⚛️ phenomenology

Testing the Pseudo-Dirac Nature of Atmospheric Neutrinos

This paper investigates the sensitivity of a DUNE-like detector to the pseudo-Dirac nature of neutrinos by analyzing how new oscillation frequencies associated with the $\nu_3$ state and sub-leading solar oscillations modify the atmospheric neutrino energy and angular spectra across a broad range of baseline distances.

Original author: Olivia M. Bitter, André de Gouvêa, Srubabati Goswami, Supriya Pan

Published 2026-11-06

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CC BY 4.0

Original author: Olivia M. Bitter, André de Gouvêa, Srubabati Goswami, Supriya Pan

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the author. For technical accuracy, refer to the original paper. Read full disclaimer

Neutrinos are the most abundant massive particles in the universe, yet they remain among the most elusive. Trillions of them pass through your body every second, born in the nuclear fires of the sun or the violent collisions of cosmic rays with Earth's atmosphere, barely interacting with the matter they traverse. For decades, physicists have known that these particles are not static; they change identity, or "flavor," as they travel. This phenomenon, called oscillation, proved that neutrinos have mass, a discovery that shattered the original rules of particle physics. However, a fundamental question remains: are these particles their own antiparticles, or do they have distinct partners? The standard model suggests they are distinct, while other theories propose they are their own mirror images. A middle ground exists where they are nearly identical but split into two very slightly different states, a scenario known as pseudo-Dirac. If this is true, it would mean that for every known neutrino, there is a hidden, sterile twin that rarely interacts with anything, creating a new, incredibly slow rhythm of transformation that only reveals itself over vast distances.

A team of researchers set out to see if a future underground detector could catch a glimpse of this hidden rhythm using neutrinos raining down from the sky. They focused on a massive experiment currently under construction in South Dakota, known as the Deep Underground Neutrino Experiment, which will use a huge tank of liquid argon to catch these ghostly particles. The scientists simulated how this detector would perform over ten years of operation, looking specifically at atmospheric neutrinos. Unlike neutrinos from a man-made beam that travel a fixed distance, atmospheric neutrinos arrive from all directions, traveling anywhere from a few dozen kilometers to the full diameter of the Earth. This variety in travel distance is crucial because the hypothetical split between a neutrino and its sterile twin would only become visible after the particle has traveled a very long way, allowing a new, slow oscillation to build up.

The researchers ran detailed computer simulations to see how well the detector could spot these subtle changes. They found that the ability to measure the direction of low-energy neutrinos is the most critical factor. If the detector can pinpoint the arrival angle of these particles with high precision, it can distinguish the slow, new rhythm from the standard, faster oscillations. In their most optimistic scenario, where the detector has excellent angular resolution, the experiment could rule out the existence of this pseudo-Dirac split if the mass difference between the twins is larger than a specific tiny value. If the split were any larger, the detector would have seen the distortion in the neutrino patterns. However, if the resolution is poorer, the experiment's ability to find this split weakens, though it would still be able to exclude the largest possible differences.

The study also examined how uncertainties in other known properties of neutrinos might cloud the results. They discovered that the precision of the measurement depends heavily on how well the experiment understands the behavior of the third type of neutrino mass state. If the researchers allow these other properties to vary within their current known limits, the sensitivity to the new pseudo-Dirac effect decreases slightly, but the experiment remains a powerful tool. Interestingly, the same atmospheric neutrinos that could reveal this new physics are not sensitive enough to measure the specific properties of the "solar" oscillations that drive the sun's neutrino changes. The data from the sky simply does not provide enough leverage to pin down those specific solar parameters, even with the best possible detector performance.

Ultimately, the work suggests that a DUNE-like detector will be a competitive and complementary tool in the search for the nature of neutrinos. It offers a unique window into mass differences that are too small to be seen by other experiments but large enough to manifest over the Earth's diameter. While the experiment may not definitively prove the pseudo-Dirac nature of neutrinos on its own, it will be able to tightly constrain the possibilities, telling us exactly how small that hidden mass difference must be if it exists. By combining these atmospheric observations with data from reactors, accelerators, and the sun, physicists will eventually be able to map the full landscape of neutrino mass, determining whether these elusive particles are truly unique or if they carry a hidden, sterile partner.

Technical Summary: Testing the Pseudo-Dirac Nature of Atmospheric Neutrinos

Problem Statement
The fundamental nature of neutrinos—whether they are Dirac or Majorana fermions—remains an open question in particle physics. An intermediate scenario posits that neutrinos are pseudo-Dirac fermions, where a dominant Dirac mass term is accompanied by small Majorana mass terms. This structure splits each active neutrino into two nearly degenerate states (active and sterile) separated by an extremely small mass-squared difference, $\Delta m^2_{PD}$ .

While current oscillation data constrains the splittings associated with the first two mass eigenstates ( $\Delta m^2_{11'}$ and $\Delta m^2_{22'}$ ) to be less than $10^{-11} \text{ eV}^2$ , constraints on the splitting associated with the third mass eigenstate ( $\Delta m^2_{33'}$ ) are significantly weaker ( $\lesssim 10^{-5} \text{ eV}^2$ ). Because these pseudo-Dirac oscillations require very long baselines ( $L$ ) relative to neutrino energy ( $E$ ) to become observable, atmospheric neutrinos are ideal probes. They traverse baselines ranging from tens of kilometers to the Earth's diameter, covering a vast $L/E$ spectrum. This paper investigates the sensitivity of a Deep Underground Neutrino Experiment (DUNE)-like detector to the pseudo-Dirac nature of the $\nu_3$ state through atmospheric neutrino flux measurements.

Methodology
The authors employ a 3 + 1 oscillation formalism within a 4 $\times$ 4 Hamiltonian framework, assuming maximal mixing between the active and sterile partners of the third mass eigenstate. The new oscillation frequency is parameterized by a dimensionless quantity $\epsilon$ , defined via the relation:
$\Delta m^2_{33'} = 2\epsilon \Delta m^2_{31}$
where $\Delta m^2_{31}$ is the standard atmospheric mass-squared difference.

The study utilizes a simulation of atmospheric neutrinos in a DUNE-like liquid argon time projection chamber (LArTPC) with a 40 kton fiducial mass and an exposure of 200 kt $\cdot$ yr (equivalent to 10 years of operation). Key methodological components include:

Flux and Cross-Sections: Atmospheric neutrino fluxes are derived from Honda files (solar minimum, Homestake site), and cross-sections are calculated using GLoBES for a $^{40}$ Ar target.
Matter Effects: Neutrino propagation through the Earth is modeled using the Preliminary Reference Earth Model (PREM) with five distinct layers (crust to inner core) to account for matter-induced modifications to active-sterile oscillations.
Detector Response: The analysis incorporates energy and angular resolution functions. Energy resolution follows $\sigma_E \propto \sqrt{E_t}$ , while angular resolution ( $\sigma_\theta$ ) is varied to test sensitivity, specifically focusing on sub-GeV neutrinos where resolution is most critical. Four resolution scenarios are tested: $15^\circ, 30^\circ, 40^\circ,$ and $50^\circ$ .
Statistical Analysis: A $\chi^2$ analysis is performed comparing predicted event rates (test) against expected rates (true) across energy and zenith angle bins. Systematic uncertainties (flux, zenith angle, cross-section, tilt, and overall systematics) are included via pull variables. The analysis profiles over standard oscillation parameters ( $\theta_{23}, \Delta m^2_{31}$ ) to assess robustness.

Key Contributions and Results
The paper quantifies the sensitivity of atmospheric neutrino data to the parameter $\epsilon$ (and consequently $\Delta m^2_{33'}$ ) under the assumption of Normal Ordering (NO).

Sensitivity to $\epsilon$ :
- The sensitivity is heavily dependent on the angular resolution of sub-GeV events.
- Conservative Scenario ( $50^\circ$ resolution): A DUNE-like experiment can exclude $\epsilon \geq 4.0 \times 10^{-2}$ at the $3\sigma$ level, corresponding to $\Delta m^2_{33'} \geq 2.0 \times 10^{-4} \text{ eV}^2$ .
- Optimistic Scenario ( $15^\circ$ resolution): The $3\sigma$ sensitivity improves to $\epsilon \geq 1.2 \times 10^{-2}$ , corresponding to $\Delta m^2_{33'} \geq 6.0 \times 10^{-5} \text{ eV}^2$ .
- The authors note that while atmospheric neutrinos access longer baselines than beam experiments, the sensitivity is often limited by the detector's ability to precisely reconstruct $L/E$ at low energies where angular resolution degrades.
Impact of Parameter Profiling:
- Profiling over standard oscillation parameters weakens the sensitivity compared to the case where parameters are fixed.
- Profiling over $\theta_{23}$ yields the strongest degradation in sensitivity, followed by $\Delta m^2_{31}$ . This is due to correlations between $\epsilon$ and these parameters in the oscillation probabilities (e.g., terms involving $\sin 2\theta_{23}$ ).
Sensitivity to Solar Parameters:
- The study also examines the ability of atmospheric neutrinos to constrain solar oscillation parameters ( $\Delta m^2_{21}$ and $\sin^2 \theta_{12}$ ), which are relevant due to similar $L/E$ scales.
- The data shows modest sensitivity to $\Delta m^2_{21}$ (excluding values $> 4 \times 10^{-4} \text{ eV}^2$ at $3\sigma$ ) but virtually no sensitivity to $\sin^2 \theta_{12}$ . This limitation is attributed to the subdominant dependence of atmospheric muon neutrino disappearance on solar parameters.

Significance and Claims
The paper asserts that atmospheric neutrinos provide a complementary probe to accelerator, reactor, and astrophysical neutrino sources for testing the pseudo-Dirac nature of neutrinos. The authors claim that a DUNE-like detector, utilizing its large mass and broad energy coverage, can probe the least constrained pseudo-Dirac splitting ( $\Delta m^2_{33'}$ ) down to the order of $10^{-5} \text{ eV}^2$ .

The study emphasizes that the angular reconstruction of sub-GeV atmospheric neutrinos is the critical factor determining the experimental reach. While the sensitivity is competitive with recent beam studies (e.g., DUNE beam studies), the authors modestly note that the relative sensitivity is slightly worse due to the trade-off between accessing longer baselines and the precision of $L/E$ determination at low energies. The work concludes that combining atmospheric neutrino observations with other neutrino sources will provide comprehensive coverage across several orders of magnitude in pseudo-Dirac mass splittings.

Technical Summary: Testing the Pseudo-Dirac Nature of Atmospheric Neutrinos

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