Nucleon decays into one lepton plus two non-strange mesons

This paper uses a model-independent effective field theory approach to correlate two-body and three-body nucleon decay processes, resulting in significantly improved lifetime bounds for various lepton and non-strange meson decay modes compared to current PDG values.

The Gist

The Cosmic Detective Agency: Solving the Mystery of the Disappearing Nucleon

Imagine you are a detective trying to solve a crime: The Case of the Vanishing Matter.

In our universe, there is a fundamental rule called "Baryon Number Conservation." Think of this like a cosmic law of accounting. It says that the number of "building blocks" (protons and neutrons, collectively called nucleons) in the universe must stay constant. They shouldn't just vanish into thin air.

However, many "Grand Theories" of physics suggest that this law might actually be breakable. If it is, a proton could suddenly decay—essentially, a piece of matter could "self-destruct" and turn into something else.

The Problem: The "Hard-to-Catch" Criminals

Detectives (physicists) usually look for the most obvious signs of this crime.

• The Two-Body Decay (The "Smoking Gun"): This is when a proton decays into one lepton (a tiny particle like an electron) and one meson (a small particle made of quarks). This is a clean, simple, two-piece crime scene. It’s easy to spot and easy to measure.
• The Three-Body Decay (The "Messy Crime Scene"): This is when the proton decays into one lepton and two mesons. It’s much more chaotic and messy. Because there are more pieces flying around, it’s incredibly hard for our detectors to catch every single one. For decades, we’ve had very weak evidence for these "messy" decays, making them hard to rule out or confirm.

The Breakthrough: The "Family Connection" Strategy

The authors of this paper, Wei-Qi Fan and colleagues, realized they didn't need to wait for a perfect, messy crime scene to be caught in the act. Instead, they used a clever mathematical trick called Effective Field Theory (EFT).

The Analogy: The DNA Connection
Imagine you are looking for a specific criminal. You haven't caught them committing a "messy" crime (the three-body decay), but you have caught their twin brother committing a "clean" crime (the two-body decay).

Because they are twins, they share the same DNA. In physics, the "DNA" is the underlying mathematical operator (the Wilson Coefficient) that causes the decay. If the "clean" crime is extremely rare (meaning the twin brother is very careful), then the "messy" crime must also be extremely rare, because they are driven by the same fundamental force.

What They Did

Instead of looking at each decay mode in isolation, the researchers performed a "Global Analysis." They took all the well-known, highly-accurate data from the "clean" crimes (the two-body decays) and used it to "map out" the limits of what the "messy" crimes could possibly look like.

They didn't just assume one single cause; they looked at all possible combinations of "DNA" simultaneously to ensure their results were robust and didn't rely on lucky guesses.

The Results: Setting the Bar Higher

By using this "DNA mapping" technique, they achieved something incredible:

1. Massive Improvements: For many of the "messy" three-body decays, they were able to set much stricter limits on how often they happen. In some cases, they improved our knowledge by three to four orders of magnitude (that’s 1,000 to 10,000 times more precise!).
2. First-of-its-kind Bounds: They established the first-ever strong limits on several "neutrino" versions of these decays.
3. Better Accuracy: They even improved the limits on some of the "clean" decays that we thought we already understood well.

Why Does This Matter?

This paper provides a new "benchmark" for future experiments (like the massive Super-Kamiokande or DUNE detectors).

By proving that the "messy" decays are just as important as the "clean" ones, they have given physicists a new toolkit. If we ever do see a proton decay, these mathematical connections will act like a forensic map, helping us work backward from the "messy" pieces to figure out exactly what kind of "New Physics" broke the cosmic law of accounting.

Technical Summary

Technical Summary: Nucleon Decays into One Lepton plus Two Non-Strange Mesons

1. Problem Statement

The search for nucleon decay is a primary objective for next-generation neutrino experiments (e.g., Hyper-Kamiokande, DUNE, JUNO) because it serves as a direct probe for Baryon Number Violation (BNV), a key prediction of Grand Unified Theories (GUTs) and leptoquark models.

While conventional searches focus on two-body decay modes (a lepton plus one pseudoscalar meson, such as $p \to e^+\pi^0$), three-body decay modes (a lepton plus two mesons, such as $p \to e^+\pi^+\pi^-$) are theoretically significant. The additional meson is produced via strong interactions, potentially making these rates competitive with two-body modes. However, three-body modes have historically received less experimental attention due to:

• Experimental Complexity: Difficulties in reconstructing multi-particle final states.
• Theoretical Uncertainties: Dependence on complex nuclear effects (Fermi motion, binding energy) and final-state interactions (FSI), which make deriving robust bounds from experimental data challenging.

2. Methodology

The authors employ a model-independent Effective Field Theory (EFT) approach to bridge the gap between well-measured two-body decays and poorly constrained three-body decays.

• Framework: They utilize Low-Energy Effective Field Theory (LEFT) to parametrize BNV interactions at the GeV scale using dimension-6 operators. They then use Chiral Perturbation Theory (ChPT) to match these quark-level operators to hadronic matrix elements involving octet baryons and pseudoscalar mesons ($\pi, \eta$).
• Global Analysis: Unlike traditional studies that assume "single-operator dominance" (varying one parameter at a time), this paper performs a global fit. They treat all relevant Wilson Coefficients (WCs)—which represent the strength and chirality of the BNV interactions—as simultaneous variables.
• Correlation Strategy: The core innovation is leveraging the fact that the same set of EFT operators induces both two-body and three-body decays. By using the highly stringent experimental lower limits on specific two-body modes (from Super-Kamiokande and IMB-3) as inputs, they constrain the multidimensional parameter space of the WCs. They then use these bounded WCs to calculate the "worst-case" (most conservative) lower limits for the three-body modes.
• Scope: The study focuses on 24 modes: 9 two-body and 15 three-body modes involving non-strange mesons ($\pi, \eta$) and leptons ($e^+, \mu^+, \bar{\nu}, \nu$).

3. Key Contributions

• Model-Independent Bounds: They provide bounds that do not rely on specific BSM models or the assumption of a single dominant operator.
• Improved Constraints: They derive significantly more stringent bounds for 15 three-body modes by exploiting the mathematical correlations between decay widths.
• First-Time Limits: They establish the first-ever lower lifetime bounds for 5 specific (anti)neutrino three-body modes.
• Refined Two-Body Limits: The analysis also improves the constraints on three specific two-body modes ($n \to e^+\pi^-$, $n \to \mu^+\pi^-$, and $p \to \hat{\nu}\pi^+$) by approximately a factor of 2.

4. Results

The paper provides a massive upgrade to the current experimental landscape (compared to PDG/IMB-3 values):

• Charged-Lepton Three-Body Modes: For modes like $p \to \ell^+(\pi^+\pi^-, \pi^0\pi^0, \pi^0\eta)$, the partial lifetime limits are pushed to $\mathcal{O}(10^{35}\text{--}10^{36})$ years. This represents an improvement of three to four orders of magnitude over previous IMB-3 bounds.
• Neutrino/Antineutrino Modes: For the 5 (anti)neutrino modes (e.g., $n \to \hat{\nu}\pi^0\pi^0$), they establish a new lower limit of $\Gamma^{-1} \gtrsim 10^{34}$ years.
• Consistency Check: The results satisfy isospin symmetry relations (e.g., relating $n \to e^+\pi^-$ to $p \to e^+\pi^0$), validating the robustness of the EFT calculation.
• Suppression Factors: The EFT calculation reveals that three-body modes are suppressed by a factor of roughly 5–100 relative to two-body modes due to phase space reduction, despite the strong interaction enhancement.

5. Significance

This work shifts the paradigm for nucleon decay searches. It demonstrates that three-body channels are as vital as two-body channels for probing new physics.

If a decay is eventually observed, the combination of two-body and three-body data will be essential to resolve operator degeneracies. Specifically, measuring the branching ratios between these modes will allow physicists to determine the exact chiral structure (the $L$ vs $R$ nature) of the underlying BNV interaction, effectively "fingerprinting" the physics beyond the Standard Model.