},\end{split}$
(1.9)

where +(-) refers to (anti)neutrino scattering, $M$ is the nucleon mass, $m$
is the lepton mass, $(s-u)=4ME_{\nu}-Q^{2}-m^{2}$, and $A$, $B$, and $C$ are
functions of the vector, axial-vector, and pseudoscalar form factors of the
nucleon (see equations 58, 59, and 60 of Ref. [4] for complete expressions).
These form factors describe the composite nature of nucleons under
interactions with different Lorentz structures.

For $E_{\nu}<<M$, the $\nu_{e}$ CCQE cross section is approximately [62]

$\begin{split}\sigma_{\nu_{e}n\to
e^{-}p}(E_{\nu})&\approx\frac{G_{F}^{2}E_{\nu}^{2}}{\pi}(g_{V}^{2}+3g_{A}^{2})\\\
&\approx 9.75\times 10^{-42}\bigg{[}\frac{E_{\nu}}{10\;{\rm
MeV}}\bigg{]}^{2}\;{\rm cm}^{2}.\end{split}$ (1.10)

In the regime $E_{\nu}\gtrsim 1\;{\rm GeV}$, the $\nu_{e}$ and $\nu_{\mu}$
CCQE cross sections are no longer suppressed by threshold effects and are thus
the same, approximately $10^{-38}\;{\rm cm}^{2}$ [4]. This cross section is
significantly larger than the elastic scattering and lower energy $\nu_{e}$
CCQE cross sections and is the dominant neutrino interaction for many
accelerator-based neutrino experiments, including two at the heart of this
thesis: MiniBooNE and MicroBooNE. Finally, we note that the cross section for
antineutrino CCQE tends to be smaller; this will be important in chapter 6.

$\nu$$\nu$$e^{-}$$e^{-}$$Z$$\nu_{e}$$e^{-}$$e^{-}$$\nu_{e}$$W$

Figure 1.5:  Diagrams contributing to $\nu e^{-}$ elastic scattering

$\overline{\nu}$$\overline{\nu}$$e^{-}$$e^{-}$$Z$$\overline{\nu}_{e}$$e^{-}$$e^{-}$$\overline{\nu}_{e}$$W^{-}$

Figure 1.6:  Diagrams contributing to $\overline{\nu}e^{-}$ elastic scattering

$\nu_{\alpha}$$\ell_{\alpha}$$n$$p$$W$$\overline{\nu}_{\alpha}$$\overline{\ell}_{\alpha}$$p$$n$$W$

Figure 1.7:  Diagrams contributing to neutrino-nucleon charged-current
quasielastic scattering Figure 1.8: CC inclusive neutrino and antineutrino
nucleon scattering cross sections as a function of neutrino energy. Figure
from Ref. [4].

###  1.3 Massive Neutrinos

The arguments and notation presented in this section follow closely from
section 2.5, chapter 4, and chapter 5 of Ref. [62] as well as chapter 11 of
Ref. [64].

Neutrinos are massless in the SM. To see this, we will exhaust the two
possible forms for a neutrino mass term in the SM Lagrangian: Dirac and
Majorana. These refer to the two possible fermionic spinor representations in
which neutrinos can be found. Dirac spinors in general have four complex
components, or degrees of freedom, while Majorana spinors have only two. The
critical question is whether the right-handed chiral projection of the
neutrino field, $\nu_{R}$, is the same as $\overline{\nu}_{R}$, the right-
handed chiral projection of the antineutrino field (Majorana case), or if it
is a new degree of freedom (Dirac case).

The definition of a free Dirac fermion field is

$\psi(x)=\int\frac{d^{3}p}{\sqrt{(2\pi)^{3}2E_{p}}}\sum_{s=\pm\frac{1}{2}}\Big{(}f_{s}(\mathbf{p})u_{s}(\mathbf{p})e^{-i\mathbf{p}\cdot\mathbf{x}}+\overline{f_{s}}^{\dagger}(\mathbf{p})v_{s}(\mathbf{p})e^{i\mathbf{p}\cdot\mathbf{x}}\Big{)},$
(1.11)

where $f_{s}(\mathbf{p})$ annihilates a single particle of momentum
$\mathbf{p}$ while $\overline{f_{s}}^{\dagger}$ creates the corresponding
antiparticle state, and $u_{s}(\mathbf{p})$ and $v_{s}(\mathbf{p})$ are
spinors with positive and negative energy, respectively, satisfying the Dirac
equations

$\begin{split}&(\gamma^{\mu}p_{\mu}-m)u_{s}(\mathbf{p})=0\\\
&(\gamma^{\mu}p_{\mu}+m)v_{s}(\mathbf{p})=0,\end{split}$ (1.12)

where $\gamma^{\mu}$ are a set of Lorentz-indexed matrices satisfying
$\\{\gamma^{\mu},\gamma^{\nu}\\}=2g^{\mu\nu}$. There are many possible
representations for the $\gamma$-matrices. We consider the Weyl basis, in
which [64]

$\gamma_{\mu}=\begin{pmatrix}0&\sigma_{\mu}\\\ \overline{\sigma}_{\mu}&0\\\
\end{pmatrix},$ (1.13)

where $\sigma_{\mu}=(\mathbb{1},\vec{\sigma})$,
$\overline{\sigma}_{\mu}=(\mathbb{1},-\vec{\sigma})$, and
$\vec{\sigma}=(\sigma_{1},\sigma_{2},\sigma_{3})$ are the Pauli matrices. This
representation is convenient for understanding the different chiral components
of the Dirac spinor $\psi$. The Lorentz generators
$S^{\mu\nu}\equiv\frac{i}{4}[\gamma^{\mu},\gamma^{\nu}]$ become block
diagonal, such that we can write the Dirac spinor of equation 1.11 as a
doublet of two-component Weyl spinors with a different chiral nature,

$\psi=\begin{pmatrix}\psi_{L}\\\ \psi_{R}\\\ \end{pmatrix},$ (1.14)

which transform under different irreducible representations of the Lorentz
group [64]. Here $\psi_{L}$ and $\psi_{R}$ refer to the left-handed and right-
handed Weyl spinor, respectively. We can isolate the different chiral
components of the Dirac spinor using the matrix $\gamma^{5}\equiv
i\gamma^{0}\gamma^{1}\gamma^{2}\gamma^{3}$, which takes the form

$\gamma^{5}=\begin{pmatrix}-\mathbb{1}&0\\\ 0&\mathbb{1}\\\ \end{pmatrix}$
(1.15)

in the Weyl basis. We can define projection operators
$P_{L}=\frac{1}{2}(1-\gamma^{5})$ and $P_{R}=\frac{1}{2}(1+\gamma^{5})$ such
that $P_{L}\psi=\psi_{L}$ and $P_{R}\psi_{R}$. It is worth noting that while
the behavior of these projection operators is especially clear in the Weyl
representation, they will isolate the chiral components of $\psi$ in any
representation of $\gamma^{\mu}$.

Dirac mass terms couple left-handed and right-handed chiral states. To see
this, consider the Dirac equation in the Weyl basis, which takes the form [64]

$(\gamma^{\mu}p_{\mu}-m)\psi=\begin{pmatrix}-m&\sigma^{\mu}p_{\mu}\\\
\overline{\sigma}^{\mu}p_{\mu}&-m\\\ \end{pmatrix}\begin{pmatrix}\psi_{L}\\\
\psi_{R}\\\ \end{pmatrix}=0.$ (1.16)

It is evident that this matrix equation mixes the left-handed and right-handed
components of $\psi$. Dirac mass terms take the form
$m\psi_{L}^{\dagger}\psi_{R}$ and $m\psi_{R}^{\dagger}\psi_{L}$, thus
requiring both chiral components. After EWSB, the non-neutrino fermions in the
SM acquire a Dirac mass from their interactions with the Higgs field.
Neutrinos, however, do not have a right-handed chiral state in the SM;
therefore, the SM cannot include a Dirac mass term for neutrinos.

Now we turn to the Majorana mass term. The expression for a Majorana field is
the same as equation 1.11, subject to a condition relating particles and
antiparticles. We see that the expression for $\psi^{*}(x)$ would involve
$f_{s}^{\dagger}(\mathbf{p})$, which creates a particle state, and
$\overline{f_{s}}(\mathbf{p})$, which annihilates an antiparticle state. It
turns out the relationship $\psi(x)=\psi^{*}(x)$ is not Lorentz invariant
[62]. To remedy this, we must define the conjugate Dirac field

$\psi^{C}(x)\equiv\gamma_{0}C\psi^{*}(x),$ (1.17)

where the representation-dependent conjugation matrix $C$ is defined by the
equation

$\begin{split}&\gamma_{0}C\sigma^{*}_{\mu\nu}=-\sigma_{\mu\nu}\gamma_{0}C,\\\
&\sigma_{\mu\nu}\equiv\frac{i}{2}[\gamma_{\mu},\gamma_{\nu}].\end{split}$
(1.18)

In the Weyl representation, for example, $C=i\gamma_{2}\gamma_{0}$. This
requirement for $C$ ensures that $\psi^{C}(x)$ transforms in the same way as
$\psi(x)$ under the Lorentz group [62]. The Lorentz-invariant Majorana
condition specifically requires

$\psi(x)=e^{i\theta}\psi^{C}(x),$ (1.19)

where $\theta$ is an arbitrary phase, which we can take to be $\theta=0$. It
is important to note that this condition can only be satisfied for fields that
carry no additive quantum numbers [64].

In the Weyl basis, equation 1.19 relates the left-handed and right-handed
components of $\psi(x)$ such that [64]

$\psi(x)=\begin{pmatrix}\psi_{L}\\\ i\sigma_{2}\psi^{*}_{L}\\\ \end{pmatrix},$
(1.20)

where the number of degrees of freedom has been reduced from four to two.
Since $i\sigma_{2}\psi^{*}_{L}$ transforms like a right-handed spinor, we can
now write mass terms of the form $im\psi_{L}^{\dagger}\sigma_{2}\psi_{L}^{*}$
and $im\psi_{L}^{\dagger}\sigma_{2}\psi_{L}^{*}$. These are Majorana mass
terms. Note that they couple the same chiral component of the fermion.

The impossibility of a neutrino Majorana mass term is a bit more nuanced.
Majorana mass terms for neutrinos in the SM contain the bi-linear expression
$\nu_{L}^{T}\sigma_{2}\nu_{L}$. However, $\nu_{L}$ belongs to an $SU(2)_{L}$
doublet in the SM, thus this Majorana mass term transforms as a triplet under
$SU(2)_{L}$. It also breaks lepton number by two units, hence it also violates
baryon minus lepton number ($B-L$), which is conserved to all orders of the SM
gauge couplings [62]. Therefore, neutrinos also cannot have a Majorana mass
term in the SM.

Despite these arguments, neutrino oscillations have given physicists
definitive evidence that at least two of the three SM neutrino masses are
nonzero (as discussed in section 1.1). This requires the presence of physics
beyond the Standard Model (BSM). The minimal extension of the SM which can
accommodate nonzero neutrino masses introduces additional right-handed
neutrino states $N_{R}$ [62, 64]. These fields, which are singlets under the
SM gauge group, can generate both Dirac and Majorana mass terms for neutrinos.
The most general expression for the neutrino mass Lagrangian is then

$-\mathcal{L}_{\rm
mass}=\frac{1}{2}\begin{pmatrix}\overline{\nu}_{L}&\overline{N^{C}_{L}}\end{pmatrix}\begin{pmatrix}0&M\\\
M^{T}&B\\\ \end{pmatrix}\begin{pmatrix}\nu_{R}^{C}\\\ N_{R}\end{pmatrix}+{\rm
h.c.},$ (1.21)

where $M$ and $B$ are the Dirac and Majorana mass matrices of the neutrino
sector, respectively, and $\nu_{L}$ and $N_{R}$ are column vectors containing
the left-handed and right-handed projections of each neutrino generation.

In order to obtain the mass eigenstates of this theory, one must diagonalize
the mass matrix in equation 1.21. If we assume one generation of neutrinos,
the eigenvalues of this mass matrix are

$m_{1,2}=\frac{1}{2}(\sqrt{B^{2}+4M^{2}}\mp B).$ (1.22)

In the limit $B>>M$, the eigenvalues are approximately given by

$m_{1}\approx\frac{M^{2}}{B},~{}~{}~{}m_{2}\approx B.$ (1.23)

This is the famous “seesaw mechanism” for neutrino mass generation [65]. One
can see that if $B$ is at roughly the GUT scale ($10^{16}$ GeV) and $M$ is at
roughly the electro-weak scale (100 GeV), we see that $m_{1}<1$ eV. This is
the right order-of-magnitude regime predicted by neutrino oscillation data and
is consistent with existing upper bounds on the neutrino mass from KATRIN
[66]. Thus, this model is an elegant explanation of the observed neutrino
oscillation phenomenon, though experimental confirmation of right-handed
neutrino fields at the GUT scale is probably not feasible for quite a long
time.

While we do not know the mechanism through which neutrinos acquire mass, it is
relevant to ask whether the resulting mass terms are Dirac or Majorana in
nature. An extensive worldwide experimental program is currently underway to
answer this question by searching for neutrino-less double beta decay, a rare
decay process in which a nucleus undergoes two simultaneous beta decays
without emitting any neutrinos in the final state [67, 68, 69]. A positive
observation would imply that neutrinos are Majorana.

As discussed in section 1.1, perhaps the most famous consequence of massive
neutrinos is the phenomenon of neutrino oscillations [37, 40, 39]. This arises
because the three weak flavor eigenstates $\nu_{\alpha}$ are not aligned with
the three mass eigenstates $\nu_{i}$. The two bases are related by the unitary
Pontecorvo–Maki–Nakagawa–Sakata (PMNS) mixing matrix $U_{\alpha i}$,

$\begin{pmatrix}\nu_{e}\\\ \nu_{\mu}\\\
\nu_{\tau}\end{pmatrix}=\begin{pmatrix}U_{e1}&U_{e2}&U_{e3}\\\ U_{\mu
1}&U_{\mu 2}&U_{\mu 3}\\\ U_{\tau 1}&U_{\tau 2}&U_{\tau 3}\\\
\end{pmatrix}\begin{pmatrix}\nu_{1}\\\ \nu_{2}\\\ \nu_{3}\end{pmatrix}.$
(1.24)

As seen in equation 1.2, neutrinos interact in the weak flavor eigenstates
$\nu_{\alpha}$. Thus, a neutrino a produced alongside a charged anti-lepton
$\overline{\ell}$ is in the state

$\ket{\nu(t=0)}=\ket{\nu_{\ell}}=\sum_{i\in\\{1,2,3\\}}U_{\ell
i}\ket{\nu_{i}}.$ (1.25)

Neutrinos propagate, however, in their mass eigenstates. Each mass eigenstate
$\nu_{i}$ is associated with a mass $m_{i}$ and four-momentum
$(p_{i})_{\mu}=(E_{i},\vec{p_{i}})$ satisfying the on-shell requirement
$(p_{i})^{2}=m_{i}^{2}$. Thus, after a time $t$, the neutrino will be in the
state

$\ket{\nu(t)}=\sum_{i}e^{-ip_{i}\cdot x}U_{\ell i}\ket{\nu_{i}}.$ (1.26)

The overlap with a different weak flavor eigenstate
$\nu_{\ell^{\prime}}\neq\nu_{\ell}$ is non-trivial, given by the expression

$\begin{split}\braket{\nu_{\ell^{\prime}}}{\nu(t)}&=\sum_{i,j}\bra{\nu_{j}}U^{\dagger}_{j\ell^{\prime}}e^{-ip_{i}\cdot
x}U_{\ell i}\ket{\nu_{i}}\\\ &=\sum_{i}e^{-ip_{i}\cdot x}U_{\ell
i}U_{\ell^{\prime}i}^{*},\end{split}$ (1.27)

where we have invoked the orthonormality of the mass basis in the last line.
The probability of finding a neutrino in flavor eigenstate
$\nu_{\ell^{\prime}}$ given an initial $\nu_{\ell}$ state is then

$\begin{split}P_{\nu_{\ell}\to\nu_{\ell^{\prime}}}(t)&=|\braket{\nu_{\ell}^{\prime}}{\nu(t)}|^{2}\\\
&=\sum_{i,j}|U_{\ell i}U_{\ell^{\prime}i}^{*}U_{\ell
j}^{*}U_{\ell^{\prime}j}|e^{-i(p_{i}-p_{j})\cdot
x+i\phi_{\ell\ell^{\prime}ij}}.\end{split}$ (1.28)

where $\phi_{\ell\ell^{\prime}ij}\equiv\rm{arg}(U_{\ell
i}U_{\ell^{\prime}i}^{*}U_{\ell j}^{*}U_{\ell^{\prime}j})$.

We now make a simplifying assumption, in which all neutrino mass eigenstates
propagate with the same momentum, i.e.
$\vec{p}_{i}=\vec{p}_{j}\equiv\vec{p}\forall i,j$. This treatment is not
necessarily physical. However, for the parameters relevant to most laboratory
neutrino experiments, it leads to the same result as the correct but
complicated full treatment of the quantum mechanical neutrino wave packet
[70]. Given this assumption along with the approximation that $m_{i}<<p_{i}$
(which should hold for all existing and near-future experiments), we can show

$\begin{split}(p_{i}-p_{j})\cdot x&=(E_{i}-E_{j})t\\\
&=\Big{(}\sqrt{\vec{p}^{2}+m_{i}^{2}}-\sqrt{\vec{p}^{2}+m_{j}^{2}}\Big{)}t\\\
&\approx\frac{\Delta m_{ij}^{2}t}{2|\vec{p}|},\end{split}$ (1.29)

where $\Delta m_{ij}^{2}=m_{i}^{2}-m_{j}^{2}$. Working in natural units
($c=\hbar=1$), we note that ultra-relativistic neutrinos satisfy
$|\vec{p}|\approx E$ and $t\approx L$, where $L$ is the distance traveled by
the neutrino. Taking only the real part of the exponential in equation 1.28,
we have

$P_{\nu_{\ell}\to\nu_{\ell^{\prime}}}(t)=\sum_{i,j}|U_{\ell
i}U_{\ell^{\prime}i}^{*}U_{\ell
j}^{*}U_{\ell^{\prime}j}|\cos\Big{(}\frac{\Delta
m_{ij}^{2}L}{2E}-\phi_{\ell\ell^{\prime}ij}\Big{)}.$ (1.30)

If we consider a two-neutrino paradigm, the unitary mixing matrix is real and
can be parameterized by a single “mixing angle” $\theta$,

$U\equiv\begin{pmatrix}U_{\ell 1}&U_{\ell 2}\\\
U_{\ell^{\prime}1}&U_{\ell^{\prime}2}\end{pmatrix}=\begin{pmatrix}\cos\theta&\sin\theta\\\
-\sin\theta&\cos\theta\end{pmatrix}.$ (1.31)

In this scenario, summing over the two mass eigenstates as in equation 1.30
gives

$P_{\nu_{\ell}\to\nu_{\ell^{\prime}}}(t)=\sin^{2}2\theta\sin^{2}\Big{(}\frac{\Delta
m^{2}L}{4E}\Big{)}.$ (1.32)

The extension to the standard three neutrino paradigm can be found in any text
on neutrino oscillations. We quote the result here. Three mass eigenstates
lead to two independent mass-squared splittings, $\Delta m_{12}^{2}$ and
$\Delta m_{23}^{2}$. The mixing matrix in equation 1.24 can be parameterized
by three real mixing angles $\theta_{ij}$ and one complex CP-violating phase
$\delta$,

$U=\begin{pmatrix}1&0&0\\\ 0&c_{23}&s_{23}\\\ 0&-s_{23}&c_{23}\\\
\end{pmatrix}\begin{pmatrix}c_{13}&0&s_{13}e^{-i\delta}\\\ 0&1&0\\\
-s_{13}e^{i\delta}&0&c_{13}\\\ \end{pmatrix}\begin{pmatrix}c_{12}&s_{12}&0\\\
-s_{12}&c_{12}&0\\\ 0&0&1\\\ \end{pmatrix}$ (1.33)

where $c_{ij}\equiv\cos\theta_{ij}$ and $s_{ij}\equiv\sin\theta_{ij}$. The
three mixing angles ($\theta_{12}$, $\theta_{13}$, $\theta_{23}$) and two
relevant mass squared splittings $\Delta m_{12}^{2}$ and $|\Delta m_{23}^{2}|$
have been measured to a precision of $\mathcal{O}(1\%-10\%)$ over the past two
decades [54, 55, 56]. An extensive experimental program is planned to measure
$\delta$ to similar precision, as well as the neutrino hierarchy (i.e., the
sign of $\Delta m_{23}^{2}$) and the octant of $\theta_{23}$ [71].

###  1.4 Anomalies in the Neutrino Sector

Despite the success of the three-neutrino mixing paradigm, several anomalous
results have appeared. Perhaps the most famous of these is the excess of
$\bar{\nu}_{e}$ candidate events observed by the Liquid Scintillator Neutrino
Detector (LSND) experiment [5]. LSND took data at Los Alamos Meson Physics
Facility (LAMPF) from 1993-1998, observing neutrino interactions from a high-
intensity decay-at-rest (DAR) source. The LSND detector was a 167-ton
cylindrical tank of mineral oil that collected scintillation and Cherenkov
light produced in neutrino interactions. The LAMPF accelerator provided a
$\sim 1\;{\rm mA}$ beam of 798 MeV protons, which were then focused on a water
or high-Z target. This process created a large number of pions, which then
decayed to produce neutrinos. Most $\pi^{-}$ came to rest and were captured by
nuclei in and around the target, and the $\pi^{+}\to\nu_{e}e^{+}$ decay chain
is helicity-suppressed due to the interplay between angular momentum
conservation and the left-chiral nature of the weak interaction. Thus the
dominant neutrino production process was
$\pi^{+}\to\nu_{\mu}(\mu^{+}\to\bar{\nu}_{\mu}\nu_{e}e^{+})$.

LSND looked specifically for $\bar{\nu}_{\mu}\to\bar{\nu}_{e}$ conversion
using $\bar{\nu}_{\mu}$ from $\mu^{+}$ DAR. The $\bar{\nu}_{e}$ events were
observed via the inverse beta decay (IBD) process. This is a very clean
channel, as one can require a coincidence between the initial positron
emission and the subsequent neutron capture on hydrogen, which releases a
characteristic $2.2\;{\rm MeV}$ photon. The intrinsic $\bar{\nu}_{e}$ flux,
coming predominately from $\pi^{-}$ decay-in-flight (DIF), was suppressed
compared to intrinsic $\bar{\nu}_{\mu}$ by a factor of $\sim 8\times 10^{-4}$.
Any significant excess of $\bar{\nu}_{e}$ would be evidence for
$\bar{\nu}_{\mu}\to\bar{\nu}_{e}$ oscillations. This is exactly what LSND
observed, as shown in figure 1.9. However, the neutrino energies
$\mathcal{O}(30\;{\rm MeV})$ and baselines $(\mathcal{O}(30\;{\rm m})$
required a mass-squared-splitting of $\Delta m^{2}\sim 1\;{\rm eV^{2}}$. This
is larger than the measured values of $\Delta m^{2}_{12}$ and $|\Delta
m^{2}_{23}|$ by at least three orders of magnitude–therefore, the LSND result
cannot be explained by the standard three neutrino oscillation paradigm. One
must introduce a fourth neutrino to the SM neutrinos in order to facilitate
such oscillations. Measurements of the invisible width of the $Z$ boson forbid
this neutrino from coupling to the weak force in the same way as the three SM
neutrinos [72]. Thus, this fourth neutrino is typically referred to as a
“sterile neutrino” ($\nu_{s}$). The sterile neutrino paradigm will be
introduced in more detail in section 1.4 and discussed thoroughly throughout
this thesis. The LSND anomaly is currently under direct investigation by the
follow-up JSNS2 experiment [73, 74], which will use a gadolinium-loaded liquid
scintillator detector [75] to measure IBD interactions at the J-PARC Materials
and Life Science Experimental Facility.

Figure 1.9: The LSND excess of $\overline{\nu}_{e}$ events on top of the
predicted SM background (green and red regions). The blue region indicates the
best fit to $\overline{\nu}_{\mu}\to\overline{\nu}_{e}$ oscillations via a
sterile neutrino state. Figure from Ref. [5]

The Mini Booster Neutrino Experiment (MiniBooNE) was designed to follow up on
the LSND anomaly [76]. MiniBooNE took data at Fermilab’s Booster Neutrino Beam
(BNB) from 2002-2019, observing the interactions of neutrinos with energy
$E\sim 500\;{\rm MeV}$ in an 800-metric-ton mineral oil (CH2) detector [15].
The Fermilab Booster accelerates protons to a kinetic energy of 8 GeV, at
which point they collide with the beryllium target of the BNB. This produces a
cascade of mesons, predominately pions. The charged mesons are focused using a
magnetic horn and decay in a 50 m decay pipe; in the nominal “neutrino mode”,
the magnetic field is generated to create a flux of mostly muon neutrinos from
$\pi^{+}$ decay-in-flight [14]. The current in the magnetic horns can be
reversed to instead focus $\pi^{-}$ along the beamline, thus creating a beam
of mostly muon antineutrinos–this is referred to as “antineutrino mode”.
MiniBooNE was situated at a baseline of $L\sim 500\;{\rm m}$ from the BNB
target, resulting in a similar characteristic $L/E$ as that of LSND, $\approx
1\;{\rm m/MeV}$. By equation 1.30, this means MiniBooNE would also be
sensitive to oscillations at $\Delta m^{2}\sim 1\;{\rm eV}^{2}$.

In 2007, MiniBooNE began to report results from their flagship analysis: the
search for an excess of $\nu_{e}$ events in the BNB [76]. MiniBooNE relied
primarily on the reconstruction of Cherenkov light from charged final state
particles to identify neutrino interactions. Thus, $\nu_{e}$ CC interactions
would show up as a “fuzzy” Cherenkov ring due to multiple scattering of the
electron as well as the induced EM shower [77]. These fuzzy Cherenkov ring
events are hereafter referred to as “electron-like” events. Starting with the
initial results [76, 78], MiniBooNE has consistently observed an excess of
electron-like events above their expected SM background, the significance of
which has grown over the 17-year data-taking campaign of the experiment [10].
Figure 2.5 shows the $4.8\sigma$ MiniBooNE electron-like excess considering
the total neutrino mode dataset, corresponding to $18.75\times 10^{20}$
protons-on-target (POT) [10]. A similar excess was observed in the
antineutrino mode dataset [79]. The as-yet-unexplained MiniBooNE excess
represents one of the most significant disagreements with the SM to date.

Though the origin of the MiniBooNE excess remains unknown, neutrino physicists
have converged on a number of potential explanations. The most famous
explanation involves sterile neutrino-driven $\nu_{\mu}\to\nu_{e}$
oscillations consistent with the LSND result ($\Delta m^{2}\sim 1\;{\rm
eV^{2}}$). While this model can explain at least some of the MiniBooNE excess,
the excess in the lowest energy region ($E_{\nu}\lesssim 400\;{\rm MeV}$) sits
above even the best-fit sterile neutrino solution. Due to the Cherenkov nature
of the detector, electrons and photons are essentially indistinguishable–both
seed EM showers which appear as fuzzy Cherenkov rings. Thus, the MiniBooNE
excess could also come from a mismodeled photon background. Though not the
subject of this thesis, there have been extensive experimental and theoretical
efforts, both within and outside of the MiniBooNE collaboration, to validate
the MiniBooNE SM photon background prediction [10, 80, 81, 82]. One can also
consider BSM sources of electron-like events in MiniBooNE. Typical models
introduce additional sources of photons and/or $e^{+}e^{-}$ events in
MiniBooNE through couplings to new dark sector particles. Resolution of the
LSND and MiniBooNE anomalies, often referred to as the short baseline (SBL)
anomalies, is a major goal within the particle physics community [83]. This
thesis specifically investigates the MiniBooNE anomaly in further detail,
covering both experimental and phenomenological studies into the origin of the
excess.

Figure 1.10: The MiniBooNE electron-like channel data and SM background
prediction for the entire neutrino mode dataset, as a function of the
reconstructed neutrino energy.

We now briefly touch on two additional classes of anomalies that have surfaced
over the years: the reactor antineutrino anomaly (RAA) and the gallium
anomaly. The RAA [8] is a $\sim 5\%$ deficit in the total $\overline{\nu}_{e}$
rate observed from nuclear reactors compared to the theoretical expectation
from the Huber-Mueller (HM) model [84, 85]. The HM model combines results
using the summation method (summing the contributions of all beta-decay
branches in the reactor) and the conversion method (relying on older
measurements of the $\overline{\nu}_{e}$ flux from the different fissionable
isotopes in the reactor). The data contributing to the RAA mostly come from
reactor neutrino experiments operating at baselines short enough that the
effects of SM neutrino oscillations are negligible. One can interpret the RAA
as due to $\overline{\nu}_{e}$ disappearance via oscillations involving a
sterile neutrino. Coincidentally, due to the relevant neutrino energies and
baselines, such a solution requires $\Delta m^{2}\gtrsim 1\;{\rm eV}^{2}$,
similar to the LSND and MiniBooNE solution [6]. Figure 1.11 shows an overview
of the RAA circa 2012, including the suite of short baseline reactor
experiments which observe a deficit with respect to the HM model with SM
neutrino oscillations (red line), as well as an example sterile neutrino
solution to the RAA (blue line). Recently, the reactor $\overline{\nu}_{e}$
flux calculation has been revisited by various groups, each of which improves
upon some aspect of the summation or conversion method used in the HM flux
model [86, 87, 88, 89]. The significance of the RAA either diminishes or
disappears in some of these models; however, these improved models have
difficulty removing the RAA while also explaining the “5-MeV bump” observed by
most short baseline reactor experiments with respect to the HM model [89].
Thus, while the RAA story is quickly evolving, our understanding of reactor
neutrino fluxes is far from clear.

Figure 1.11: Data contributing to the reactor antineutrino anomaly, indicating
the $\sim 5\%$ flux deficit observed by short-baseline reactor neutrino
experiments. The red line indicates the prediction incorporating SM neutrino
oscillations only, while the blue line shows an example prediction including a
sterile neutrino. Figure from Ref. [6].

The gallium anomaly refers to a series of gallium-based detectors that have
observed a deficit of $\nu_{e}$ capture events on 71Ga with respect to the
theoretical expectation. The original harbingers of the anomaly, SAGE [90] and
GALLEX [91], were designed to measure solar neutrinos using the ${}^{71}{\rm
Ga}\nu_{e}\to{}^{71}{\rm Ge}e^{-}$ capture process. Each detector was
calibrated using electron capture $\nu_{e}$ sources, including 51Cr and 37Ar.
Combining all available calibration data across both experiments, the observed
71Ge production rate was lower than the expectation by a factor of $0.87\pm
0.05$ [90]. Though the statistical significance of the anomaly was only modest
($2-3\sigma$), the community was already beginning to interpret the anomaly as
$\nu_{e}\to\nu_{s}$ transitions via an eV-scale sterile neutrino [92]. A
follow-up experiment to the SAGE and GALLEX anomaly, BEST [9], released their
first results in 2021. BEST placed a 3.414 MCi 51Cr $\nu_{e}$ source at the
center of two nested 71Ga volumes, each with a different average distance from
the source. The ratio of observed to the predicted 71Ge production rate was
$R_{in}=0.79\pm 0.05$ ($R_{out}=0.77\pm 0.05$) for the inner (outer) volume,
thus reaffirming the gallium anomaly [9]. No evidence for a difference in the
deficit between the inner and outer volumes was observed, which would have
been a smoking gun signature of a baseline-dependent effect like
$\nu_{e}\to\nu_{s}$ oscillations. However, the statistical significance of the
gallium anomaly is now much stronger; the combined SAGE, GALLEX, and BEST
results give evidence for a deficit at the $5.0\sigma$ level [7]. The datasets
contributing to this anomaly are summarized in figure 1.12.

Figure 1.12: Data contributing to the gallium anomaly, indicating the $\sim
20\%$ deficit in the 71Ge production rate observed by SAGE, GALLEX, and BEST.
Figure from Ref. [7].

As alluded to above, the most common BSM interpretation of the SBL, reactor
antineutrino, and gallium anomalies is the “3+1 model”, which involves the
addition of a new neutrino state–the sterile neutrino–at the eV scale. The
sterile neutrino introduces a fourth weak interaction eigenstate $\nu_{s}$ and
mass eigenstate $\nu_{4}$ to the standard three-neutrino mixing paradigm.
Thus, equation 1.24 becomes

$\begin{pmatrix}\nu_{e}\\\ \nu_{\mu}\\\ \nu_{\tau}\\\
\nu_{s}\end{pmatrix}=\begin{pmatrix}U_{e1}&U_{e2}&U_{e3}&U_{e4}\\\ U_{\mu
1}&U_{\mu 2}&U_{\mu 3}&U_{\mu 4}\\\ U_{\tau 1}&U_{\tau 2}&U_{\tau 3}&U_{\tau
4}\\\ \end{pmatrix}\begin{pmatrix}\nu_{1}\\\ \nu_{2}\\\ \nu_{3}\\\
\nu_{4}\end{pmatrix}.$ (1.34)

As we are interested in an eV-scale sterile neutrino, the mass-squared
splittings between the three active neutrinos are smaller by at least 2-3
orders of magnitude compared to their mass-squared splittings with the fourth
mass eigenstate. This means that the active neutrino mass splittings are
negligible for short-baseline experiments, i.e. those in which the argument of
the second $\sin^{2}$ term in equation 1.32 is small. Experiments contributing
to the aforementioned anomalies all satisfy this condition. Thus, when
considering sterile neutrino explanations for these anomalies, we can make the
approximation

$\Delta m^{2}_{41}\approx\Delta m^{2}_{42}\approx\Delta m^{2}_{43}\equiv\Delta
m^{2},$ (1.35)

where we hereafter use $\Delta m^{2}$ to refer to the mass-squared splitting
of the fourth mass eigenstate. This approximation holds regardless of the
hierarchy of SM neutrino mass eigenstates.

The experiments discussed in this thesis are sensitive only to
$\overset{\textbf{(---)}}{\nu}_{e}$ and $\overset{\textbf{(---)}}{\nu}_{\mu}$
interactions. The sterile neutrino can facilitate short-baseline oscillations
between these flavor states; the oscillation probability expressions, which
can be derived using equation 1.30 within the 3+1 framework, are given by [93]

$\begin{split}&P_{\nu_{e}\to\nu_{e}}=1-4\sin^{2}2\theta_{ee}\sin^{2}(1.27\Delta
m^{2}L/E)\\\
&P_{\nu_{\mu}\to\nu_{\mu}}=1-4\sin^{2}2\theta_{\mu\mu}\sin^{2}(1.27\Delta
m^{2}L/E)\\\ &P_{\nu_{\mu}\to\nu_{e}}=4\sin^{2}2\theta_{\mu
e}\sin^{2}(1.27\Delta m^{2}L/E),\end{split}$ (1.36)

where $\Delta m^{2}$, $L$, and $E$ are in units of eV2, km, and GeV,
respectively, and

$\begin{split}&\sin^{2}2\theta_{ee}=4(1-|U_{e4}|^{2})|U_{e4}|^{2}\\\
&\sin^{2}2\theta_{\mu\mu}=4(1-|U_{\mu 4}|^{2})|U_{\mu 4}|^{2}\\\
&\sin^{2}2\theta_{\mu e}=4|U_{\mu 4}|^{2}|U_{e4}|^{2}.\end{split}$ (1.37)

The first expression in equation 1.36 can potentially explain the deficit of
$\overline{\nu}_{e}$ and $\nu_{e}$ events observed in the RAA and gallium
anomaly, respectively. Though both anomalies stem qualitatively from the same
phenomenon–$\overset{\textbf{(---)}}{\nu}_{e}$ disappearance at short
baseline–the gallium anomaly in general prefers a larger value of
$\sin^{2}2\theta_{ee}$ than the RAA. This is evident in figure 1.13, which
shows the regions in $\sin^{2}2\theta_{ee}$–$\Delta m^{2}$ parameter space
preferred by the RAA and gallium anomalies, as well as global constraints from
other experiments. These constraints come from short-to-medium-baseline
reactor experiments, including NEOS [94], RENO [95], and Daya Bay [96], as
well as very-short-baseline reactor experiments, including STEREO [97], DANSS
[98], and PROSPECT [99]. Each of these experiments searches for
$\overline{\nu}_{e}$ disappearance in a reactor-flux-agnostic way: the former
though comparisons of the reactor $\overline{\nu}_{e}$ spectra measured by
different detectors [100], and the latter through the use of modular or
movable detectors capable of comparing $\overline{\nu}_{e}$ interaction rates
across different baselines. The KATRIN experiment, which is sensitive to the
neutrino mass via an extremely precise measurement of the tritium beta
spectrum endpoint, also places strong constraints on $\sin^{2}2\theta_{ee}$ in
the $\Delta m^{2}\gtrsim 10~{}{\rm eV}^{2}$ region [101].

Figure 1.13: Preferred regions in $\sin^{2}2\theta_{ee}$–$\Delta m^{2}$
parameter space to explain the RAA [8] (green contour) and gallium anomaly [9]
(blue regions). The total excluded region from other experiments (grey region)
is also shown. Figure from Ref. [9].

The second expression in equation 1.36 can potentially explain the SBL
anomalies. This is because both LSND and MiniBooNE operated at accelerator
neutrino sources for which the neutrino flux was generated mainly by charged
pion decay [5, 14]; thus, due to helicity suppression, the flavor composition
was dominated muon-flavored (anti)neutrinos. This means that even a small
value of $\sin^{2}2\theta_{\mu e}$ could generate an observable level of
$\overset{\textbf{(---)}}{\nu}_{e}$ appearance on top of the SM
$\overset{\textbf{(---)}}{\nu}_{e}$ flux prediction. Figure 1.14 shows the
allowed regions in $\sin^{2}2\theta_{\mu e}$–$\Delta m^{2}$ parameter space
from LSND and MiniBooNE [10]. Strikingly, both anomalies generally prefer the
same region of parameter space. However, as the MiniBooNE excess tends to peak
more sharply at lower energies, the 3+1 fit prefers lower values of $\Delta
m^{2}$ compared to the LSND result.

It is important to note that the fits performed in figure 1.14 account only
for $\overset{\textbf{(---)}}{\nu}_{\mu}\to\overset{\textbf{(---)}}{\nu}_{e}$
oscillations, ignoring any potential $\overset{\textbf{(---)}}{\nu}_{e}$ or
$\overset{\textbf{(---)}}{\nu}_{\mu}$ disappearance in the SM background
prediction. This is a reasonable approximation, however, the inclusion of the
latter effects does indeed impact the MiniBooNE allowed regions. This effect
was only accounted for recently in Ref. [102], which is presented in section
5.3.1 of this thesis.

Figure 1.14: Preferred regions in $\sin^{2}2\theta_{\mu e}$–$\Delta m^{2}$
parameter space to explain the LSND anomaly [5] (filled contours) and
MiniBooNE anomaly [10] (open contours). Figure from Ref. [10].

While there are indications of short baseline
$\overset{\textbf{(---)}}{\nu}_{\mu}\to\overset{\textbf{(---)}}{\nu}_{e}$
appearance and $\overset{\textbf{(---)}}{\nu}_{e}$ disappearance in the global
anomaly picture, direct observation of $\overset{\textbf{(---)}}{\nu}_{\mu}$
disappearance via the third expression in equation 1.36 remains elusive. Long
baseline experiments such as MINOS/MINOS+ [103, 104] and CCFR84 [105] have
searched for muon neutrino disappearance from an accelerator neutrino source.
Additionally, the IceCube experiment has searched for a sterile-induced matter
resonance impacting muon neutrinos as they transit through the earth [106]. So
far, no definitive evidence for $\overset{\textbf{(---)}}{\nu}_{\mu}$
disappearance has been found (up to a $\sim 2\sigma$ preference in the IceCube
results [106]).

The lack of $\overset{\textbf{(---)}}{\nu}_{\mu}$ disappearance introduces
significant tension when one tries to fit global neutrino data within a
consistent 3+1 model. This conclusion has been reached by multiple 3+1 global
fitting efforts [93, 11, 12]; figure 1.15 shows a representation of the
tension between appearance and disappearance experiments observed in global
fits. This tension persists even with the inclusion of the recent BEST result,
which prefers larger values of $|U_{e4}|^{2}$ (thus allowing lower values of
$|U_{\mu 4}|^{2}$ to fit the $\overset{\textbf{(---)}}{\nu}_{e}$ appearance
anomalies) [12]. Thus, the 3+1 model, while still an important benchmark BSM
scenario, has become disfavored as a solution to all observed anomalies in the
neutrino sector. The state of the sterile neutrino explanation of the SBL
anomalies is discussed in more detail throughout this thesis.

In recent years, neutrino physicists have begun to turn toward alternative
explanations of the anomalies, often involving dark sector particles with
additional interactions. Chapter 6 of this thesis covers one such explanation
of the MiniBooNE anomaly, involving heavy right-handed neutrinos with a
transition magnetic moment coupling to the active neutrinos.

(a) From Ref. [11]

(b) From Ref. [12]

Figure 1.15: Graphical representation of the tension observed in 3+1 global
fits between different subsets of the experimental landscape. Figure 1.15(a)
shows the tension between $\nu_{e}$ appearance experiments and
$\nu_{e}$/$\nu_{\mu}$ disappearance experiments observed in Ref. [11]. Figure
1.15(b) shows the tension between allowed regions from $\nu_{e}$ appearance
(lower right), $\nu_{e}$ disappearance (upper right), and $\nu_{\mu}$
disappearance (upper left) experiments observed in Ref. [12], which includes
the latest results from the BEST experiment.

##  Chapter 2 The MiniBooNE Experiment

This chapter is intended to give the reader an overview of the Mini Booster
Neutrino Experiment (MiniBooNE), specifically concerning the excess of
electron-like events observed by MiniBooNE in data taken between 2002–2019 at
Fermilab’s Booster Neutrino Beam (BNB). The MiniBooNE excess is at the center
of this thesis; the research presented here covers both experimental follow-up
and theoretical interpretations of this anomaly. Thus, the remaining chapters
require a thorough discussion of the MiniBooNE experiment and its most famous
result.

###  2.1 Overview of MiniBooNE

MiniBooNE was originally designed as an experimental follow-up to the LSND
excess of $\overline{\nu}_{e}$ events observed at the Los Alamos Meson Physics
Facility (LAMPF) [5]. As described in section 1.4, the LAMPF flux comprised
mostly of $\overline{\nu}_{\mu}$, which dominated over the
$\overline{\nu}_{e}$ flux by three orders of magnitude [107]. Because of this,
LSND was able to perform a low-background search for the IBD interaction
$\overline{\nu}_{e}p\to e^{+}n$. An excess of IBD events was observed above
the intrinsic $\overline{\nu}_{e}$ flux prediction from the beam dump
source–this is known as the “LSND amonaly” [5].

The LSND anomaly has traditionally been interpreted as evidence for
$\overline{\nu}_{\mu}\to\overline{\nu}_{e}$ oscillations at $\Delta
m^{2}\approx 1\;{\rm eV}^{2}$. The LSND detector sat relatively close to the
LAMPF nuclear target; the characteristic length-to-energy ratio in the
experiment was $L/E\sim 30\;{\rm m}/30\;{\rm MeV}$. According to equation
1.32, in order to be sensitive to the oscillation-based interpretation of the
LSND anomaly, one must maintain the same ratio $L/E$. This was the design
strategy of the MiniBooNE experiment, which observed the interactions of
neutrinos from the BNB with characteristic energy $E_{\nu}\sim 500\;{\rm
MeV}$, at a baseline of $L\sim 500\;{\rm m}$ from the BNB beryllium target.
The BNB produced mostly $\nu_{\mu}$ from pion decay-in-flight; thus, MiniBooNE
searched for $\nu_{\mu}\to\nu_{e}$ oscillations in the BNB at $\Delta
m^{2}\approx 1\;{\rm eV}^{2}$.

####  2.1.1 The Booster Neutrino Beam

The BNB, which is still operational, follows the typical design of a neutrino
beamline [107]. Protons are accelerated in a synchrotron up to a momentum of
8.89 GeV, at which point they are kicked out of the synchrotron and interact
within the Be target of the BNB, producing a cascade of secondary particles
[14]. The charged mesons in this cascade are then focused using a toroidal
magnetic field from an aluminum horn. By switching the direction of the
current in the horn (and thus the direction of the magnetic field), one can
choose whether to focus positively-charged mesons and de-focus negatively-
charged mesons (“neutrino mode”), or vice-versa (“antineutrino mode”). After
focusing, charged mesons pass through a concrete collimator and enter a
50-meter-long air-filled region where they decay to neutrinos. The neutrinos
travel through another 474 meters of bedrock before reaching the MiniBooNE
detector. A schematic depiction of this process is shown in figure 2.1.

The MiniBooNE flux is described in detail in Ref. [14]; we summarize the most
important details here. In neutrino (antineutrino) mode, the flux is dominated
by $\nu_{\mu}$ ($\overline{\nu}_{\mu}$) from $\pi^{+}$ ($\pi^{-}$) decay.
Wrong-sign $\overline{\nu}_{\mu}$ ($\nu_{\mu}$), coming mostly from the decay
of oppositely-charged pions, contribute at the 5% (15%) level. Two and three-
body kaon decays also contribute to the $\nu_{\mu}$ and $\overline{\nu}_{\mu}$
flux at the few-percent level. The BNB also produces electron (anti)neutrinos,
which represent $<1\%$ of the total flux in both neutrino and antineutrino
mode. These come from two main sources: the decay of the secondary muon
produced in the original charged pion decay, which is dominant for
$E_{\nu}\lesssim 1\;{\rm GeV}$, and two-body kaon decay, which is dominant for
$E_{\nu}\gtrsim 1\;{\rm GeV}$. The BNB flux breakdown in neutrino and
antineutrino mode are shown in figure 2.2.

The $\pi^{\pm}$ production rate from p-Be interactions has been measured by
the HARP [108] and BNL E910 [109] experiments. HARP took data at the BNB
proton incident momentum (8.89 GeV/c) with a replica of the BNB beryllium
target, while E910 took data at varying incident proton momenta above and
below the nominal BNB value. These data were used to constrain a Sanford-Wang
parameterization of the $\pi^{\pm}$ differential production cross section in
the BNB [110]. The charged and neutral kaon production rates in p-Be were
constrained by measurements from other experiments at proton momenta around
8.89 GeV/c; the Feynman scaling hypothesis was used to relate these
measurements to the BNB proton momentum [14].

Figure 2.1: A schematic depiction of the BNB at Fermilab, including the
downstream MiniBooNE detector. Figure from Ref. [13].

Figure 2.2: Breakdown of the neutrino flux at the BNB in neutrino (left) and
antineutrino (right) mode. Figure from Ref. [14]

####  2.1.2 The MiniBooNE Detector

The MiniBooNE detector is an 818-ton, 6.1-meter-radius spherical volume filled
with mineral oil (approximately CH2) [15]. It was designed to measure the
Cherenkov light produced from charged particles created in the charged-current
interactions of BNB neutrinos within the detector volume. To do this, the
inner surface of the sphere was instrumented with 1280 photo-multiplier tubes
(PMTs), corresponding to a photocathode coverage of 11.3%. An additional 240
PMTs were used to instrument the surrounding veto region, which rejected
cosmic muons and neutrino interactions outside the detector volume with an
efficiency of $\sim 99.99\%$ [15]. Mineral oil was chosen as the detector
medium due to its high index of refraction (n=1.47), leading to more Cherenkov
light production by electrons traversing the detector volume. The exact
mineral oil mixture, Marcol 7, was selected by optimizing the behavior of
photons with wavelengths between 320 nm and 600 nm (e.g., requiring an
extinction length greater than 20 m) [15]. The detector was situated in a
cylindrical vault just below ground level, under $\sim 3\;{\rm m}$ of dirt. A
schematic depiction of the MiniBooNE detector is shown in figure 2.3.

The reconstruction of the final state from a neutrino interaction in MiniBooNE
relied on the detection of Cherenkov light. Specifically, the collaboration
developed reconstruction algorithms that turned the spatiotemporal
distribution of photon hits on the PMTs into kinematic information on each
observable final state particle [77]. These algorithms used maximum likelihood
estimators to estimate the starting location, direction, and energy of final
state particles using the observed photon hits in each PMT, relying on the
known transport properties of Cherenkov photons within the detector medium.
Cherenkov photons are emitted when a charged particle travels faster than the
speed of light in a medium, at an angle of $\cos\theta_{C}=1/n\beta$ with
respect to the charged particle track. This results in a characteristic ring-
like pattern on the detector wall. Such Cherenkov rings formed the basis of
the MiniBooNE reconstruction algorithm.

There were two main classes for observable final state particles in MiniBooNE:
muon-like ($\mu$-like) and electron-like ($e$-like). Each elicits a different
Cherenkov ring pattern [77]. At MiniBooNE energies, muons are typically
minimum-ionizing particles and thus would appear as a uniform ring in the PMT
array. The ring would be filled in if the muon exits the detector volume
before going below the Cherenkov threshold, and would be open otherwise.
Electrons, on the other hand, undergo radiative processes as they travel,
emitting photons via the Bremsstrahlung process, which then undergo pair-
production to $e^{+}e^{-}$, which then emit more photons, and so on. This
process is typically called an “electromagnetic (EM) shower”. The multiple
constituent electrons and positrons in this EM shower would result in a
distorted Cherenkov ring in the PMT array. Importantly, high energy photons
also produced these distorted rings after undergoing an initial pair-
production interaction; thus, electrons and photons were essentially
indistinguishable in MiniBooNE and were both classified as $e$-like. Another
relevant final-state particle in MiniBooNE was the neutral pion, which could
be identified via two separate distorted Cherenkov rings via the
$\pi^{0}\to\gamma\gamma$ decay. It is also important to note that $\pi^{0}$
events could be misclassified as $e$-like if one of the photons was not
reconstructed, which could happen if one of the photons escaped the detector
without pair producing or had energy below the detection threshold. A
schematic diagram of the detector signature of muons, electrons, and neutral
pions in MiniBooNE is shown in figure 2.4(a).

A separate likelihood was calculated for three different final state particle
hypotheses: electron, muon, and neutron pion [77]. Ratios of these likelihoods
were used to distinguish one particle from another in MiniBooNE. As an
example, we show the separation of electron and muon events as characterized
by the log-likelihood-ratio as a function of reconstructed neutrino energy in
figure 2.4(b). This ratio was the main selection tool in selecting $e$-like
events for MiniBooNE’s flagship search for $\nu_{\mu}\to\nu_{e}$ oscillations
in the BNB.

Figure 2.3: The MiniBooNE detector situated in the cylindrical detector hall
(left) and an image of the interior of the MiniBooNE detector (right), showing
the PMTs in both the signal and veto regions. Figure from Ref. [15].

(a) From Ref. [76]

(b) From Ref. [77]

Figure 2.4: Visual representations of particle identification in MiniBooNE.
Figure 2.4(a) shows a schematic representation of the detector signature from
the three main particle classes in MiniBooNE: muons, electrons, and neutral
pions. Figure 2.4(b) shows the MiniBooNE log-likelihood-ratio between the
$e$-like and $\mu$-like hypothesis as a function of reconstructed neutrino
energy, considering both simulated $\nu_{e}$ CCQE (top) and $\nu_{\mu}$ CCQE
(bottom) interactions.

###  2.2 The MiniBooNE Low Energy Electron-Like Excess

As stated above, MiniBooNE was designed to test the LSND excess of
$\overline{\nu}_{e}$ events discussed in section 1.4. To do this, MiniBooNE
isolated a sample of $e$-like events using the likelihood ratios described in
the previous section [76]. This sample was optimized to select $\nu_{e}$ CCQE
interactions within the detector while rejecting $\nu_{\mu}$ interaction
backgrounds, thus maximizing sensitivity to potential $\nu_{\mu}\to\nu_{e}$
oscillations within the BNB. MiniBooNE’s flagship $e$-like analysis, which has
remained stable over the lifetime of the experiment, achieved a $\nu_{e}$ CCQE
efficiency of $\sim 20\%$ while rejecting $\sim 99.9\%$ of $\nu_{\mu}$
backgrounds [10]. The full MiniBooNE dataset consists of $18.75\times 10^{20}$
($11.27\times 10^{20}$) protons-on-target (POT) in neutrino (antineutrino)
mode collected over 17 years of operation. In this dataset, the $e$-like
analysis observes 2870 (478) data events in neutrino (antineutrino) mode,
compared to an SM prediction of 2309.4 (400.6) events [10]. Combining neutrino
and antineutrino mode data, MiniBooNE observes an excess of $638.0\pm
52.1\;({\rm stat.})\pm 122.2\;({\rm sys.})$ $e$-like events, corresponding to
a Gaussian significance of $4.8\sigma$ [10].

Figure 2.5 shows the reconstructed neutrino energy distribution of the
MiniBooNE $e$-like excess in both neutrino and antineutrino mode. The stacked
histogram corresponds to the SM prediction from the NUANCE event generator
[44], while the data points correspond to the observed number of $e$-like
events in each bin. The error bars on the stacked histogram correspond to the
systematic uncertainty on the SM prediction, calculated within a covariance
matrix formalism. The dominant sources of systematic uncertainty include
neutrino cross section modeling (derived largely using MiniBooNE’s own cross
section measurements [111, 112, 113, 114]), nuclear effects, detector response
and optical modeling, and BNB flux estimation [79, 10]. The presented error in
each bin of the $\nu_{e}$ and $\overline{\nu}_{e}$ sample incorporates a
constraint from MiniBooNE’s dedicated $\nu_{\mu}$ and $\overline{\nu}_{\mu}$
CCQE samples. The dashed line corresponds to the best fit of the MiniBooNE
excess to the $3+1$ sterile neutrino model described in section 1.4. As one
can see, the excess in data events is strongest in the lowest energy bins; for
this reason, this anomaly is often referred to as the MiniBooNE low-energy
excess (LEE).

As MiniBooNE used a Cherenkov detector, it was not sensitive to the final
state hadronic activity in a neutrino interaction. Thus, kinematic
reconstruction of the original neutrino relied entirely on the final state
lepton. Under the assumption that the neutrino underwent a CCQE interaction
off of a nucleon at rest within the nucleus, the original neutrino energy is
given by [111]

$E_{\nu}^{\rm
QE}=\frac{2(M_{n}^{\prime})E_{\ell}-((M_{n}^{\prime})^{2}+m_{\ell}^{2}-M_{p})}{2[(M_{n}^{\prime})-E_{\ell}+\sqrt{E_{\ell}^{2}-m_{\ell}^{2}}\cos\theta_{\ell}]},$
(2.1)

where $E_{\ell}$ is the total lepton energy, $\cos\theta_{\ell}$ is the lepton
scattering angle, and $M_{n}$, $M_{p}$, and $m_{\ell}$ are the neutron,
proton, and lepton mass, respectively. The adjusted neutron energy is defined
as $M_{n}^{\prime}\equiv M_{n}-E_{B}$, where $E_{B}$ is the nuclear binding
energy of the initial state neutron. An analogous relation exists for
antineutrino energy reconstruction in a CCQE interaction [115]. This is the
reconstructed energy definition used to generate the histograms in figure 2.5.

Figure 2.6 shows the visible energy and $\cos\theta$ distributions of the
final state lepton in MiniBooNE’s $e$-like neutrino mode sample. The visible
energy distribution shows the strongest discrepancy for softer lepton kinetic
energies, as expected for a low-energy excess. For the angular distribution,
it is worth noting that while there is an excess across the entire range, the
largest deviation above the SM prediction comes from the
$\cos\theta\in[0.9,1.0]$ bin. The angular distribution of the MiniBooNE LEE is
an important piece of information for potential solutions to the anomaly–as we
will discuss throughout this thesis, BSM physics models often cannot explain
the energy and angular distributions of the MiniBooNE LEE simultaneously.

The green contributions to the stacked histograms of figure 2.5 represent the
interactions of intrinsic $\nu_{e}$ or $\overline{\nu}_{e}$ in the BNB. At low
energies, these events come mostly from the decay of the secondary muon in the
$\pi^{+}\to\mu^{+}$ or $\pi^{-}\to\mu^{-}$ decay chain, while $\nu_{e}$ and
$\overline{\nu}_{e}$ from kaon decays start to contribute more at higher
energies [14].

The red and brown contributions to the stacked histograms represent
misidentified photon backgrounds that are reconstructed as a single distorted
Cherenkov ring. The largest photon background comes from misidentified
$\pi^{0}$ created via $\nu_{\mu}$ and $\overline{\nu}_{\mu}$ neutral-current
(NC) resonant scattering, in which the initial state nucleon is excited to a
$\Delta$ resonance before decaying to nucleon-pion pair. The $\pi^{0}$ decay
promptly to a pair of photons, which should nominally appear as a pair of
distorted Cherenkov rings as in figure 2.4(a). However, if one of the photons
exits the detector before converting to an $e^{+}e^{-}$ pair, or if the
original pion energy is distributed asymmetrically such that the visible
energy of one of the photons sits below the reconstruction threshold of 140
MeV [76], the $\pi^{0}$ decay will be misidentified as an $e$-like event. An
enhancement of the NC $\pi^{0}$ background in figure 2.5 could in principle
explain the observed excess. However, MiniBooNE constrained the rate of this
NC $\pi^{0}$ background in situ via a measurement of the two-gamma invariant
mass peak in well-reconstructed NC $\pi^{0}$ events [10]. Additionally, the
radial distribution of the excess peaks toward the center of the detector,
while misidentified NC $\pi^{0}$ backgrounds happen more often toward the edge
of the detector, where it is more likely for a photon to escape before pair-
producing.

The next-largest photon background comes from rare $\Delta\to N\gamma$ decays
in $\nu_{\mu}$ and $\overline{\nu}_{\mu}$ NC resonant scattering interactions.
As this process has never been observed directly, it was not possible for
MiniBooNE to constrain the $\Delta\to N\gamma$ event rate in situ. It was
instead constrained indirectly by the NC $\pi^{0}$ two-gamma invariant mass
distribution [10]. A factor 3.18 enhancement in $\Delta\to N\gamma$ events
could explain the MiniBooNE LEE; however, this hypothesis has since been
disfavored by recent results from the MicroBooNE experiment [80]. The
MicroBooNE experiment will be covered in more detail in chapters 3, 4 and 5.

MiniBooNE has also studied neutrino interactions outside the detector volume
which result in a single photon entering the detector (the “dirt” backgrounds
in figure 2.5). The timing distribution of the MiniBooNE $e$-like dataset
suggests that the excess comes primarily in time with the beam, while dirt
background events are often delayed by $\sim 10\;{\rm ns}$ [10]. This result
disfavors an enhancement of external neutrino interactions as an explanation
of the MiniBooNE excess.

Therefore, the $4.8\sigma$ MiniBooNE excess remains unexplained. Resolution of
the MiniBooNE LEE is one of the major goals of the neutrino community [83].

(a) $\nu_{e}$ sample, from Ref. [10]

(b) $\overline{\nu}_{e}$ sample, from Ref. [79]

Figure 2.5: The $E_{\nu}^{\rm QE}$ distribution of the MiniBooNE $e$-like
excess in the total neutrino mode (figure 2.5(a)) and antineutrino mode
(figure 2.5(b)) datasets. The observation and SM prediction in each bin are
shown by the data points and colored histograms, respectively.

(a) Lepton $E_{\rm vis}$ distribution

(b) Lepton $\cos\theta$ distribution

Figure 2.6: The lepton visible energy (figure 2.6(a)) and $\cos\theta$ (figure
2.6(b)) distributions of the MiniBooNE $e$-like excess in the total neutrino
mode dataset. The observation and SM prediction in each bin are shown by the
data points and colored histograms, respectively. Figures from Ref. [10].

The MiniBooNE LEE is most commonly interpreted within the context of the 3+1
model introduced in section 1.4. This is primarily because the MiniBooNE
excess has historically been considered alongside the LSND excess, as both
results can be explained by short-baseline $\nu_{\mu}\to\nu_{e}$ and
$\overline{\nu}_{\mu}\to\overline{\nu}_{e}$ appearance. Strikingly, the
MiniBooNE and LSND anomalies both prefer similar regions in sterile neutrino
parameter space, as shown in figure 1.14. This is further supported by figure
2.7, which shows the rising nature of the MiniBooNE and LSND excesses as a
function of the ratio $L/E$, behavior that is consistent with a sterile
neutrino explanation.

There are, however, complications regarding a sterile neutrino explanation of
the MiniBooNE excess. The 3+1 model has difficulty reproducing the lowest
energy and lowest scattering angle region of the excess. Figure 2.6 shows that
the best fit 3+1 prediction, indicated by the dotted line, still falls below
the observed data in the lowest lepton $E_{\rm vis}$ bin and highest lepton
$\cos\theta$ bin. Additionally, as discussed in section 1.4, there is
significant tension between the MiniBooNE and LSND observation of
$\nu_{e}$/$\overline{\nu}_{e}$ appearance and experiments searching for
$\nu_{e}$/$\overline{\nu}_{e}$ and $\nu_{\mu}$/$\overline{\nu}_{\mu}$
disappearance. Finally, the follow-up MicroBooNE experiment has not observed
an excess of $\nu_{e}$ events consistent with the expectation from the
MiniBooNE LEE [116]. The MicroBooNE $\nu_{e}$ analysis is one of the main
results of this thesis and will be explored in more detail in chapters 4 and
5. While the non-observation of a MiniBooNE-like excess of $\nu_{e}$ events in
the BNB does set constraints on $3+1$ parameter space, it does not fully
exclude the MiniBooNE allowed regions [102]. This point will be discussed
further in chapter 5.

These complications with the eV-scale sterile neutrino interpretation of the
MiniBooNE LEE have prompted the community to explore alternative explanations.
Many of these are relatively simple extensions beyond $3+1$, such as $3+N$
models involving $N$ additional sterile neutrino states [93], decaying sterile
neutrino models [117, 118, 119], and sterile neutrinos with altered dispersion
relations from large extra dimensions [120, 121, 122]. Other explanations for
the MiniBooNE LEE introduce a number of new particle species prescribed with
new interactions that create an additional source of photons or $e^{+}e^{-}$
pairs in MiniBooNE. Such models include heavy neutral leptons (HNLs) which
decay to photons via a transition magnetic moment [123, 124, 125, 126, 127,
128, 129, 130, 131, 132, 133, 134, 27, 135, 31] and models with heavy
neutrinos coupled to a “dark sector” involving, for example, new vector or
scalar mediators [136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146].
Chapter 6 of this thesis explores one such explanation of MiniBooNE involving
an HNL with a transition magnetic moment coupling to active neutrinos, which
we hereby refer to as a “neutrissimo”. Neutrissimo decays in MiniBooNE provide
an additional source of single photons which could explain the $e$-like excess
[27, 31].

Thus, there are many potential explanations for the MiniBooNE anomaly.
Distinguishing between these explanations requires careful consideration of
the kinematic distributions of the MiniBooNE excess [147, 31]. Further, these
models are often subject to constraints from existing accelerator neutrino
experiments, such as MINERvA and NA62 [146, 139]. A complete evaluation of
constraints from existing data is essential in determining the most viable
models among the many proposed MiniBooNE explanations. The work presented in
chapter 6 takes a step in this direction by calculating constraints from
MINERvA on the neutrissimo model.

Figure 2.7: The MiniBooNE and LSND excesses as a function of the ratio $L/E$.
The MiniBooNE data is separated into neutrino and antineutrino mode. Figure
from Ref. [10].

##  Chapter 3 The MicroBooNE Detector

In order to ascertain the nature of the MiniBooNE excess, one needs a detector
capable of providing more detailed event-by-event information than MiniBooNE’s
Cherenkov detector. This is the concept behind the MicroBooNE experiment. The
MicroBooNE detector is a large-scale liquid argon time projection chamber
(LArTPC) with the ability to record high-resolution images of neutrino
interactions. MicroBooNE recently released its first results investigating the
nature of the MiniBooNE excess [116, 80], which will be presented in chapters
4 and 5. This chapter introduces the detector that made this measurement
possible.

###  3.1 Liquid Argon Time Projection Chamber

MicroBooNE used an 85-metric-ton fiducial volume LArTPC detector to observe
the interactions of neutrinos in the BNB [16, 148]. This makes MicroBooNE the
first $\mathcal{O}(100~{}{\rm t})$ LArTPC operated in the United States. The
idea for a LAr-based total absorption detector originated in the 1970s [149].
The introduction of the LArTPC detector concept came from Carlo Rubbia in 1977
[150], extending earlier work from David Nygren [151] and Georges Charpak
[152]. The first operational large-scale LArTPC was the 500-metric-ton active
volume ICARUS T600 detector [153], which came online in 2010. ICARUS observed
cosmic ray and neutrino interactions at the Gran Sasso underground National
Laboratory [154] and even set constraints on $\nu_{\mu}\to\nu_{e}$
interpretations of the LSND and MiniBooNE anomalies using the CERN to Gran
Sasso neutrino beam [155]. On a smaller scale, the ArgoNeuT experiment
operated a 0.25-metric-ton LArTPC at Fermilab’s Neutrino Main Injector
beamline from 2009-2010, where it performed the first measurements of
neutrino-argon cross sections [156].

The MicroBooNE detector is situated $70$ m downstream of the MiniBooNE
detector along the BNB and operated from 2015 to 2021, observing a total of
approximately $1.5\times 10^{21}$ POT [148]. MicroBooNE LArTPC data come in
the form of high-resolution three-dimensional images of the ionization energy
deposited by final state charged particles in neutrino interactions. The
information contained in these images allows for the event-by-event separation
of photons and electrons–an essential capability for determining the source of
the MiniBooNE excess. MicroBooNE can also reconstruct hadronic activity in the
final state of the neutrino interaction, which helps further distinguish
between the possible sources of the MiniBooNE excess.

We begin with a brief overview of the MicroBooNE reconstruction procedure.
Charged-current neutrino interactions in the LAr volume produce charged
particles in the final state, which ionize argon atoms as they traverse the
detector. Thus, each charged particle leaves behind a trail of ionized
electrons which, in theory, can drift freely through the noble element
detector medium without being captured. This drift is controlled via an
external electric field with strength $|E|\sim 273$ V/cm, accelerating the
ionized electrons to a final velocity $v\sim 0.11$ cm/$\mu$s toward three
anode wire planes [148]. MicroBooNE employs a right-handed coordinate system,
in which BNB neutrinos travel along the $\hat{z}$ direction, ionization
electrons drift along the $-\hat{x}$ direction, and $\hat{y}$ represents the
vertical direction [16]. The anode planes consist of two induction planes and
one collection plane, each containing a series of wires spaced 3 mm apart and
oriented at $\pm 60^{\circ}$ and $0^{\circ}$ with respect to the $\hat{y}$
direction for the induction and collection planes, respectively. Each plane is
biased such that ionization electrons drift past the induction plane wires,
generating a signal via induction, and terminate on the collection plane
wires, generating a signal via direct charge collection. The signals on the
anode wire planes allow for two-dimensional reconstruction of the charged
particle trajectory in the $\hat{y}-\hat{z}$ plane, transverse to the drift
direction. The $\hat{x}$ dimension of the charged particle trajectory can be
reconstructed using the arrival time of signals on the anode wires in
conjunction with the known drift time of the ionization electrons. In order
for this technique to work, one must know the initial time at which the
charged particle entered the detector. This can be established using either an
external beam trigger or an internal trigger from the light collection system,
which operates on much shorter time scales, $\mathcal{O}({\rm ns})$, compared
to characteristic electron drift times of $\mathcal{O}({\rm ms})$. A schematic
of this process is shown in figure 3.1.

(a)

(b)

Figure 3.1: Schematic depictions of the MicroBooNE LArTPC. Figure 3.1(a) shows
the detection process for charged particles from a neutrino interaction in a
MicroBooNE-like LArTPC. Figure 3.1(b) shows a cross-sectional view of the
MicroBooNE detector along the $-\hat{z}$ direction. Figures from Ref. [16].

####  3.1.1 Cryogenics

The MicroBooNE detector is relatively large–the LArTPC volume spans 2.6 m, 2.3
m, and 10.4 m in the $\hat{x}$, $\hat{y}$, and $\hat{z}$ direction,
respectively [16]. Thus, ionization electrons must drift through
$\mathcal{O}(m)$ of LAr before reaching the anode wire planes. Reconstruction
of these ionization electrons requires careful control of the drift process.
This is the main objective of the MicroBooNE cryogenic system.

The LArTPC is housed within a larger cylindrical cryostat, which itself is
supported by an argon purification system and nitrogen refrigeration system
[16]. The purification system consists of two recirculation pumps and two
filter skids that remove electronegative impurities from the LAr, mainly
oxygen (O2) and water (H2O). These impurities must be kept below the 100
parts-per-trillion O2-equivalent level in order to maintain electron drift
lengths of at least 2.5 m [157, 16]. Additionally, the nitrogen contamination
must be kept below 2 parts-per-million in order to maintain an argon
scintillation light attenuation length greater than the size of the detector
[158]. Nitrogen cannot be appreciably removed from the argon via the
purification system; rather, the initial nitrogen contamination is fixed by
the quality of the delivered argon, and additional contamination must be
controlled by minimizing the atmosphere leakage rate into the cryostat.

The nitrogen refrigeration system is designed to combat the heat load on the
LAr from the environment and electrical power systems, maintaining thermal
homogeneity throughout the active volume. It consists of two condensers, each
designed to handle a heat load of approximately 9.5 kW [16]. The temperature
of the LAr volume must be stable to $\pm 0.1$ K in order to keep the $\hat{x}$
direction resolution of charged particle tracks below 0.1% [16].

####  3.1.2 LArTPC Drift System

The drift system inside the LArTPC volume consists of three major subsystems:
the cathode plane, the field cage, and the three anode wire planes. The
purpose of the drift system is to maintain a uniform electric field throughout
the active volume such that ionization electrons are transported to the anode
plane at a stable drift velocity.

The cathode consists of nine stainless steel sheets connected to a supporting
frame to form a single plane. Laser tracker measurements indicate that a
majority of the cathode plan is flat to within $\pm 3$ mm [16]. The cathode
plane is kept at a negative potential of approximately $-70$ kV via a high
voltage feedthrough on the cryostat. The field cage maintains a uniform
electric field between the cathode plane and anode planes. It consists of 64
stainless steel tubes wrapped around the LArTPC active volume. A resistor
divider chain connects each tube to its neighbor, sequentially stepping the
voltage from $-70$ kV to ground in $1.1$ kV increments. The chain provides a
resistance of 250 M$\Omega$ between adjacent tubes such that the current flow
is approximately 4.4 $\mu$A, much larger than the $\mathcal{O}({\rm nA})$
current from signals on anode plane wires [16]. Figure 3.2 shows the
MicroBooNE cathode and field cage, as well as a simulated map of the electric
field within the LArTPC active volume.

Perhaps the most critical components of the MicroBooNE detector are the three
anode wire planes. The U and V induction planes contain 2400 wires each, while
the Y collection plane contains 3456 wires. As mentioned above, the U and V
plane wires are oriented at $\pm 60^{\circ}$ with respect to the vertical,
while the Y plane is oriented vertically. The U, V, and Y planes are biased at
-200 V, 0 V, and +440 V, respectively, to ensure termination of ionization
electrons on the Y collection plane. Each wire is 150 $\mu$m in diameter and
is spaced 3 mm from its neighbors. The planes themselves are spaced 3 mm from
one another. The wires are held in place by wire carrier boards, which house
16 wires each in the U and V planes and 32 wires in the Y plane. Each wire is
terminated using a semi-automated wrapping procedure around a 3 mm diameter
brass ferrule. On the wire carrier boards, each wire makes contact with a gold
pin that connects to the electronic read-out system. The anode planes are held
in place by a single stainless steel frame, which houses each wire carrier
board via an array of precision alignment pins. Wires are tested to withstand
three times the nominal load of 0.7 kg without breakage, both before and after
placement onto the wire carrier board. Figure 3.3(a) shows an image of a
single Y plane wire carrier board with 32 mounted wires. An image of the
fully-assembled MicroBooNE LArTPC is shown in figure 3.3(b), specifically
highlighting the anode planes mounted on the stainless steel frame.

(a)

(b)

Figure 3.2: Figure 3.2(a) shows a close-up image of the cathode plane of the
MicroBooNE LArTPC. The stainless steel field cage tubes can also be seen
surrounding the active volume. Figure 3.2(b) shows a cross-sectional map of
the electric field at the edge of the active volume, considering a cathode
plane voltage of -128 kV. The legend shows the field strength in units of V/m.
Figures from Ref. [16].

(a)

(b)

Figure 3.3: Figure 3.3(a) shows a photograph of a single wire carrier board
with 32 mounted wires. Figure 3.3(b) shows the fully-assembled MicroBooNE
LarTPC, highlighting the anode plane mounted on the stainless steel frame.
Figures from Ref. [16].

####  3.1.3 Light Collection System

Liquid argon is a prolific scintillation medium due to its low cost, high
scintillation yield ($\mathcal{O}(10^{4})$ photons per MeV of deposited
energy), and transparency to its own scintillation light [158]. This last
feature comes from the scintillation mechanism in LAr: when argon atoms are
ionized, they combine with one another to form singlet and triplet excimer
states. When these excimer states decay, they emit 128 nm photons which pass
unattenuated through the surrounding atomic argon [159]. The decay of the
singlet (triplet) state happens on timescales of $\mathcal{O}$(ns)
($\mathcal{O}$($\mu$s)) [160, 161]. Thus, scintillation light emission happens
on much shorter timescales than the $\mathcal{O}$(ms) drift time of the
ionization electrons.

The light collection system in MicroBooNE is designed to detect the
scintillation photons produced in a neutrino interaction. It consists of 32
8-inch Hammamatsu R5912-02mod cryogenic PMTs situated behind an acrylic plate
coated with tetraphenyl butadiene (TPB) [16]. An image of one such PMT
assembly is shown in figure 3.5(a). TPB is a wavelength shifter that absorbs
the 128 nm argon scintillation light and re-emits a photon in the visible
range. The necessity of this procedure is shown in figure 3.4, which
demonstrates that, unlike direct LAr scintillation light, TPB emission is well
within the wavelength acceptance range of the PMTs.