⚛️ phenomenology

Nucleon decays into three leptons plus a kaon

This paper systematically investigates baryon-number-violating nucleon decays into three leptons and a kaon using low-energy effective field theory and chiral perturbation theory to derive decay widths, establish experimental bounds on partial lifetimes, and constrain the underlying dimension-9 Wilson coefficients.

Original authors: Jin-Han Liang, Xiao-Dong Ma, Xiang Zhao

Published 2026-10-28

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CC BY 4.0

Original authors: Jin-Han Liang, Xiao-Dong Ma, Xiang Zhao

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

Deep within the heart of every atom lies a tiny, stable building block called a nucleon. For decades, physicists have operated under a fundamental rule: these particles are eternal. They do not simply vanish or change into something else on their own. This stability is so deeply ingrained in our understanding of the universe that if a nucleon were ever to decay, it would shatter a cornerstone of modern physics, revealing that matter itself is not as permanent as we thought. Such a discovery would point to a hidden force or a new kind of interaction that violates the conservation of baryon number, a principle that counts the total number of these heavy particles in the universe. While scientists have spent years searching for simple ways a nucleon might decay, such as turning into a single particle and a light wave, the universe might be hiding more complex, exotic transformations that have been overlooked until now.

A team of researchers has turned their attention to one of these overlooked possibilities: a nucleon breaking apart not into two pieces, but into four. Specifically, they investigated a scenario where a proton or neutron transforms into three light particles known as leptons and a heavier particle called a kaon. Leptons include familiar particles like electrons and muons, as well as ghostly neutrinos that rarely interact with anything. The kaon is a short-lived particle containing a strange quark, a type of matter that does not exist in ordinary atoms. The researchers used a mathematical framework called effective field theory to map out every possible way this four-part breakup could happen. They identified twenty-six distinct modes of decay, covering every combination of charged particles and neutrinos that could emerge from this process, and calculated how likely each one would be to occur based on the laws of physics they proposed.

To make sense of these complex calculations, the team had to bridge the gap between the invisible world of quarks and the visible world of atoms. They translated their theoretical equations into a language that describes how protons and neutrons interact with other particles at low energies. This allowed them to predict the speed at which these decays would happen if they were real. With these predictions in hand, they turned to the Super-Kamiokande detector in Japan, a massive tank of water buried deep underground that has been watching for signs of nucleon decay for years. Although no one had ever looked specifically for these four-particle events, the researchers realized that the signals these decays would leave behind—flashes of light from the charged particles and the decay products of the kaon—would look very similar to signals from other, more common searches the detector had already performed.

By re-examining the vast archives of data from the Super-Kamiokande experiment, the team applied their new theoretical models to see if any of the recorded events could be these exotic decays. They found no evidence of such events occurring. Instead, they used the silence of the data to set strict new limits on how long a nucleon can survive before it might undergo this specific transformation. Their analysis showed that if these decays happen at all, they are incredibly rare. The researchers calculated that a nucleon must live for at least between 10^31 and 10^34 years before it might decay in this manner. To put this in perspective, the universe is only about 1.4 × 10^10 years old, meaning these particles are stable for a time span so vast it is difficult for the human mind to grasp.

These new limits are far more precise than previous estimates, narrowing the window for where this new physics might hide. The team then used these lifetime limits to constrain the strength of the hypothetical forces that could cause such a decay. They determined that if such a force exists, it must operate at an energy scale of roughly 40 to 200 trillion electron volts. This is a range that is currently beyond the reach of our most powerful particle colliders, suggesting that nature is keeping this secret well hidden. The study provides a clear roadmap for future experiments, showing exactly what signals to look for in upcoming, even larger detectors like Hyper-Kamiokande and JUNO. By defining the specific signatures of these four-body decays, the researchers have given the next generation of scientists a precise target, ensuring that if the universe does decide to reveal its most elusive secrets, we will be ready to recognize them.

Technical Summary: Nucleon Decays into Three Leptons plus a Kaon

Problem Statement
This work addresses a gap in the systematic investigation of baryon-number-violating (BNV) nucleon decays. While previous studies have analyzed three-body nucleon decays into three leptons ( $n \to \ell_x \ell_y \ell_z$ ) mediated by dimension-6 and dimension-9 operators, those analyses were restricted to operators involving only up and down quarks. Consequently, they could not probe BNV physics involving strange quarks. This paper investigates the kinematically allowed four-body decay modes where a nucleon decays into three leptons and a kaon ( $K^+$ or $K^0$ ), mediated by local dimension-9 operators containing a strange quark ( $l^3qqs$ ). Although no dedicated experimental searches exist for these specific modes, their signatures in water-Cherenkov detectors overlap with existing searches for two-body decays and specific three-body decays, allowing for a reinterpretation of current data.

Methodology
The authors employ a Low-Energy Effective Field Theory (LEFT) framework to systematically analyze these decays:

Operator Classification: The study constructs a complete basis of dimension-9 BNV operators with the field configuration $l^3qqs$ . These operators are classified according to their transformation properties under the QCD chiral symmetry group $SU(3)_L \otimes SU(3)_R$ . The analysis covers four general chiral structures and their chirality-flipped partners, covering all possible lepton flavor combinations ( $e, \mu, \tau$ ) and neutrino states.
Chiral Matching: To evaluate the hadronic matrix elements, the LEFT operators are matched onto Chiral Perturbation Theory (ChPT). The authors derive the relevant spurion fields and construct the leading-order chiral Lagrangian. This yields two types of interaction vertices:
- Contact diagrams: Five-point vertices involving a nucleon, a kaon, and three leptons.
- Non-contact diagrams: Four-point vertices involving a nucleon, a hyperon, and three leptons, connected to the kaon via standard baryon-meson interactions.
Decay Width Calculation: Using the derived vertices, the authors calculate the decay widths for all kinematically allowed four-body modes. The calculation includes the integration over the four-body phase space using a Monte Carlo procedure. The results are expressed in terms of the LEFT Wilson coefficients (WCs) and low-energy constants (LECs) derived from lattice QCD and dimensional analysis.
Experimental Reinterpretation: Since no dedicated searches exist, the authors reinterpret existing Super-Kamiokande (Super-K) data.
- For modes with at most one charged lepton, they recast limits from searches for conventional two-body decays ( $p \to \ell^+ K^0$ , $n \to \ell^- K^+$ , etc.) and invisible particle searches.
- For modes with two or more charged leptons, they recast limits from the search for the three-body decay $p \to (e^+, \mu^+) \pi^0 \pi^0$ , noting that the Cherenkov ring topologies are similar.
- Kinematic efficiencies are re-evaluated for each specific operator and decay mode to account for the modified phase space distributions.

Key Contributions

Operator Basis: The paper provides the first complete classification of dimension-9 BNV operators involving a strange quark that mediate four-body nucleon decays, organized by chiral irreducible representations.
Chiral Realization: It derives the explicit chiral realizations for these operators, providing a model-independent framework to connect UV-complete scenarios to low-energy nucleon decay observables.
Decay Widths: Analytical expressions for the decay widths of 26 distinct four-body decay modes are provided in terms of the LEFT Wilson coefficients.
Experimental Limits: The study establishes the first lower bounds on the partial lifetimes of these four-body modes by reanalyzing Super-K data.

Results

Lifetime Bounds: The recast analysis yields lower limits on the partial lifetimes ranging from $10^{31}$ to $10^{34}$ years. Specifically, limits for modes with at most one charged lepton reach up to $\sim 10^{33}$ years, while modes with multiple charged leptons are constrained to $\sim 10^{31}$ years. These limits are up to two orders of magnitude more stringent than previous inclusive bounds for similar final states.
Wilson Coefficient Constraints: Translating the lifetime limits into constraints on the effective scales ( $\Lambda_{\text{eff}}$ ) of the dimension-9 operators, the authors find sensitivity in the range of 40–200 TeV.
Comparison to Previous Work: The constraints on the effective scales for these four-body modes are found to be typically a factor of 2–5 weaker than those derived for purely triple-lepton three-body decays. This reduction is attributed to the additional phase-space suppression inherent in four-body decays and the slightly weaker lifetime bounds obtained in the recast analysis.

Significance
The paper claims to provide a convenient and systematic EFT framework for connecting underlying BNV interactions involving strange quarks to experimental searches. By demonstrating that existing data can be reinterpreted to constrain these exotic four-body decays, the work highlights the potential for discovering BNV physics beyond standard two-body channels. The authors note that while their current limits are derived from conservative recasts, future dedicated searches at large-fiducial-mass experiments like Hyper-Kamiokande and JUNO could significantly improve sensitivity. Specifically, JUNO's ability to detect particles below the Cherenkov threshold offers unique advantages for modes involving low-momentum muons, while water-Cherenkov detectors remain well-suited for modes involving $K^0$ due to their multi-ring reconstruction capabilities.

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