Probing Quantum Foundations in Long-Baseline Neutrino Oscillations: Wave Packet Approach from MINOS Data to DUNE Predictions

Neutrinos are ghostly particles that zip through the universe, passing through planets and stars as if they were made of air. For decades, physicists have known that these particles come in three distinct flavors—electron, muon, and tau—and that they have a peculiar habit of changing their identity as they travel. A muon neutrino born in a particle accelerator can transform into an electron or tau neutrino by the time it reaches a detector hundreds of miles away. This phenomenon, known as oscillation, proved that neutrinos have mass, a discovery that reshaped our understanding of the fundamental laws of physics. The standard way scientists have described this transformation for years treats the neutrino as a perfect, infinite wave, a mathematical idealization that works well for many calculations but ignores the messy reality of how these particles are actually created and detected in a lab.

A new study by researchers in India and Italy challenges this simplified view by treating neutrinos not as endless waves, but as localized packets of energy with a specific, finite size. The team investigated whether this more realistic description changes the predictions for how neutrinos behave over long distances, specifically looking at data from the MINOS experiment and making new predictions for the upcoming Deep Underground Neutrino Experiment, or DUNE. They found that the size of these neutrino packets matters significantly when the particles have lower energy, correcting a mismatch between theory and observation that the old, infinite-wave model could not explain. Furthermore, the researchers discovered that even when the basic probability of a neutrino changing flavor looks the same under both models, the internal quantum structure of the particle reveals subtle differences that only the new, packet-based approach can detect.

The researchers began by revisiting the data from the MINOS experiment, which sent a beam of muon neutrinos 735 kilometers through the Earth to a detector in Minnesota. When they compared the standard infinite-wave predictions against the actual measurements, they noticed a problem: the old model failed to match the data in the lower-energy range, specifically for neutrinos with energies between 525 and 1,500 million electron volts. In this low-energy zone, the standard theory predicted a smooth pattern that simply did not fit the observed events. To fix this, the team applied their wave packet formalism, which accounts for the fact that neutrinos are produced in tiny, localized bursts with a finite spatial width. By adjusting the size of this packet to a value of approximately 0.24 times 10 to the negative 15 meters, they found that the theoretical curve snapped into place, matching the low-energy data points with much greater accuracy than the traditional model. This specific size is consistent with the scale of the atomic processes that create neutrinos, suggesting that the finite size of the packet is a real physical feature, not just a mathematical trick.

Having established that this model works for the existing data, the team turned their attention to the future. They applied the same wave packet logic to the Deep Underground Neutrino Experiment, which will send a beam 1,300 kilometers from Fermilab in Illinois to a massive detector in South Dakota. Because this distance is nearly twice as long as the MINOS baseline, the effects of the wave packet's size become even more complex, especially as the neutrinos travel through varying densities of the Earth's crust. The researchers simulated how the oscillation patterns would look for DUNE under different assumptions about the packet size. They found that while the overall shape of the oscillation remains similar to the standard predictions at high energies, the low-energy behavior changes dramatically depending on the packet's width. If the packet is very small, the oscillations wash out completely at lower energies, leaving a flat line where the standard model would still show a wavy pattern. This suggests that when DUNE begins collecting data, the way the oscillations behave at the lower end of the energy spectrum will be a critical test for determining the true size of the neutrino wave packet.

To understand exactly where this new model offers the most insight, the team used a statistical tool called classical Fisher information. This method acts like a sensitivity meter, showing which parts of the energy spectrum are most capable of revealing the size of the wave packet. Their analysis revealed that the ability to measure the packet size is concentrated entirely in the low-energy region, precisely where the wave packet and the infinite wave models diverge. For the MINOS experiment, the sensitivity peaks around 1.5 GeV, confirming that this is the energy range where the finite size of the packet is most important. For DUNE, the researchers showed that the location of this peak sensitivity shifts depending on the actual size of the packet. If the packet is smaller, the region of highest sensitivity moves to higher energies. This provides a clear roadmap for future experiments: by looking at the specific energy range where the data deviates from the standard model, scientists can pinpoint the exact size of the neutrino's wave packet.

Beyond simply correcting the oscillation probabilities, the study delved into the deeper quantum nature of the neutrino using a framework known as triality. This concept explores the balance between three properties of a quantum system: how predictable the outcome is, how strong the interference pattern is, and how entangled the particle is with the rest of the system. In the language of quantum mechanics, a neutrino traveling through space is not just a single particle but a complex web of connections between its different possible flavors. The researchers calculated these three quantities for both MINOS and DUNE under the wave packet model. They found that even in energy ranges where the probability of a neutrino changing flavor looks identical to the standard prediction, the internal balance of these three properties is different. For instance, at certain energies, the neutrino might appear to be behaving like a solid particle with a definite identity, while at others, it is deeply entangled with its potential future forms.

The study showed that as the wave packet size changes, the way these three properties share the "quantum budget" shifts. In scenarios where the wave packet is very small and decoherence is strong, the entanglement between the neutrino and its undetected flavor modes becomes the dominant feature, carrying most of the quantum information even when the visible interference patterns have faded away. This means that looking only at the simple probability of a neutrino changing flavor is not enough to fully understand its behavior. The researchers demonstrated that the wave packet model leaves a distinct fingerprint on these quantum relationships, offering a new way to probe the foundations of quantum mechanics. Even when the standard model and the wave packet model agree on the final numbers, they disagree on the underlying quantum story, and the wave packet approach reveals a richer, more nuanced reality.

The implications of this work extend beyond just fitting a curve to existing data. By treating the neutrino as a localized packet with a finite size, the researchers have provided a more faithful description of the physical processes occurring in long-baseline experiments. They showed that the wave packet approach is not just a theoretical refinement but a necessary correction for low-energy neutrinos, resolving discrepancies that the infinite wave model could not explain. The study also highlights that the quantum information carried by neutrinos is far more complex than previously thought, with entanglement playing a crucial role in how flavor information is distributed. As DUNE prepares to begin its operations, these findings suggest that the experiment will be able to test these ideas directly, potentially measuring the size of the neutrino wave packet and gaining a deeper understanding of the quantum mechanics that govern the universe's most elusive particles. The work confirms that the wave packet formalism offers a consistent and experimentally motivated framework for exploring the quantum foundations of neutrino physics, bridging the gap between abstract theory and the concrete reality of experimental data.