⚛️ phenomenology

LUNAR: a Monte Carlo generator for bound-nucleon decay in liquid argon

The paper introduces LUNAR, a fast and open-source Monte Carlo generator that simulates two-body bound-nucleon decays in liquid argon by incorporating diverse nuclear models and intranuclear cascade effects to quantify how final-state interactions and nuclear binding reshape decay kinematics for the DUNE experiment.

Original authors: Jaroslaw Nowak

Published 2026-07-01

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Jaroslaw Nowak

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 a giant, ultra-sensitive underwater camera (a liquid-argon detector) waiting to catch a rare event: a proton, the tiny building block of matter, spontaneously falling apart. Physicists believe this might happen if the universe follows certain grand theories, but it's incredibly hard to spot because the proton is usually stuck inside a crowded atomic nucleus, like a person trapped in a dense crowd.

This paper introduces LUNAR, a new computer program designed to simulate exactly what happens when a proton inside an Argon atom decides to decay. Think of LUNAR as a "physics flight simulator" for subatomic particles.

Here is a breakdown of what the paper says, using simple analogies:

1. The Problem: The Crowd Effect

If a proton were floating alone in empty space, its decay would be simple and predictable, like a firework exploding in a vacuum. But inside an atom, the proton is part of a busy crowd (the nucleus).

The Jostle (Fermi Motion): The proton isn't sitting still; it's jiggling around with energy. This makes the debris from the explosion fly off in slightly different directions and speeds than expected.
The Weight (Binding Energy): The proton is held tight by the crowd. It's "heavier" in a sense because it's bound, which changes the energy available for the explosion.
The Obstacle Course (Final-State Interactions): After the proton explodes, the new particles (like pions or kaons) have to fight their way out of the crowd. They might bounce off neighbors, get absorbed, or change their identity before they ever reach the detector.

2. The Solution: LUNAR

Before this paper, scientists had to use massive, complex software designed for studying neutrinos (ghostly particles) to simulate proton decay. It was like using a heavy-duty truck to deliver a single letter—too slow and too complicated.

LUNAR is the lightweight, specialized delivery van.

It's Fast: It can simulate millions of decays in seconds.
It's Transparent: You can see exactly how it works. If you want to change how the "crowd" behaves, you just tweak one setting, not the whole engine.
It's Modular: It has different "lenses" to view the nucleus. You can choose to see the nucleus as a simple gas, a structured shell, or a complex web of interactions.

3. What the Simulation Revealed

The authors used LUNAR to answer three big questions:

A. What shapes the explosion?
They found that two things control the result, but they do different jobs:

The "Jiggle" (Momentum Model): This determines how spread out the debris is. If the crowd is very active, the debris scatters widely.
The "Weight" (Binding Model): This determines the center of the explosion. It shifts the whole result up or down but doesn't change how spread out it is.
Analogy: Imagine throwing a ball. How hard you throw it (binding) decides how far it goes. How much you shake your hand while throwing it (momentum) decides how much the landing spot varies.

B. Who survives the crowd?
This was the most surprising finding. The type of particle created matters immensely:

The "Ghost" (Kaon): If the proton turns into a Kaon (a specific type of particle), it is almost invisible to the crowd. It slips through the nucleus without hitting anything. About 99% of them escape.
The "Bouncers" (Pions, Eta, Antikaons): If the proton turns into these other particles, they crash into the crowd constantly. About half of them get stopped, absorbed, or changed before they can be seen.
Analogy: The Kaon is like a ninja sneaking through a party unnoticed. The Pion is like a loud person who gets stopped by security, bumped into, or dragged away before leaving the room.

C. What does this mean for the future?
The paper looks ahead to the DUNE experiment (a massive detector being built underground).

Because the "Ghost" (Kaon) survives so well, the search for the proton decaying into a Kaon is the "Golden Channel." It's the cleanest signal.
For the other particles, the "crowd" effect is huge. If scientists don't account for the fact that half the particles get eaten by the nucleus, they will miss the signal or miscount the events.

Summary

LUNAR is a specialized tool that helps physicists understand how the "crowd" inside an atom affects a proton's death. It proves that while some decay products (like Kaons) slip through easily, others (like Pions) get heavily filtered by the nucleus. This tool will help the DUNE experiment know exactly what to look for and how to interpret the data, ensuring they don't miss the discovery of the century.

The code is now open for everyone to use, allowing scientists to run their own simulations quickly and easily.

Technical Summary: LUNAR – A Monte Carlo Generator for Bound-Nucleon Decay in Liquid Argon

Problem Statement
The search for nucleon decay in liquid-argon time-projection chambers (LArTPCs), particularly the Deep Underground Neutrino Experiment (DUNE), requires a precise quantitative description of how the bound nuclear environment alters decay-product kinematics. Unlike free nucleons, bound nucleons possess intrinsic momentum (Fermi motion) and exist below their free mass due to binding energy (removal energy). These effects smear the daughter particle spectrum and shift the available energy, potentially forbidding certain decay modes. Furthermore, the decay meson must traverse the residual nucleus, undergoing final-state interactions (FSI) such as scattering, charge exchange, or absorption before detection. While general-purpose neutrino event generators (e.g., GENIE, NuWro, GiBUU) contain nuclear models, they are engineered for neutrino-nucleus interactions and are often too heavy or opaque for dedicated nucleon-decay studies. There is a specific need for a lightweight, transparent, and extensible tool dedicated to the unique kinematics of bound-nucleon decay.

Methodology: The LUNAR Generator
The authors present LUNAR (Lancaster University Nucleon-decay ARgon generator), a header-only C++17 Monte Carlo generator designed specifically for two-body decays of protons and neutrons bound in Argon-40 ( $^{40}$ Ar). The generator operates through a modular pipeline:

Initial State Sampling:
- Momentum: The bound nucleon is drawn from one of ten selectable momentum distributions ( $n(p)$ ). These range from simple mean-field Fermi gases (global and local) to models incorporating short-range correlations (SRC), Bodek–Ritchie gases, harmonic-oscillator shell models, and Gaussian distributions. Two options utilize spectral functions: one using tabulated grids from the Jefferson Lab (benhar) and an analytic construction (ankowski).
- Binding/Off-Shell Kinematics: The nucleon is bound off the mass shell using one of three removal-energy prescriptions: a momentum-dependent optical potential (default), a constant separation energy, or a shell-model level scheme. For correlated nucleons, the removal energy is determined by the recoil of the partner nucleon.
- The generator ensures the decay is kinematically allowed; if the off-shell invariant mass $W$ falls below the sum of daughter masses, the nucleon is resampled.
Decay:
- The two-body decay ( $N \to d_1 + d_2$ ) is performed in the nucleon's rest frame using relativistic kinematics based on the off-shell mass $W$ .
- The resulting four-vectors are boosted to the laboratory frame.
- LUNAR supports 14 standard channels, including supersymmetry-favored modes (e.g., $p \to K^+\bar{\nu}$ ) and Grand Unified Theory (GUT) modes (e.g., $p \to e^+\pi^0$ ), covering both proton and neutron decays.
Final-State Interactions (FSI):
- The decay meson is propagated out of the nucleus via a semi-classical intranuclear cascade, modeled after the NuWro kaskada approach.
- The cascade tracks the hadron through the Woods-Saxon density, calculating interaction probabilities based on hadron-nucleon cross sections (using Metropolis tables for pions/nucleons and interpolated data for strange/eta mesons).
- Processes include elastic scattering, charge exchange, absorption, and multi-meson production. Pauli blocking is enforced for outgoing nucleons.
- An optional "formation zone" can be enabled, allowing newly produced mesons to free-stream for a distance $L_f$ before interacting, simulating the time required for a color singlet to form.

Key Contributions

Modular Design: The code is structured as independent modules (momentum, binding, kinematics, cascade), allowing users to swap nuclear models or decay channels without redesigning the core. It is released as open-source software with no external dependencies beyond the C++17 standard library.
Decoupling Nuclear Effects: The generator enables the isolation of Fermi motion (which controls the spectral width) from nuclear binding (which controls the spectral central value).
Channel-Specific FSI Quantification: It provides a detailed breakdown of meson survival probabilities across different decay modes, moving beyond generic efficiency assumptions.

Results
Using LUNAR, the authors analyzed the impact of nuclear effects on observable meson spectra and expected event yields for DUNE (assuming a 20 kt fiducial mass and 400 kt·yr exposure):

Spectral Shape: The width of the observable daughter momentum spectrum is determined by the choice of the momentum model (specifically the high-momentum tail content), while the central value is fixed by the binding model. The two uncertainties are largely orthogonal.
Final-State Interactions:
- $K^+$ Mode: The nucleus is nearly transparent to $K^+$ mesons. Approximately 99% escape without interaction, and FSI effects are negligible (a few percent shift in momentum).
- Pion, $\eta$ , and Antikaon Modes: These channels suffer significant suppression. Roughly 40–60% of pions, $\eta$ mesons, and antikaons are absorbed or charge-exchanged. For example, the $p \to e^+\pi^0$ yield is reduced by roughly 50% due to absorption.
- Formation Zone: Enabling the formation zone significantly increases the survival yield for strongly interacting pions (from ~49% to ~81% for $p \to e^+\pi^0$ at $L_f=1.0$ fm), identifying it as a leading systematic uncertainty for non-kaon channels.
Event Yields: Translating current Super-Kamiokande limits into expected DUNE yields reveals that while the "golden" $p \to K^+\bar{\nu}$ channel remains clean, other modes (e.g., $n \to \bar{\nu}K^0$ , $p \to \bar{\nu}\pi^+$ ) could see tens to hundreds of events. However, for these non-kaon modes, the FSI suppression is the dominant systematic effect, reducing rates by roughly half—an effect larger than the $\pm 10\%$ spread induced by the choice of nuclear momentum model.

Significance and Claims
The paper claims that LUNAR fills a critical gap for the nucleon-decay community by providing a dedicated, transparent tool that avoids the complexity of general-purpose neutrino generators. Its primary significance lies in:

Validating the "Golden" Channel: Reinforcing that $p \to K^+\bar{\nu}$ is the cleanest probe for liquid-argon detectors, as it is largely immune to nuclear FSI.
Quantifying Systematics: Demonstrating that for all other standard decay modes, final-state interactions are the leading correction, dominating over uncertainties in the nuclear initial state.
Utility: Offering a fast, extensible tool for signal efficiency studies, systematic uncertainty estimation (via the spread of nuclear models), and pedagogical exploration of nucleon decay physics.

The authors maintain a modest stance, acknowledging that the analytic momentum models are parametrized rather than fitted, the cascade uses representative cross sections, and detector response is not included. They position LUNAR as a foundational instrument for the nuclear physics of nucleon decay in liquid argon, intended to be extended and refined by the community.

1. The Problem: The Crowd Effect

2. The Solution: LUNAR

3. What the Simulation Revealed

Summary

Technical Summary: LUNAR – A Monte Carlo Generator for Bound-Nucleon Decay in Liquid Argon

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