⚛️ phenomenology

Flavor Symmetry and Proton Decay in PeV-Scale Supersymmetry

This paper investigates how Froggatt-Nielsen flavor symmetries suppress dimension-five operators in PeV-scale supersymmetry to mitigate proton decay constraints, utilizing a Bayesian analysis of flavor, CP, and baryon-number-violating observables to define the theory's viable parameter space.

Original authors: Akifumi Chitose, Masahiro Ibe, Satoshi Shirai

Published 2026-02-26

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Akifumi Chitose, Masahiro Ibe, Satoshi Shirai

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 authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe is a giant, incredibly complex machine. For decades, physicists have been trying to figure out how the gears inside this machine fit together. One of the most popular theories for how these gears work is called Supersymmetry (SUSY). It suggests that for every particle we know (like an electron), there is a heavier, invisible "super-partner" hiding somewhere.

For a long time, scientists hoped these super-partners were just around the corner, waiting to be found in particle colliders. But they haven't been found yet. This has led to a new idea: maybe these super-partners are so heavy they are like "ghosts" that only show up at energies a million times higher than what our current machines can reach. This is called PeV-scale Supersymmetry.

However, making these super-partners super-heavy creates a new set of problems. It's like trying to fix a leaky roof by building a skyscraper on top of the house; you might solve the leak, but now you have a whole new structural crisis.

Here is what this paper does, explained through a few simple stories:

1. The "Too Heavy" Problem (The Flavor Puzzle)

In our universe, particles come in three "families" (like generations of a family tree), and they have very different weights. An electron is light, a top-quark is heavy. This is the Flavor Puzzle.

If you just throw random numbers at the math to explain why particles have different weights, the universe would be chaotic. It would be like a recipe book where every ingredient is added in random amounts, resulting in a soup that tastes terrible and explodes. In physics, this chaos leads to "Flavor Changing Neutral Currents" (FCNCs)—processes that shouldn't happen, like a neutron spontaneously turning into a different type of particle.

The paper asks: How do we keep the super-partners heavy (to avoid detection) without making the universe explode with these weird particle changes?

2. The "Traffic Cop" Solution (Flavor Symmetry)

To fix the chaos, the authors introduce a concept called the Froggatt-Nielsen (FN) mechanism. Think of this as a strict Traffic Cop or a VIP Pass system.

Imagine a party (the universe) where everyone wants to mix and interact.

Without the Traffic Cop: Everyone mingles freely. The heavy particles (super-partners) interact too much with the light ones, causing chaos (FCNCs) and making the proton (the building block of matter) fall apart too quickly.
With the Traffic Cop: The Traffic Cop assigns everyone a "charge" (a VIP level). Only people with compatible charges can talk to each other. If a heavy super-partner tries to talk to a light particle, the Traffic Cop says, "No, your charges don't match!" and blocks the interaction.

This "charge" system naturally explains why particles have different weights (some get VIP access, some don't) and, crucially, it stops the dangerous interactions that would destroy the proton.

3. The "Proton Decay" Alarm Clock

The biggest threat to this theory is Proton Decay. Protons are supposed to be stable; they hold atoms together. But in many supersymmetric theories, protons can decay (disappear) into lighter particles like pions and positrons.

The Problem: If the super-partners are too heavy, or if the "Traffic Cop" isn't strict enough, the proton might decay in a blink of an eye. But we know protons live for a very long time (billions of years).
The Paper's Investigation: The authors ran a massive statistical simulation (a Bayesian Analysis). Imagine they have a giant bag of marbles, where each marble represents a different version of the universe with different charge assignments. They asked: "Which marbles (universes) survive the test of not exploding (FCNCs) and not having their protons vanish too fast (Proton Decay)?"

4. The Results: A Multi-Messenger Detective Story

The paper concludes that you can't just look at one clue. You need a Multi-Messenger Approach.

The Flavor Clue: Does the model explain why the electron is light and the top-quark is heavy?
The CP Clue: Does the model explain why the universe prefers matter over antimatter?
The Proton Clue: Does the model predict a proton that lives long enough?

The Findings:

Some models work: Certain "charge assignments" (Traffic Cop rules) work beautifully. They allow the super-partners to be heavy (PeV scale) while keeping the proton safe and the particle weights correct.
The "Planck Scale" Danger: There is a catch. The "Traffic Cop" works great for interactions at the GUT scale (Grand Unified Theory scale), but what if there are interactions happening at the Planck Scale (the absolute limit of physics, where gravity gets strong)? If the Traffic Cop doesn't stop these ultra-high-energy interactions, the proton will still decay too fast, even if the super-partners are heavy.
The Future: The paper suggests that if we wait for the next generation of giant detectors (like Hyper-Kamiokande, a massive tank of water deep underground), we might finally catch a proton decaying. If we see it, it will tell us exactly which "Traffic Cop rules" (Flavor Symmetry) the universe is using.

The Bottom Line

This paper is a guidebook for navigating the "PeV-scale" universe. It tells us that simply making super-partners heavy isn't enough; we need a specific, organized system (Flavor Symmetry) to keep the universe stable.

It's like saying: "We can't just build a bigger wall to keep the monsters out; we need to install a specific lock system that only lets the right people in." By combining clues from particle weights, matter-antimatter differences, and the stability of the proton, we can figure out what that lock system looks like. If we get lucky, the next big experiment might hand us the key.

1. Problem Statement

Supersymmetric Standard Models (SSM) beyond the TeV scale (specifically in the PeV range) offer theoretical advantages, such as accommodating the 125 GeV Higgs mass and alleviating the cosmological gravitino problem. However, these models face two critical challenges:

Flavor and CP Violation: Generic soft supersymmetry-breaking terms induce Flavor-Changing Neutral Currents (FCNCs) and CP-violating observables (e.g., Electric Dipole Moments) that are tightly constrained by experiment.
Proton Decay: Even with R-parity conservation, dimension-five ( $d=5$ ) baryon-number-violating operators (arising from GUTs or Planck-scale physics) can induce rapid proton decay.

The core problem is that in a generic "anarchic" scenario where dimensionless couplings are $\mathcal{O}(1)$ , PeV-scale sfermions are strongly excluded by flavor/CP constraints, and proton decay rates are often unacceptably high. The paper investigates whether Flavor Symmetries, specifically the Froggatt-Nielsen (FN) mechanism, can simultaneously explain the fermion mass hierarchy and suppress these dangerous operators to allow for a viable PeV-scale spectrum.

2. Methodology

The authors employ a Bayesian statistical framework to quantify the compatibility of various flavor models with experimental data.

Model Setup:
- Spectrum: A "mini-split" scenario where sfermions ( $m_0$ ) and Higgsinos ( $\mu$ ) are at the PeV scale, while gauginos (specifically the Wino) are at the TeV scale (motivated by Anomaly Mediated Supersymmetry Breaking, AMSB).
- Operators: The analysis includes dimension-five operators ( $O_{5L}, O_{5R}$ ) responsible for proton decay, dressed by gaugino/Higgsino loops to generate dimension-six effective operators.
- Flavor Symmetry: The FN mechanism is implemented via a $U(1)_{FN}$ symmetry. Yukawa couplings, sfermion masses, and dimension-five operator coefficients are suppressed by powers of a small parameter $\epsilon \sim 0.2$ , determined by the difference in FN charges between fields.
Bayesian Analysis:
- Priors: In the absence of symmetry, dimensionless parameters are assumed to be complex numbers of $\mathcal{O}(1)$ (Gaussian priors). In FN models, the fundamental parameters are the $\mathcal{O}(1)$ coefficients ( $\kappa$ ) multiplying the FN-suppressed structures.
- Likelihood: The likelihood function ( $L_{obs}$ $L_{o b s}$ ) combines:
  - Yukawa Sector: Fits to fermion masses and mixing angles (CKM and PMNS matrices).
  - Flavor/CP Observables: Constraints from neutral meson mixing ( $K^0, D^0, B^0, B_s^0$ ) and fermion Electric Dipole Moments (EDMs).
  - Proton Decay: Constraints from Super-Kamiokande and projected Hyper-Kamiokande sensitivities for various decay modes ( $p \to e^+\pi^0, p \to \bar{\nu}K^+$ , etc.).
- Metric: The Bayes Factor (BF) is calculated. It compares the marginalized likelihood of a specific model (with finite sfermion mass $m_0$ ) against a reference "decoupling limit" ( $m_0 \to \infty$ ). A low BF indicates strong tension with data.
Benchmark Models: Several charge assignments were tested:
- Model N: No FN symmetry (anarchic).
- Models A, G, B, C: Various FN charge assignments designed to fit Yukawa hierarchies.
- Variations: Models where FN charges do not suppress the dimension-five operators (e.g., Model A/B) or where Higgs fields carry non-zero charges (Model $A_{Hd(3)}$ ).

3. Key Contributions

Systematic Bayesian Quantification: The paper provides a rigorous statistical quantification of how flavor symmetries affect the viability of PeV-scale supersymmetry, moving beyond simple order-of-magnitude estimates.
Decoupling of Constraints: It demonstrates that flavor/CP constraints and proton decay constraints are not always correlated in the same way across different flavor models. A model that solves the flavor puzzle might still fail on proton decay, and vice versa.
Role of FN Charges on $d=5$ Operators: The study explicitly analyzes scenarios where the FN symmetry suppresses Yukawas but fails to suppress Planck-scale dimension-five operators, showing this leads to immediate exclusion.
Multi-Messenger Probing: It establishes that a combination of flavor, CP, and proton decay observables is necessary to distinguish between different underlying flavor structures in high-scale SUSY.

4. Key Results

Anarchic Scenario (Model N):
- Without flavor symmetry, the Bayes factor drops below 0.1 for sfermion masses as low as 1 PeV due to FCNC constraints (specifically $K^0-\bar{K}^0$ mixing).
- Proton decay constraints are even more severe, excluding PeV-scale SUSY entirely unless the cutoff scale is extremely high or the operators are accidentally suppressed.
Flavor Symmetry Success (Models A & G):
- Models with FN charges aligned to reproduce the observed Yukawa hierarchy (e.g., Model A and the GUT-motivated Model G) successfully suppress FCNCs.
- Proton Decay: In these models, the FN mechanism also suppresses the dimension-five operators. For a Planck-scale cutoff ( $\Lambda_B = M_{Pl}$ ), the predicted proton lifetimes are consistent with current bounds even at $m_0 \sim 1$ PeV.
- GUT Scale Cutoff: If the cutoff is at the GUT scale ( $\Lambda_B \sim 10^{16}$ GeV), the predicted lifetimes for $p \to \bar{\nu}K^+$ fall within the reach of future experiments like Hyper-Kamiokande.
Sensitivity to Charge Assignments:
- Model A/B (No FN suppression on $d=5$ ): If the FN symmetry does not suppress the baryon-number-violating operators, the proton decay rate is enhanced, and the model is excluded even at the Planck scale.
- Model $A'$ and $A_{Hd(3)}$ : Changing the signs of lepton charges or assigning charges to Higgs fields alters the suppression factors of the $d=5$ operators. These variations can shorten the proton lifetime by factors of $\epsilon^6$ , leading to tension with experimental limits.
- Model B: Features a charge pattern that makes sfermion mass matrices nearly flavor-diagonal, relaxing FCNC constraints significantly. However, proton decay constraints remain the dominant limiting factor.
Cosmological Implications:
- The analysis suggests that for AMSB scenarios with a Wino LSP, the sfermion mass scale $m_0$ is cosmologically preferred to be $\lesssim 10$ PeV to avoid overproducing dark matter via non-thermal gravitino decays. This range is precisely where the flavor/proton decay constraints are most active.

5. Significance and Conclusion

The paper concludes that PeV-scale supersymmetry is not ruled out, but its viability is highly dependent on the specific structure of the flavor symmetry.

Proton Decay as a Probe: Proton decay is identified as a crucial "multi-messenger" probe. While flavor observables constrain the sfermion mass scale, proton decay rates are sensitive to the specific FN charge assignments and the scale of baryon-number violation ( $\Lambda_B$ ).
GUT Connection: Models with FN charges mimicking SU(5) GUT relations (Model G) naturally suppress proton decay and predict rates testable by next-generation detectors, offering a unique window into Grand Unification.
Requirement for Symmetry: The results imply that if SUSY exists at the PeV scale, a flavor symmetry (like FN) is likely required not just to explain fermion masses, but also to suppress Planck-scale baryon-number-violating operators. If such symmetries are broken by quantum gravity effects (Planck scale), alternative mechanisms (e.g., baryon triality) may be necessary to ensure proton stability.

In summary, the work provides a comprehensive statistical framework linking high-scale SUSY spectra, flavor symmetries, and experimental observables, highlighting that future proton decay searches are essential for testing the fundamental structure of supersymmetry.