Axion-neutrino interactions in seesaw models and astrophysical probes

This paper investigates axion-neutrino interactions within Type-I and inverse seesaw models, finding that while the effective coupling is constrained by astrophysical limits on axion-electron couplings, the resulting optical depths for axion-mediated neutrino scattering are too small to produce observable signatures with current sensitivities.

The Gist

Imagine the universe is a giant, bustling city. For a long time, we thought we knew the rules of this city: the Standard Model is like the city's official rulebook, describing how particles (the citizens) interact. But there are two mysterious groups of citizens that the rulebook doesn't quite explain well: Neutrinos (ghostly, invisible travelers who barely touch anything) and Axions (hypothetical, ultra-light particles proposed to solve a specific puzzle in physics).

This paper asks a simple question: What if these two ghostly groups are actually whispering secrets to each other?

Here is the story of the research, broken down into everyday concepts:

1. The Setup: The "Seesaw" Connection

Physicists have a theory called the "Seesaw Mechanism" to explain why neutrinos have mass (weight). Imagine a playground seesaw. On one side sits a heavy adult (a heavy, invisible particle), and on the other side sits a tiny child (the light neutrino we see). To balance the seesaw, the child must be very light.

The author of this paper, Polina Kivokurtseva, asked: If we add a third person to this playground—the Axion—how does it interact with the seesaw?

In many theories, the strength of a particle's interaction depends on how "heavy" it is. Since neutrinos are very light, they shouldn't talk to axions very loudly. But the paper investigates exactly how loud that whisper would be.

2. The Detective Work: Following the Clues

The problem is that we can't easily catch neutrinos or axions in a lab to test this. They are too shy.

However, we do know a lot about how axions interact with electrons (the particles that make up the atoms in your body). Astronomers have been watching stars (like red giants) and looking for signs that axions are stealing energy from them. These observations have set a strict "speed limit" on how much axions can talk to electrons.

The paper uses a clever trick: The Family Tree Analogy.

• Imagine the Axion is a parent.
• The Electron and the Neutrino are its children.
• In this specific family tree (the "Seesaw models"), the way the parent talks to the child (Neutrino) is mathematically tied to how it talks to the other child (Electron).

So, the author took the strict "speed limit" we already know for the Electron and applied it to the Neutrino. The result? The Neutrino is allowed to whisper to the Axion, but it must be an extremely quiet whisper.

3. The Test: Two Cosmic Scenarios

To see if this whisper is loud enough to be heard, the author imagined two cosmic scenarios where neutrinos travel through space.

Scenario A: The "Ghostly Crowd" (Cosmic Neutrino Background)

Imagine a neutrino traveling from a distant supernova (a star explosion) to Earth. It has to pass through a sea of ancient, leftover neutrinos from the Big Bang (the Cosmic Neutrino Background).

• The Idea: If the neutrino bumps into these ghosts and exchanges an axion, it might get delayed, arriving later than expected.
• The Result: The author calculated the odds. It's like trying to hear a pin drop in a hurricane. The "optical depth" (a measure of how likely a collision is) is $10^{-53}$. To put that in perspective, if you had a trillion universes, you still wouldn't see this happen. The neutrinos sail right through without noticing.

Scenario B: The "Axion Fog" (Dark Matter)

Now, imagine the universe is filled with a thick fog made of axion dark matter.

• The Idea: If neutrinos fly through this fog, they might scatter off the axions. Since dark matter is everywhere, maybe the fog is thick enough to slow the neutrinos down?
• The Result: Even with the "fog" being very dense, the interaction is still too weak. The chance of a collision is about $10^{-15}$. This is still so small that it's effectively zero. It's like trying to catch a specific grain of sand in a desert using a net made of spider silk.

4. The Conclusion: The Whisper is Too Quiet

The paper concludes that within the standard, "minimal" versions of these theories, we will not see any effect.

The axion-neutrino interaction is tied so tightly to the axion-electron interaction that the limits from stars (which are very strict) force the neutrino interaction to be incredibly weak.

The Takeaway:
If you are hoping to detect axions by watching neutrinos arrive late or change direction, this paper says: Don't hold your breath. The signal is too faint for our current telescopes and detectors.

However, the paper leaves the door open for the future. It suggests that if the "rules of the family" are different (a more complex theory where the axion talks to neutrinos without talking to electrons), or if we find a place in the universe with an incredibly dense concentration of dark matter, we might finally hear that whisper. But for now, the neutrinos and axions are keeping their secrets.

Technical Summary

Here is a detailed technical summary of the paper "Axion–neutrino interactions in seesaw models and astrophysical probes" by Polina Kivokurtseva.

1. Problem Statement

The paper addresses the phenomenology of axion-neutrino interactions ($g_{a\nu}$) within minimal extensions of the Standard Model (SM) that generate neutrino masses. While axion-photon and axion-electron couplings are well-constrained by laboratory and astrophysical data, the axion-neutrino sector remains less explored.

The central problem is determining the magnitude of the effective axion-neutrino coupling ($g_{a\nu}$) in theoretically motivated frameworks (specifically Type-I and Inverse Seesaw models). Unlike models where $g_{a\nu}$ is treated as a free parameter, this work investigates whether $g_{a\nu}$ is intrinsically linked to the axion decay scale ($f_a$) and the axion-electron coupling ($g_{ae}$) via the underlying symmetry structure. The authors aim to determine if current astrophysical limits on $g_{ae}$ impose strict constraints on $g_{a\nu}$, thereby rendering neutrino propagation effects unobservable in standard astrophysical environments.

2. Methodology

Theoretical Framework

The authors analyze two minimal neutrino-mass generation mechanisms:

1. Type-I Seesaw: Introduces right-handed neutrinos ($N_R$). The axion couples to $N_R$, and through active-sterile mixing ($\Theta \approx m_D/M_R$), an effective coupling to light neutrinos is generated.
2. Inverse Seesaw (ISS): Introduces right-handed neutrinos ($N_R$) and additional singlet fermions ($S_R$). Here, the smallness of the neutrino mass is controlled by a lepton-number-violating parameter $\mu$ rather than the mixing angle, potentially allowing for larger couplings.

In both frameworks, the Lagrangian includes derivative couplings of the axion field ($a$) to fermions:
$$\mathcal{L} \supset \frac{C_f}{f_a} (\partial_\mu a) \bar{f} \gamma^\mu \gamma_5 f$$
where $C_f$ represents the Peccei-Quinn (PQ) charge.

Derivation of Constraints

The core methodological step is relating the neutrino coupling to the electron coupling. By integrating out heavy states, the authors derive a relationship between the effective axion-neutrino coupling ($g_{a\nu}$) and the axion-electron coupling ($g_{ae}$):
$$g_{a\nu} \approx g_{ae} \frac{C_\nu}{C_e} \frac{m_\nu}{m_e}$$

• $C_\nu/C_e$: Ratio of PQ charges (assumed $\mathcal{O}(1)$).
• $m_\nu/m_e$: Ratio of neutrino to electron mass.

The authors utilize existing, stringent astrophysical and laboratory bounds on $g_{ae}$ (derived from Red Giant branch star cooling, solar axion searches, and direct detection experiments like XENON100) to infer upper limits on $g_{a\nu}$.

Astrophysical Benchmarks

To test the observability of these interactions, the authors calculate the optical depth ($\tau = n \sigma D$) for neutrino propagation in two scenarios:

1. Resonant Scattering with the Cosmic Neutrino Background (C$\nu$B):
   • Process: $\nu + \nu_{C\nu B} \to a \to \nu + \nu$.
   • Source: SN 1987A (neutrinos traveling $\sim 50$ kpc).
   • Assumption: Resonant condition $s \approx m_a^2$.
2. Scattering on Axion Dark Matter:
   • Process: $\nu + a_{DM} \to \nu + a$.
   • Target: Local Galactic Dark Matter density ($\rho_{DM} \approx 0.4 \text{ GeV/cm}^3$).
   • Focus: Ultralight axions where the number density is high.

3. Key Contributions

• Model-Dependent Coupling Derivation: The paper moves beyond phenomenological parameter scans by deriving $g_{a\nu}$ strictly from Type-I and Inverse Seesaw models. It demonstrates that in these minimal frameworks, $g_{a\nu}$ is suppressed by the ratio of neutrino mass to electron mass ($m_\nu/m_e \sim 10^{-6}$).
• Translation of Bounds: It provides a robust translation of existing $g_{ae}$ limits into $g_{a\nu}$ constraints, showing that the neutrino coupling is orders of magnitude smaller than the electron coupling.
• Quantitative Optical Depth Estimates: The authors provide specific order-of-magnitude calculations for the optical depth ($\tau$) in realistic astrophysical scenarios, moving from theoretical coupling limits to observable propagation effects.

4. Results

• Constraint on Coupling: Using the relation $g_{a\nu} \propto (m_\nu/m_e) g_{ae}$, the inferred upper bound on $g_{a\nu}$ is extremely small due to the tiny neutrino mass.
• Scenario 1 (C$\nu$B Resonance):
  • Even assuming the maximum allowed $g_{a\nu}$ and resonant enhancement, the optical depth for SN 1987A neutrinos is calculated to be:
    $$\tau \approx 10^{-53}$$
  • Conclusion: The probability of scattering is negligible; neutrinos propagate freely.
• Scenario 2 (Axion Dark Matter):
  • For ultralight axion dark matter, the number density is high. However, the optical depth remains:
    $$\tau \approx 10^{-15}$$
  • Conclusion: While significantly larger than the C$\nu$B case, this is still far below unity. Furthermore, for ultralight axions, the interaction is better described as a coherent classical field effect rather than particle scattering, but the magnitude remains unobservable.
• Other Channels: The authors briefly checked other channels (e.g., scattering into three neutrinos via Fermi interaction) and found them similarly unobservable.

5. Significance and Conclusion

• Negative Result for Minimal Models: The primary conclusion is that within minimal Type-I and Inverse Seesaw models, axion-neutrino interactions are too weak to produce observable signatures in current or near-future astrophysical probes (like time delays or spectral distortions).
• Theoretical Implication: The coupling $g_{a\nu}$ is not a free parameter but is "tied" to the axion scale and charged lepton constraints. The suppression by the neutrino mass makes these interactions negligible in standard environments.
• Future Directions:
  • Observable effects would require non-minimal model-building that decouples $g_{a\nu}$ from $g_{ae}$ (e.g., via higher-order theories allowing lower $f_a$ values without violating photon constraints).
  • Alternatively, detection would require environments with drastically enhanced target densities (e.g., dense dark matter clumps) far exceeding standard cosmological assumptions.

In summary, the paper establishes that while axion-neutrino interactions are theoretically allowed, they are effectively invisible in the context of standard seesaw mechanisms and current astrophysical sensitivities.