The Mini and Micro BooNE Mystery, Part 2: Theory

Title: “Search for an Excess of Electron Neutrino Interactions in MicroBooNE Using Multiple Final State Topologies”

Authors: MicroBooNE Collaboration

References: https://arxiv.org/pdf/2110.14054.pdf

This is the second post in a series on the latest MicroBooNE results, covering the theory side. Click here to read about the experimental side. 

Few stories in physics are as convoluted as the one written by neutrinos. These ghost-like particles, a notoriously slippery experimental target and one of the least-understood components of the Standard Model, are making their latest splash in the scientific community through MicroBooNE, an experiment at FermiLab that unveiled its first round of data earlier this month. While MicroBooNE’s predecessors have provided hints of a possible anomaly within the neutrino sector, its own detectors have yet to uncover a similar signal. Physicists were hopeful that MicroBooNE would validate this discrepancy, yet the tale is turning out to be much more nuanced than previously thought.

Unexpected Foundations

Originally proposed by Wolfgang Pauli in 1930 as an explanation for missing momentum in certain particle collisions, the neutrino was added to the Standard Model as a massless particle that can come in one of three possible flavors: electron, muon, and tau. At first, it was thought that these flavors are completely distinct from one another. Yet when experiments aimed to detect a particular neutrino type, they consistently measured a discrepancy from their prediction. A peculiar idea known as neutrino oscillation presented a possible explanation: perhaps, instead of propagating as a singular flavor, a neutrino switches between flavors as it travels through space. 

This interpretation emerges fortuitously if the model is modified to give the neutrinos mass. In quantum mechanics, a particle’s mass eigenstate — the possible masses a particle can be found to have upon measurement — can be thought of as a traveling wave with a certain frequency. If the three possible mass eigenstates of the neutrino are different, meaning that at most one of the mass values could be zero, this creates a phase shift between the waves as they travel. It turns out that the flavor eigenstates — describing which of the electron, muon, or tau flavors the neutrino is measured to possess — are then superpositions of these mass eigenstates. As the neutrino propagates, the relative phase between the mass waves varies such that when the flavor is measured, the final superposition could be different from the initial one, explaining how the flavor can change. In this way, the mass eigenstates and the flavor eigenstates of neutrinos are said to “mix,” and we can mathematically characterize this model via mixing parameters that encode the mass content of each flavor eigenstate.

These massive oscillating neutrinos represent a radical departure from the picture originally painted by the Standard Model, requiring a revision in our theoretical understanding. The oscillation phenomenon also poses a unique experimental challenge, as it is especially difficult to unravel the relationships between neutrino flavors and masses. Thus far, physicists have only been able to determine the sum of neutrino masses, and have found that this value is constrained to be exceedingly small, posing yet another mystery. The neutrino experiments of the past three decades have set their sights on measuring the mixing parameters in order to determine the probabilities of the possible flavor switches.

A Series of Perplexing Experiments

In 1993, scientists in Los Alamos peered at the data gathered by the Liquid Scintillator Neutrino Detector (LSND) to find something rather strange. The group had set out to measure the number of electron neutrino events produced via decays in their detector, and found that this number exceeded what had been predicted by the three-neutrino oscillation model. In 2002, experimentalists turned on the complementary MiniBooNE detector at FermiLab (BooNE is an acronym for Booster Neutrino Experiment), which searched for oscillations of muon neutrinos into electron neutrinos, and again found excess electron neutrino events. For a more detailed account of the setup of these experiments, check out Oz Amram’s latest piece.

While two experiments are notable for detecting excess signal, they stand as outliers when we consider all neutrino experiments that have collected oscillation data. Collaborations that were taking data at the same time as LSND and MiniBooNE include: MINOS (Main Injector Neutrino Oscillation Search), KamLAND (Kamioka Liquid Scintillator Antineutrino Detector), and IceCube (surprisingly, not a fancy acronym, but deriving its name from the fact that it’s located under ice in Antarctica), to name just a few prominent ones. Their detectors targeted neutrinos from a beamline, nearby nuclear reactors, and astrophysical sources, respectively. Not one found a mismatch between predicted and measured events. 

The results of these other experiments, however, do not negate the findings of LSND and MiniBooNE. This extensive experimental range — probing several sources of neutrinos, and detecting with different hardware specifications — is necessary in order to consider the full range of possible neutrino mixing parameters and masses. Each model or experiment is endowed with a parameter space: a set of allowed values that its parameters can take. In this case, the neutrino mass and mixing parameters form a two-dimensional grid of possibilities. The job of a theorist is to find a solution that both resolves the discrepancy and has a parameter space that overlaps with allowed experimental parameters. Since LSND and MiniBooNE had shared regions of parameter space, the resolution of this mystery should be able to explain not only the origins of the excess, but why no similar excess was uncovered by other detectors.

A simple explanation to the anomaly emerged and quickly gained traction: perhaps the data hinted at a fourth type of neutrino. Following the logic of the three-neutrino oscillation model, this interpretation considers the possibility that the three known flavors have some probability of oscillating into an additional fourth flavor. For this theory to remain consistent with previous experiments, the fourth neutrino would have to provide the LSND and MiniBooNE excess signals, while at the same time sidestepping prior detection by coupling to only the force of gravity. Due to its evasive behavior, this potential fourth neutrino has come to be known as the sterile neutrino. 

The Rise of the Sterile Neutrino

The sterile neutrino is a well-motivated and especially attractive candidate for beyond the Standard Model physics. It differs from ordinary neutrinos, also called active neutrinos, by having the opposite “handedness”. To illustrate this property, imagine a spinning particle. If the particle is spinning with a leftward orientation, we say it is “left-handed”, and if it is spinning with a rightward orientation, we say it is “right-handed”. Mathematically, this quantity is called helicity, which is formally the projection of a particle’s spin along its direction of momentum. However, this helicity depends implicitly on the reference frame from which we make the observation. Because massive particles move slower than the speed of light, we can choose a frame of reference such that the particle appears to have momentum going in the opposite direction, and as a result, the opposite helicity. Conversely, because massless particles move at the speed of light, they will have the same helicity in every reference frame. 

This frame-dependence unnecessarily complicates calculations, but luckily we can instead employ a related quantity that encapsulates the same properties while bypassing the reference frame issue: chirality. Much like helicity, while massless particles can only display one chirality, massive particles can be either left- or right-chiral. Neutrinos interact via the weak force, which is famously parity-violating, meaning that it has been observed to preferentially interact only with particles of one particular chirality. Yet massive neutrinos could presumably also be right-handed — there’s no compelling reason to think they shouldn’t exist. Sterile neutrinos could fill this gap.

They would also lend themselves nicely to addressing questions of dark matter and baryon asymmetry. The former — the observed excess of gravitationally-interacting matter over light-emitting matter by a factor of 20 — could be neatly explained away by the detection of a particle that interacts only gravitationally, much like the sterile neutrino. The latter, in which our patch of the universe appears to contain considerably more matter than antimatter, could also be addressed by the sterile neutrino via a proposed model of neutrino mass acquisition known as the seesaw mechanism. 

In this scheme, active neutrinos are represented as Dirac fermions: spin-½ particles that have a unique anti-particle, the oppositely-charged particle with otherwise the same properties. In contrast, sterile neutrinos are considered to be Majorana fermions: spin-½ particles that are their own antiparticle. The masses of the active and sterile neutrinos are fundamentally linked such that as the value of one goes up, the value of the other goes down, much like a seesaw. If sterile neutrinos are sufficiently heavy, this mechanism could explain the origin of neutrino masses and possibly even why the masses of the active neutrinos are so small. 

These considerations position the sterile neutrino as an especially promising contender to address a host of Standard Model puzzles. Yet it is not the only possible solution to the LSND/MiniBooNE anomaly — a variety of alternative theoretical interpretations invoke dark matter, variations on the Higgs boson, and even more complicated iterations of the sterile neutrino. MicroBooNE was constructed to traverse this range of scenarios and their corresponding signatures. 

Open Questions

After taking data for three years, the collaboration has compiled two dedicated analyses: one that searches for single electron final states, and another that searches for single photon final states. Each of these products can result from electron neutrino interactions — yet both analyses did not detect an excess, pointing to no obvious signs of new physics via these channels. 

Although confounding, this does not spell death for the sterile neutrino. A significant disparity between MiniBooNE and MicroBooNE’s detectors is the ability to discern between single and multiple electron events — MiniBooNE lacked the resolution that MicroBooNE was upgraded to achieve. MiniBooNE also was unable to fully distinguish between electron and photon events in the same way as MicroBooNE. The possibility remains that there exist processes involving new physics that were captured by LSND and MiniBooNE — perhaps decays resulting in two electrons, for instance.  

The idea of a right-handed neutrino remains a promising avenue for beyond the Standard Model physics, and it could turn out to have a mass much larger than our current detection mechanisms can probe. The MicroBooNE collaboration has not yet done a targeted study of the sterile neutrino, which is necessary in order to fully assess how their data connects to its possible signatures. There still exist regions of parameter space where the sterile neutrino could theoretically live, but with every excluded region of parameter space, it becomes harder to construct a theory with a sterile neutrino that is consistent with experimental constraints. 

While the list of neutrino-based mysteries only seems to grow with MicroBooNE’s latest findings, there are plenty of results on the horizon that could add clarity to the picture. Researchers are anticipating the output of more data from MicroBooNE as well as more specific theoretical studies of the results and their relationship to the LSND/MiniBooNE anomaly, the sterile neutrino, and other beyond the Standard Model scenarios. MicroBooNE is also just one in a series of planned neutrino experiments, and will operate alongside the upcoming SBND (Short-Baseline Neutrino Detector) and ICARUS (Imaging Cosmic Rare and Underground Signals), further expanding the parameter space we are able to probe.

The neutrino sector has proven to be fertile ground for physics beyond the Standard Model, and it is likely that this story will continue to produce more twists and turns. While we have some promising theoretical explanations, nothing theorists have concocted thus far has fit seamlessly with our available data. More data from MicroBooNE and near-future detectors is necessary to expand our understanding of these puzzling pieces of particle physics. The neutrino story is pivotal to the tome of the Standard Model, and may be the key to writing the next chapter in our understanding of the fundamental ingredients of our world.

Further Reading

1. A review of neutrino oscillation and mass properties: https://pdg.lbl.gov/2020/reviews/rpp2020-rev-neutrino-mixing.pdf
2. An in-depth review of the LSND and MiniBooNE results: https://arxiv.org/pdf/1306.6494.pdf

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