⚛️ phenomenology

Comprehensive investigation on baryon number violating nucleon decays involving an axion-like particle

This paper systematically investigates baryon number violating nucleon decays into axion-like particles using a complete set of dimension-eight effective operators and chiral perturbation theory to derive new decay expressions, which are then constrained by reanalyzing Super-Kamiokande data to establish significantly more stringent limits on effective scales and predict bounds on neutron and hyperon decays.

Original authors: Wei-Qi Fan, Yi Liao, Xiao-Dong Ma, Hao-Lin Wang

Published 2026-02-17

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CC BY 4.0

Original authors: Wei-Qi Fan, Yi Liao, Xiao-Dong Ma, Hao-Lin Wang

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

The Big Picture: Hunting for a "Ghost" Particle

Imagine the universe is a giant, complex machine made of tiny building blocks called protons and neutrons (collectively, nucleons). For decades, physicists have believed these blocks are indestructible. They thought a proton would live forever.

However, some theories suggest that protons can decay, but they do so incredibly slowly—so slowly that we've never seen it happen. If a proton decays, it turns into lighter particles, like a positron (a positive electron) or a neutrino.

But there's a twist. This paper investigates a specific, exotic scenario: What if a proton decays, but instead of just turning into normal particles, it also spits out a "Ghost Particle"?

This ghost particle is called an Axion-Like Particle (ALP). It's invisible, has no electric charge, and barely interacts with anything. It's like a magician's assistant who vanishes into thin air, leaving behind only a faint clue.

The Detective Work: The "Rulebook" of Physics

To understand how this might happen, the authors used a tool called Effective Field Theory (EFT). Think of this as a "rulebook" for how particles interact at low energies.

The Old Rulebook: Previous studies only looked at the most obvious, simple rules in the book. They ignored a whole section of the rulebook because they thought those rules were too complicated or too weak to matter.
The New Discovery: This paper says, "Wait a minute! We need to read the entire rulebook." The authors found a specific set of rules (called Dimension-8 operators) that were previously ignored.
- The Analogy: Imagine you are trying to solve a mystery by looking at footprints. Previous detectives only looked at the big, muddy boot prints. These authors realized there are also tiny, delicate shoe prints (the new rules) that were just as important. They found that these "tiny prints" can actually lead to the same destination as the big ones.

The Chiral Puzzle: Sorting the Blocks

The authors had to sort these new rules into categories based on a symmetry called Chiral Symmetry.

The Analogy: Imagine you have a box of LEGO bricks. Some are red, some are blue. You need to build a specific structure (a decaying proton).
Previous studies only used the red and blue bricks that fit together in a standard way.
This paper found a new type of brick (the $6_L \otimes 3_R$ representation) that looks different but can actually build the exact same structure just as well. In fact, for some specific decay patterns (like changing the "isospin" by 3/2 units), you can't build the structure without these new bricks. They are essential, not optional.

The Experiment: Listening for the Ghost

Since we can't build a proton in a lab and wait for it to decay (it takes longer than the age of the universe!), the authors looked at data from Super-Kamiokande, a massive underground tank of water in Japan.

How it works: When a particle moves through water faster than light does in water, it creates a flash of blue light called Cherenkov radiation (like a sonic boom, but with light). Detectors see these flashes as rings.
The Problem: If a proton decays into a visible particle (like a positron) and a ghost (the ALP), the ghost disappears. The detector only sees the positron.
The Trick: The authors realized that because the ghost steals some energy, the visible particle (the positron) will have a different momentum (speed and direction) than if the proton had decayed into only visible particles.
- Analogy: Imagine a magician pulls a rabbit out of a hat. If the rabbit is heavy, the magician's hand moves slowly. If the rabbit is light, the hand moves fast. If there's a ghost rabbit you can't see, the magician's hand moves at a weird speed that doesn't match any normal rabbit.
- The authors simulated millions of these "ghost" decays and compared the resulting speed patterns to the actual data from Super-Kamiokande.

The Results: Tightening the Net

The authors found two major things:

Stricter Limits: By looking at the specific speed patterns (momentum distributions) of the particles, they could rule out these exotic decays much more effectively than before.
- The Result: They set new, much stricter limits on how likely these decays are. They found that if these decays happen, the "scale" of the new physics (the energy level where this happens) must be incredibly high—trillions of times higher than what we can currently build in particle accelerators.
- The Improvement: Their new limits are orders of magnitude (thousands or millions of times) stronger than the old, rough estimates used in previous studies.
New Predictions: Because they tightened the net on protons, they could also predict what should happen to other particles, like neutrons and hyperons (heavier cousins of protons).
- They predicted that if we look for neutrons decaying into a ghost and a pion, we should see very specific patterns. This gives future experiments (like JUNO or DUNE) a clear "treasure map" to follow.

Summary in a Nutshell

The Goal: Find out if protons can decay into invisible "ghost" particles (ALPs).
The Method: The authors wrote a complete "rulebook" for these interactions, including a section of rules everyone else ignored. They used math to predict what these decays would look like.
The Check: They compared their predictions to real data from a giant water tank in Japan.
The Discovery: They found that the "ignored rules" are actually very important. By using them, they proved that these ghost-decays are even rarer than we thought.
The Takeaway: The universe is still very stable, but we now have a much sharper set of tools to hunt for the rarest, most exotic events in nature. If these ghosts exist, they are hiding in a place we are now much better equipped to find.

1. Problem Statement

Baryon number violation (BNV) is a crucial ingredient for explaining the matter-antimatter asymmetry of the universe. While extensive searches for nucleon decays involving only Standard Model (SM) particles have placed stringent limits, the possibility of decays involving new light invisible particles, such as Axion-Like Particles (ALPs), remains less constrained.

Previous studies (e.g., Ref. [18]) investigated BNV nucleon decays with ALPs within a low-energy effective field theory (aLEFT) but only considered a subset of dimension-8 operators. Specifically, they focused on operators belonging to the usual chiral irreducible representations (irreps) $8_L \otimes 1_R$ and $3_L \otimes \bar{3}_R$ , neglecting 12 operators belonging to the "new" chiral irreps $6_L \otimes 3_R$ (and their parity partners). The authors argue that these neglected operators contribute at the same leading chiral order and are uniquely responsible for processes changing isospin by $\Delta I = 3/2$ (e.g., $n \to \pi^+ \ell^- a$ ). Furthermore, existing experimental bounds on these exotic modes were often derived from inclusive limits, which are significantly weaker than direct constraints.

2. Methodology

The authors employ a systematic Effective Field Theory (EFT) approach combined with Chiral Perturbation Theory (ChPT) to bridge the gap between quark-level interactions and hadronic observables.

Theoretical Framework (aLEFT):
- They utilize an aLEFT framework extended by an ALP ( $a$ ) with shift symmetry, ensuring the ALP appears only via derivatives ( $\partial_\mu a$ ).
- They construct a complete set of 20 dimension-8 BNV operators involving three light quarks ( $u, d, s$ ) and a lepton field.
- Chiral Decomposition: The operators are decomposed under the QCD chiral group $SU(3)_L \times SU(3)_R$ $S U (3)_{L} \times S U (3)_{R}$ . This reveals three distinct classes of irreps:
  1. $8_L \otimes 1_R$ (and $1_L \otimes 8_R$ )
  2. $3_L \otimes \bar{3}_R$ (and $\bar{3}_L \otimes 3_R$ )
  3. New Irreps: $6_L \otimes 3_R$ (and $3_L \otimes 6_R$ ).
- Spurion Analysis: Using the spurion field method, they map these quark-level operators onto hadronic degrees of freedom (octet baryons and pseudoscalar mesons) within the ChPT formalism. They derive the specific spurion matrices ( $P$ ) corresponding to each operator class.
Hadronic Matching:
- They match the aLEFT operators to the leading-order chiral Lagrangian involving octet baryons ( $B$ ) and mesons ( $\Pi$ ).
- They derive general expressions for the amplitudes of:
  - Two-body decays: $B \to \ell + a$ (e.g., proton/hyperon decay).
  - Three-body decays: $N \to \ell + M + a$ (e.g., nucleon decay with a meson).
- The amplitudes include contributions from both "contact" terms (direct BNV vertex) and "non-contact" terms (involving intermediate baryon states via standard ChPT interactions).
Phenomenological Analysis:
- Momentum Distributions: They calculate normalized differential decay widths ( $d\tilde{\Gamma}/d|p|$ ) for charged leptons and mesons. This is critical for distinguishing operator structures, as different chiral irreps yield distinct kinematic distributions.
- Experimental Recasting: They reanalyze data from the Super-Kamiokande (Super-K) experiment. Instead of relying on loose inclusive bounds, they simulate specific decay topologies (two-body and three-body) using analytical distributions. They account for detector resolution, efficiency, and Cherenkov thresholds to derive direct lower bounds on partial lifetimes ( $\Gamma^{-1}$ ).

3. Key Contributions

Inclusion of New Chiral Irreps: The paper is the first to systematically include the 12 operators belonging to the $6_L \otimes 3_R$ (and $3_L \otimes 6_R$ ) irreps. They demonstrate that these operators are not sub-leading; they contribute at the same order as the usual irreps and are the only mediators for $\Delta I = 3/2$ transitions.
Kinematic Discrimination: They show that operators in the new chiral irreps produce markedly different momentum distributions compared to those in the usual irreps. For instance, in $p \to \ell^+ \pi^0 a$ , the new irrep operators tend to concentrate at higher pion momenta. This provides a potential experimental handle to distinguish between different BNV mechanisms.
Improved Experimental Constraints: By recasting Super-K data with proper treatment of kinematic distributions and detector effects, they establish bounds on the inverse decay widths that are several orders of magnitude more stringent than the inclusive bounds previously used in the literature.
Comprehensive Operator Basis: They provide a complete mapping of all 20 dimension-8 operators to their hadronic counterparts, including explicit expressions for Wilson coefficients (WCs) and decay widths for various baryon and nucleon modes.

4. Results

Constraints on Effective Scales ( $\Lambda_{eff}$ ):
- The authors derive lower limits on the effective new physics scale $\Lambda_{eff} \equiv |C_i|^{-1/4}$ as a function of the ALP mass ( $m_a$ ).
- For operators involving $u, d$ quarks (e.g., $p \to e^+ a$ ), the recast constraints reach $\Lambda_{eff} \sim 10^7$ GeV, significantly improving upon previous limits.
- The constraints on the new chiral irreps ( $6_L \otimes 3_R$ ) are found to be of the same order of magnitude as those for the usual irreps, refuting the assumption that they are negligible.
- For operators involving strange quarks ( $u, d, s$ ), the constraints are five to six orders of magnitude stronger than previous limits derived from BESIII hyperon searches.
Predictions for Future Searches:
- Using the derived bounds, they predict branching ratios for various hyperon decays (e.g., $\Sigma^+ \to e^+ a$ , $\Lambda^0 \to \nu a$ ) and neutron decays.
- Hyperon decays are predicted to have extremely small branching ratios ( $< 10^{-45}$ ), making them currently unobservable.
- Neutron decays (e.g., $n \to \nu \pi^0 a$ ) are predicted to have branching ratios within the reach of next-generation experiments like JUNO and DUNE.
Momentum Distribution Features:
- The study confirms that the shape of the momentum distribution is a robust discriminator. For example, in $n \to \ell^+ \pi^- a$ , the new irrep operators exhibit a distinct high-momentum tail compared to the usual operators, which could be exploited in future data analysis.

5. Significance

This work represents a major advancement in the search for BNV physics involving light scalars. By correcting the incomplete operator basis in previous literature and utilizing a rigorous chiral matching procedure, the authors provide a more accurate theoretical framework. The recasting of Super-K data significantly tightens the constraints on BNV interactions, effectively ruling out a large portion of the parameter space for ALP-mediated nucleon decays.

The identification of unique kinematic signatures for the $6_L \otimes 3_R$ operators offers a new strategy for experimentalists to disentangle the underlying physics of any potential signal. Furthermore, the prediction that neutron decays involving ALPs are within the sensitivity of upcoming neutrino experiments provides a clear target for future searches, bridging the gap between theoretical model-building and experimental discovery.