Neutrino Masses and Phenomenology in Nnaturalness

This paper demonstrates that $N$naturalness scenarios naturally suppress neutrino masses through a mechanism involving numerous mixing partners, leading to a specific tower of additional neutrino mass eigenstates that offers unique, testable signatures in terrestrial oscillation, mass, and neutrinoless double beta decay experiments, thereby extending the model's phenomenological reach beyond cosmology.

The Gist

The Big Mystery: Why are Neutrinos so light?

Imagine the universe is a giant construction site. Most particles are like heavy steel beams; they have significant weight (mass). But then there are neutrinos. They are like ghostly wisps of smoke. They zip through everything, barely interacting, and they are incredibly light—so light that for decades, scientists thought they might be weightless.

Scientists have two big problems to solve:

1. The Hierarchy Problem: Why is the "Higgs boson" (the particle that gives things mass) so light compared to the massive energy scales expected in the universe?
2. The Neutrino Problem: Why are neutrinos so incredibly light?

Usually, the answer to the neutrino problem is the "Seesaw Mechanism." Imagine a playground seesaw. On one end, you have a tiny child (the light neutrino). On the other end, you have a giant, invisible elephant (a super-heavy particle) sitting far away. The weight of the elephant pushes the child up, making them seem light. This relies on heavy, "UV" physics (high energy).

The New Idea: "Nnaturalness"

This paper introduces a different way to think about things, called Nnaturalness. Instead of using a heavy elephant to push the neutrino up, imagine a massive crowd of tiny people.

In the Nnaturalness theory, our universe isn't the only one. There are thousands (or even quadrillions) of "parallel sectors" or "dark universes" existing alongside ours. Each of these universes has its own version of the Higgs field.

• In most of these universes, the Higgs is heavy.
• In a few, it's light.
• By sheer statistical luck, we happen to live in the one where the Higgs is light. This solves the Hierarchy Problem without needing heavy elephants.

The "Ghostly Choir" Analogy

Now, how does this explain the light neutrino?

Imagine our neutrino is a solo singer. In the old "Seesaw" model, it sings a duet with one giant, heavy bass singer. The heavy bass pulls the pitch down.

In the Nnaturalness model, our solo singer doesn't sing with one giant. Instead, they are surrounded by a massive choir of thousands of backup singers from those parallel universes.

• Our neutrino tries to sing, but it gets "distracted" by all these other singers.
• Because there are so many of them (let's call the number N), the energy of our neutrino gets spread out, or "diluted," across the whole choir.
• The more singers in the choir, the quieter (lighter) our specific neutrino sounds.

The paper shows that this "dilution" effect is a natural consequence of having many parallel universes. You don't need to tune the knobs perfectly; the math just works out that if you have enough parallel universes, the neutrino must be light.

The "Tower" of Neutrinos

Here is the most exciting part of the paper.

In the old "extra dimension" theories (like the ADD model), these extra particles form a neat, predictable ladder (a "KK tower").
In Nnaturalness, the paper finds that these extra neutrinos also form a ladder, but a slightly different one.

• The Analogy: Imagine a staircase.
  • Step 1: Our normal neutrino.
  • Step 2, 3, 4...: A whole tower of "dark" neutrinos that are slightly heavier.
  • The Top Step: A very heavy neutrino at the top.

The paper calculates exactly how heavy each step is and how strongly our neutrino mixes with them. It turns out that if you break the perfect symmetry of the parallel universes (which is realistic), you get a specific pattern of masses.

How Can We Test This? (Bringing it Down to Earth)

For a long time, scientists thought you could only test Nnaturalness by looking at the Big Bang or the cosmos (looking "up" at the sky). This paper argues: No! We can test this right here on Earth.

Here is how:

1. Neutrino Oscillations (The Dance):
   Neutrinos change flavors (dance) as they travel. If Nnaturalness is true, our neutrino is dancing with that massive choir of dark neutrinos.

   • The Signal: The paper predicts that the "dance steps" (oscillation patterns) will look slightly different than standard physics. Specifically, the frequency of the dance will change in a way that depends on the number of parallel universes (N).
   • The Experiment: Future experiments like JUNO or DUNE (massive underground detectors) are sensitive enough to see these tiny changes in the dance.

2. Distinguishing Dirac vs. Majorana:
   Physicists don't know if neutrinos are their own antiparticles (Majorana) or distinct particles (Dirac).

   • The Magic Trick: In most theories, it's hard to tell the difference. But in Nnaturalness, the "ladder" of masses grows differently depending on whether the neutrino is Dirac or Majorana.
   • The Result: By looking at the oscillation patterns, we might finally be able to tell which type of neutrino we have.

3. Neutrino Mass Meters (KATRIN):
   There are experiments trying to weigh the neutrino directly. Because Nnaturalness predicts a whole tower of slightly heavier neutrinos, these experiments might see a "fuzzy" mass spectrum instead of a single sharp weight.

The Conclusion

The paper concludes that Nnaturalness is not just a theory about the early universe; it has a "fingerprint" that we can look for in our laboratories.

• Old View: Neutrinos are light because of heavy, invisible particles far away in energy.
• New View (Nnaturalness): Neutrinos are light because they are sharing the stage with a massive crowd of invisible partners in parallel universes.

The authors are essentially saying: "We used to think we needed to build a giant telescope to find these parallel universes. But actually, if we just look really closely at how neutrinos wiggle and dance in our underground labs, we might find them right here on Earth."

This opens the door to testing a theory that was previously thought to be purely cosmological, bringing the search for "parallel universes" down from the sky to the ground.

Technical Summary

1. Problem Statement

The paper addresses two fundamental open questions in particle physics:

1. The Hierarchy Problem: Why is the Higgs mass ($\mu^2$) so much smaller than the Planck scale or the UV cutoff, despite quantum corrections?
2. The Neutrino Mass Problem: What is the origin of the tiny, non-zero neutrino masses?

While the Seesaw Mechanism (a "UV solution") explains small neutrino masses by introducing heavy right-handed neutrinos at high energy scales, the author argues for Infrared (IR) solutions. These models suppress neutrino masses not via heavy particles, but through a large number of light degrees of freedom (mixing partners). Previous IR models include the ADD (Arkani-Hamed-Dimopoulos-Dvali) model with large extra dimensions and the Dvali-Redi (DR) model with many copies of the Standard Model (SM).

The specific gap this paper fills is the application of the Nnaturalness framework (originally proposed by Arkani-Hamed et al. to solve the hierarchy problem via cosmological selection) to neutrino mass generation and its resulting phenomenology. Unlike ADD or DR, Nnaturalness does not rely on lowering the fundamental gravity scale to the TeV range but rather on a landscape of hidden Higgs sectors.

2. Methodology

The author employs a theoretical field-theoretic approach to extend the Nnaturalness scenario to the neutrino sector:

• Model Construction:

  • The model posits $N$ dark sectors, each containing a Higgs field with a mass parameter $\mu_i^2$ uniformly distributed in $[-\Lambda_H^2, \Lambda_H^2]$.
  • The Standard Model is identified as the sector with the lightest Vacuum Expectation Value (VEV), $v_0 \sim \Lambda_H / \sqrt{N}$.
  • Neutrino Coupling: The author assumes the existence of right-handed neutrinos ($\nu_R$) in every sector. Since $\nu_R$ is a singlet under the SM gauge group, it can mix across all $N$ sectors.
  • Operators: Two mechanisms are analyzed for generating neutrino masses:
    1. Dirac Mass: Via a Yukawa coupling matrix $\lambda_{ij}$ connecting SM left-handed neutrinos to the $N$ right-handed neutrinos.
    2. Majorana Mass: Via a Weinberg operator (potentially mediated by a reheaton field $S$) involving two Higgs fields and two lepton doublets.

• Matrix Diagonalization:

  • The author constructs the $N \times N$ neutrino mass matrix.
  • A "totally democratic" coupling ($a=b$) is shown to be ruled out by oscillation data (as it yields massless neutrinos).
  • The paper analyzes the case where couplings deviate slightly from democracy ($a \neq b$), treating the deviation as a perturbation.
  • The mass matrix is diagonalized to find the eigenvalues (mass spectrum) and eigenvectors (mixing composition).

• Phenomenological Analysis:

  • The survival probability of neutrinos is calculated, accounting for the interference between the lightest mass eigenstate and a "tower" of heavier states.
  • The scaling of mass squared differences ($\Delta m^2_{ij}$) is derived for both Dirac and Majorana cases.
  • The results are compared against existing experimental data (MINOS, Daya Bay) and projected for future experiments (JUNO, DUNE, KATRIN, $0\nu\beta\beta$).

3. Key Contributions

1. Extension of Nnaturalness to Neutrinos: The paper demonstrates that Nnaturalness naturally generates small neutrino masses through the mixing with $N$ dark sector partners, similar to ADD and DR models, but with a distinct origin (Higgs VEV landscape vs. extra dimensions).
2. Ruling Out Total Democracy: It proves that a perfectly democratic coupling matrix ($a=b$) results in $N-1$ massless states and one heavy state, which contradicts neutrino oscillation data. Therefore, a specific breaking of the democratic symmetry ($a \neq b$) is required.
3. Distinctive Mass Scaling: The paper derives a unique scaling law for the neutrino mass tower that depends on the sector index $i$:
   • Dirac Case: $m_i \propto \sqrt{2i + r}$.
   • Majorana Case: $m_i \propto (2i + r)$.
   • Crucially, the mass squared differences $\Delta m^2_{ij}$ are fully predicted by the theory (dependent on $\Lambda_H, N, \lambda$) rather than being free parameters.
4. Discrimination between Dirac and Majorana: Unlike standard models where oscillation experiments cannot easily distinguish Dirac vs. Majorana nature, the different scaling of the mass tower in Nnaturalness leads to different oscillation frequencies for the two cases, making them distinguishable in terrestrial experiments.

4. Results

• Mass Suppression:
  • For $N \sim 10^4$, the suppression is insufficient to explain neutrino masses without fine-tuning Yukawa couplings.
  • For $N \sim 10^{16}$, the suppression is natural. In the Majorana case with $N=10^{16}$, the predicted mass for the lightest neutrino is $m_0 \approx 6.05 \times 10^{-5}$ eV, which aligns well with experimental observations without extreme fine-tuning.
• Oscillation Phenomenology:
  • The survival probability $P_{surv}$ exhibits a specific pattern where the lightest and heaviest modes dominate the oscillation amplitude with a strength of $\sim 1/N^2$.
  • The "tower" of states creates a distinct spectral distortion.
  • Figure Analysis: Simulations for MINOS and Daya Bay show that for $N=10$ and $N=5$, the oscillation amplitude is suppressed compared to the SM, but the frequency shift is detectable.
• Experimental Signatures:
  • Neutrino Oscillations (MINOS, Daya Bay, JUNO, DUNE): The unique $\Delta m^2$ scaling allows these experiments to test the model. Future high-precision experiments could distinguish between the Dirac and Majorana scenarios based on the oscillation frequency.
  • Neutrino Mass Measurements (KATRIN): The presence of the heavy tower could be resolved in the beta-decay spectrum (Kurie plot), providing constraints on $N$ and $r$.
  • Neutrinoless Double Beta Decay ($0\nu\beta\beta$): The model predicts contributions from heavy Majorana states, potentially altering the effective Majorana mass $m_{\beta\beta}$.
  • Matter Effects: The existence of many light states enhances the probability of resonant matter effects (MSW effect) in experiments like IceCube.

5. Significance

• Terrestrial Testing of Cosmology: Historically, Nnaturalness has been tested primarily through cosmological constraints (e.g., reheating temperature, dark radiation). This paper opens the door for terrestrial, low-energy particle physics experiments to test the model.
• General IR Mechanism: It reinforces the idea that "Infrared Solutions" to the neutrino mass problem (relying on many light mixing partners) are a general class of theories distinct from UV Seesaw mechanisms.
• Model Discrimination: The ability to distinguish between Dirac and Majorana mass generation via oscillation frequencies is a unique and powerful prediction, as standard oscillation experiments are typically insensitive to the Majorana phase in the absence of $0\nu\beta\beta$ signals.
• Interplay with Axions: The paper notes that the value of $N$ (whether $10^4$ or $10^{16}$) has implications for axion physics and quantum gravity consistency, linking neutrino phenomenology to broader theoretical constraints.

In conclusion, the paper establishes that Nnaturalness is a viable solution to the neutrino mass problem that yields rich, testable phenomenology, shifting the focus of testing this theory from the sky (cosmology) to the earth (neutrino experiments).