Exploring New Propagation Scales With Galactic Neutrinos

This paper assesses the sensitivity of upcoming IceCube and KM3NeT measurements of Galactic neutrinos to new physics, demonstrating that a global network of neutrino telescopes can probe quasi-Dirac neutrino mass-squared differences in the range of $10^{-13.6}$ to $10^{-12.3}~\mathrm{eV^2}$ and neutrino decay mass-over-lifetime ratios exceeding $10^{-12.8}~\mathrm{eV^2}$.

The Gist

Imagine the universe as a giant, cosmic highway. For decades, we've been watching cars (neutrinos) travel short distances on this highway, like driving from one city to another. These short trips have taught us that neutrinos have mass and can change their "color" (flavor) as they drive. But we've never been able to watch them drive across the entire galaxy, a journey so long and vast that it might reveal secrets about how they are built that we've never seen before.

This paper is like a proposal to build a new, ultra-sensitive traffic monitoring system to watch these particles travel across the Milky Way. Here is the breakdown of what the authors are doing, using simple analogies.

The Big Idea: A Galactic Road Trip

The authors are looking at high-energy neutrinos coming from deep inside our own galaxy. Because these particles travel such massive distances (thousands of light-years) before hitting our detectors on Earth, they are perfect for testing two specific "what-if" scenarios about how neutrinos behave.

Think of the distance these particles travel divided by their energy as the "Trip Length." The paper suggests that if we look at Trip Lengths we've never seen before, we might spot new physics.

The Two "What-If" Scenarios

The paper tests two main ideas about what might be happening to these neutrinos during their long journey:

1. The "Split Personality" Scenario (Quasi-Dirac Neutrinos)

• The Analogy: Imagine a neutrino isn't just one single car, but a car with a hidden, identical twin passenger. Usually, they drive together perfectly in sync. But on a very long road trip, the twin might start to "phase" in and out of sync with the driver.
• The Effect: If this happens, the neutrino might suddenly disappear or change its flavor in a rhythmic pattern, like a strobe light flickering on and off.
• The Paper's Claim: The authors calculate that if we combine data from two giant telescopes (IceCube in Antarctica and KM3NeT in the Mediterranean), we can detect this "flickering" if the twins are separated by a very tiny, specific amount of mass. They predict we can find this if the mass difference is between $10^{-13.6}$ and $10^{-12.3}$ electron-volts squared.

2. The "Leaking Bucket" Scenario (Neutrino Decay)

• The Analogy: Imagine the neutrino is a bucket of water traveling down a very long, bumpy road. In the standard model, the bucket is solid and holds all its water. In this new scenario, the bucket has a tiny hole. The longer the trip, the more water leaks out.
• The Effect: If the bucket leaks, fewer neutrinos will arrive at the destination, especially the slower ones (which take longer to travel).
• The Paper's Claim: The authors look for a "leak" where the neutrino turns into something we can't see (invisible decay) or something lighter (visible decay). They find that by combining the two telescopes, they can detect a leak rate (mass divided by lifetime) greater than $10^{-12.8}$ electron-volts squared.

The Tools: Two Eyes on the Sky

To see these subtle effects, the authors propose using two different "eyes":

• IceCube (The South Pole Eye): This detector is buried in the ice. It is great at seeing "cascades" (explosions of light), which tell us the energy of the neutrino very well, but it's a bit blurry on where the neutrino came from.
• KM3NeT (The Mediterranean Eye): This detector is underwater. It is excellent at seeing "tracks" (long lines of light), which tell us the direction very precisely, but it's a bit fuzzier on the exact energy.

Why combine them?
The authors use a metaphor of a blurry photo vs. a sharp photo. If you only have the blurry photo (IceCube), you might miss the pattern. If you only have the sharp photo (KM3NeT), you might miss the energy details. But if you overlay them, you get a clear picture. The paper claims that only by combining both telescopes can they distinguish between a "leaking bucket" and a "split personality," because the two telescopes see these effects differently.

The Results: What They Found

The authors ran simulations to see what the data would look like in the year 2040 (assuming both telescopes have been running for a long time).

• The "Split Personality" (Quasi-Dirac): They found that the combined telescopes could spot this effect if the mass difference is in a specific, previously unexplored range. It's like finding a new gear in a car engine that no one knew existed.
• The "Leaking Bucket" (Decay): They found that the combined telescopes could detect if neutrinos are decaying into invisible particles, provided the decay rate is above a certain threshold. Interestingly, they found that for some types of decay, looking at just one telescope isn't enough; you need the combination to see the difference.

The Limitations (The "Noise" in the Room)

The paper is very honest about the challenges.

• The "Fog": The galaxy is full of other particles (background noise) that look like neutrinos. It's like trying to hear a whisper in a crowded, noisy stadium.
• The "Blur": Because neutrinos come from all over the galaxy, some travel short distances and some travel long distances. This mixes up the "flickering" or "leaking" patterns, making them harder to see.
• The "Unknown Map": We don't know exactly how many neutrinos are being produced in the galaxy. It's like trying to count cars on a highway when you don't know how many cars started the trip. The authors have to assume a lot about this, which limits how precise their predictions are.

Summary

In short, this paper says: "We have two giant telescopes that can look at neutrinos traveling across our galaxy. If we combine their data, we might be able to spot two new, weird behaviors of neutrinos—either that they have hidden twins or that they are slowly falling apart. We can't do this with just one telescope, and we can't do this with just short trips; we need this specific long-distance galactic view to see these new physics."

Technical Summary

Title: Exploring New Propagation Scales With Galactic Neutrinos

Problem Statement
The discovery of neutrino oscillations established that neutrinos have non-zero mass, necessitating extensions to the Standard Model (SM). However, the scale of the mass generation mechanism remains unknown. While terrestrial experiments have probed specific mass-squared differences ($\Delta m^2$), other scales associated with neutrino mass mysteries remain unexplored. This paper addresses the potential to probe new physics affecting neutrino propagation on ultra-long baselines ($L/E \sim 10^{13} \text{ eV}^{-2}$) using high-energy Galactic neutrinos. Specifically, the authors investigate two Beyond the Standard Model (BSM) scenarios: quasi-Dirac (QD) neutrinos, which introduce new oscillation scales via hyperfine mass splitting ($\delta m^2$), and neutrino decay, characterized by mass-over-lifetime ratios ($\alpha = m/\tau$). These phenomena manifest on length and energy scales far exceeding those accessible to terrestrial sources.

Methodology
The study forecasts the sensitivity of upcoming measurements from the IceCube Neutrino Observatory and the KM3NeT/ARCA detector to these BSM scenarios. The methodology involves:

1. Source Modeling: The authors utilize the TANDEM model suite to describe the three-dimensional distribution of Galactic neutrino production. This model integrates cosmic ray (CR) fluxes (from the Global Spline Fit) against differential neutrino production cross-sections (from AAfrag) and gas maps. The analysis focuses on the diffuse Galactic neutrino flux, assuming a production flavor ratio of $(\nu_e : \nu_\mu : \nu_\tau) = (1:2:0)$ from pion decays.
2. Propagation Physics:
   • Quasi-Dirac Scenario: The survival probability is calculated using the PMNS matrix and hyperfine mass splittings $\delta m^2_i$. The known mass differences are averaged out for Galactic baselines.
   • Neutrino Decay: The authors consider invisible decays (to undetectable daughters) and visible decays (specifically $\nu_3 \to \nu_1$). The decay probability depends on the mass-to-lifetime ratio $\alpha_i$.
   • The flux at Earth is computed by integrating the emission predictions along lines of sight, weighted by the BSM survival probabilities.
3. Detector Simulation:
   • IceCube: Modeled using effective areas and resolutions for cascade events (dominated by $\nu_e$ and $\nu_\tau$) over a 28-year period (projected to 2040).
   • KM3NeT/ARCA: Modeled using effective areas and resolutions for track events (dominated by $\nu_\mu$) over a 10-year period.
   • Complementarity: The analysis exploits the complementary nature of the detectors: IceCube (South Pole) suffers from atmospheric muon backgrounds for track searches but has high statistics for cascades; KM3NeT (Mediterranean) allows for track searches with low atmospheric backgrounds due to Earth shielding but has superior angular resolution.
4. Statistical Analysis: A binned likelihood ratio test is performed assuming Poisson statistics. The analysis profiles over nuisance parameters for the Galactic neutrino flux normalization ($\xi$) and the diffuse astrophysical flux normalization ($\eta$) to account for significant uncertainties in the absolute flux magnitude.

Key Contributions

• First Application to Galactic Neutrinos: This work is the first to systematically evaluate the potential of Galactic neutrinos to probe new physics on ultra-long baselines, specifically targeting the $L/E$ regime of $10^9 - 10^{15} \text{ km/GeV}$.
• Joint Analysis Framework: The paper demonstrates the necessity of a joint analysis between IceCube and KM3NeT. While individual experiments have limited sensitivity due to flux normalization uncertainties and background smearing, the flavor-dependent signatures of BSM physics (affecting tracks and cascades differently) allow a combined analysis to break degeneracies.
• Directional Dependence: The study highlights that the BSM signal is directionally dependent due to the varying propagation distances from different regions of the Galaxy (e.g., Galactic center vs. anti-center), which introduces spectral distortions that are smeared by detector resolution but remain distinct in shape.

Results
The authors present projected sensitivities for a 2040 analysis (28 years of IceCube cascades and 10 years of KM3NeT tracks):

• Quasi-Dirac Neutrinos: The combined analysis is sensitive to mass-squared differences in the range $\delta m^2 \in [2.5 \times 10^{-14}, 5 \times 10^{-13}] \text{ eV}^2$ at the 90% confidence level (CL). This probes a parameter space largely unexplored by solar neutrino measurements (which constrain $\delta m^2_1$ down to $\sim 10^{-12} \text{ eV}^2$) and previous astrophysical limits.
• Neutrino Decay:
  • For the visible decay scenario ($\nu_3 \to \nu_1$), the combined analysis is sensitive to $\alpha_3 > 1.6 \times 10^{-13} \text{ eV}^2$ at 90% CL. This region overlaps with constraints derived from solar antineutrino spectra but extends the probe to the Galactic scale.
  • For the invisible decay scenario ($\nu_3 \to \text{invisible}$), the analysis does not reach 90% CL sensitivity in any part of the parameter space, primarily due to the difficulty in distinguishing normalization shifts from flux uncertainties without a visible spectral feature.
• Limitations: The sensitivity is limited by the intrinsic smearing of $L/E$ signatures caused by the spread in propagation baselines within the Galaxy, systematic uncertainties in the Galactic flux normalization, and large atmospheric backgrounds that obscure spectral features.

Significance and Claims
The paper claims that measurements of Galactic neutrinos by a global network of neutrino telescopes can probe signatures of neutrino mass models in parameter space previously inaccessible to laboratory experiments. The authors emphasize that the unique $L/E$ scale of Galactic neutrinos offers a distinct window into new physics, specifically testing quasi-Dirac mass splittings and decay lifetimes that are orders of magnitude smaller than those probed by solar or atmospheric neutrinos.

The study concludes that while current backgrounds and flux uncertainties limit the reach, future improvements—such as constraining the Galactic flux normalization via gamma-ray correlations, discovering point sources with well-defined baselines, or utilizing improved angular resolution in water-based detectors—could significantly extend these sensitivities. The work establishes a framework for using the Milky Way as a laboratory for ultra-long baseline neutrino physics.