Understanding the impact of nuclear effects on proton decay searches with the GiBUU model

This study utilizes the GiBUU framework to demonstrate that while pion final-state interactions have a moderate impact on proton decay search sensitivity in water Cherenkov detectors, the choice of Fermi momentum distribution constitutes the dominant systematic uncertainty affecting atmospheric neutrino background estimates.

The Gist

The Great Proton Hunt: Why the "Noise" Matters More Than You Think

Imagine you are a detective trying to find a single, incredibly rare event: a proton (a tiny building block of matter) spontaneously vanishing and turning into a positron and a pion. This is the "Holy Grail" of particle physics because finding it would prove that the universe's fundamental forces are unified, a theory called Grand Unified Theory (GUT).

But here's the catch: Protons are so stubborn that they might live for $10^{35}$ years. That's 100,000,000,000,000,000,000,000,000,000,000,000 years. To catch one, scientists are building massive underwater detectors (like Hyper-Kamiokande) filled with 200,000 tons of pure water. They wait for a proton to "pop" and leave a specific signature: a flash of light in a perfect triangle shape.

The Problem: Most protons in that water aren't lonely; they are stuck inside oxygen atoms. When a proton inside an atom decays, it doesn't just vanish cleanly. It's like a firework exploding inside a crowded room. The debris (the particles created by the decay) bumps into the furniture (other protons and neutrons) before it can escape. This "bumping" scrambles the signal, making it hard to tell if you saw a real proton decay or just a random noise event.

This paper is about figuring out exactly how much that "crowded room" messes up the detective's view.

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The Detective's Toolkit: The "GiBUU" Simulator

The authors used a sophisticated computer program called GiBUU to simulate this process. Think of GiBUU as a hyper-realistic video game engine for nuclear physics.

• Old Way: Previous studies used "ad hoc" models. Imagine trying to predict how a billiard ball moves by just guessing, or using a simple rule like "it bounces off at a 45-degree angle." It's a rough approximation.
• The New Way (GiBUU): This model treats the nucleus like a busy, chaotic dance floor. It simulates every single collision, every push, and every pull between particles using the laws of physics (specifically, the Boltzmann transport equation). It's like simulating the entire dance floor rather than just guessing where the dancers will end up.

The Two Main "Culprits" of Confusion

The paper identifies two main reasons why the signal gets messy:

1. The "Fermi Motion" (The Wobbly Dancer)

Inside an atom, protons and neutrons aren't sitting still. They are jittering around with high speed, like bees in a jar. This is called Fermi Motion.

• The Analogy: Imagine trying to take a photo of a runner sprinting. If the runner is moving fast, the photo is blurry.
• The Impact: Because the decaying proton is already moving, the particles it creates don't fly out in a perfect, predictable pattern. They are "blurred."
• The Surprise: The authors found that the exact way you model this jitter matters a lot. If you assume the particles are jittering a bit more wildly (a "high-momentum tail" in the distribution), you get a lot more "fake" background noise that looks like a proton decay. This is the biggest source of uncertainty in their study.

2. The "Final-State Interactions" (The Bumpy Ride)

Once the decay happens, the new particles (specifically the neutral pion) have to travel through the rest of the atom to get out.

• The Analogy: Imagine a messenger trying to run out of a crowded stadium. On the way out, they might get tackled, bumped into a wall, or have their message stolen.
• The Impact: The pion might get absorbed (disappear), change its charge, or bounce off other particles. This changes the shape of the light flash the detector sees.
• The Finding: While this definitely messes up the signal, the authors found that their new model handles this "bumpy ride" reasonably well. The uncertainty here is moderate, not as scary as the Fermi Motion issue.

The Verdict: Are We Ready for the Next Big Detector?

The team compared their new, ultra-realistic simulation against the data from the current champion detector, Super-Kamiokande.

• The Good News: Their new model predicts a signal detection rate and background noise level that is almost identical to what the current experiments see. This gives us confidence that the new, massive Hyper-Kamiokande detector will work as expected.
• The Bad News (The Systematic Uncertainty): The paper highlights a hidden danger. If we are wrong about how much the protons are "jittering" (the Fermi momentum), our estimate of the background noise could be off by nearly 70%.
  • Why this matters: If you think there are fewer background noises than there actually are, you might think you found a proton decay when you didn't. Or, you might miss a real decay because you set your filters too high to avoid the "noise."

The Big Picture: Why This Paper Matters

This paper is like a mechanic telling a race car team: "Your engine is great, and your car will be fast. But if you don't account for how the wind changes at different speeds, you might crash."

By using the GiBUU model, the authors have provided a more consistent, unified way to understand the "noise" in the water. They aren't just guessing anymore; they are simulating the chaos of the atomic nucleus with high precision.

In short:

1. Proton decay is real (or will be found soon), but it's incredibly hard to spot because atoms are messy.
2. The "jitter" of protons inside atoms is the biggest source of confusion for scientists.
3. The new simulation tools confirm that the next generation of detectors (Hyper-Kamiokande) is on the right track, but scientists need to be very careful about how they calculate the background noise to avoid false alarms.

This work ensures that when we finally catch a proton decaying (if it happens), we know for sure it's a discovery and not just a trick of the light.

Technical Summary

1. Problem Statement

Proton decay is a unique prediction of Grand Unified Theories (GUTs), with the $p \to e^+ \pi^0$ channel being a primary target for next-generation water Cherenkov detectors like Hyper-Kamiokande (HK). Current limits from Super-Kamiokande (SK) are approaching $10^{34}$ years, and HK aims to probe the $10^{35}$ year regime.

At these sensitivity levels, systematic uncertainties arising from nuclear effects become the dominant limitation. Approximately 80% of protons in water are bound in oxygen nuclei. When a bound proton decays, the decay products are modified by:

• Initial-state effects: Fermi motion (FM), binding energy, and Short-Range Correlations (SRCs).
• Final-state interactions (FSIs): Rescattering, absorption, and charge exchange of the $\pi^0$ within the nucleus.

Previous studies often used "ad hoc" or factorized nuclear models (e.g., separate initial state models and intranuclear cascade generators like GENIE or NEUT) to estimate these effects. This paper argues that such approaches may not consistently model the interplay between signal (proton decay) and background (atmospheric neutrinos), potentially leading to biased sensitivity estimates.

2. Methodology

The authors employ the GiBUU (Giessen Boltzmann-Uehling-Uhlenbeck) transport model to provide a unified, self-consistent treatment of nuclear effects for both the signal and the background.

• Unified Framework: Unlike standard event generators that treat initial states and FSIs separately, GiBUU solves the Boltzmann transport equation, treating the entire reaction process (from initial interaction to particle exit) within a single dynamical framework.
• Signal Generation ($p \to e^+ \pi^0$):
  • Free Protons: Modeled as back-to-back emission with monoenergetic momentum (459 MeV/c).
  • Bound Protons (Oxygen): Simulated using two distinct initial-state models:
    1. Local Fermi Gas (LFG): Standard Thomas-Fermi model.
    2. Cioffi Degli Atti & Simula (CdA): Includes high-momentum tails representing SRCs.
  • FSIs: The $\pi^0$ propagates through the nuclear medium, undergoing absorption, charge exchange, and scattering. The model includes medium modifications such as Oset broadening (modification of the $\Delta$-resonance width) and in-medium cross-section suppression.
• Background Generation: Atmospheric neutrino interactions ($\nu$-nucleus) are simulated using the same GiBUU settings to ensure consistency. Secondary interactions (SIs) in water (e.g., $\pi^0$ production from secondary hadrons) are modeled using WCSim (Geant4-based).
• Detector Response: A mock detector response mimicking Super-Kamiokande's reconstruction performance (angular and momentum resolution, ring counting, particle ID) is applied to the simulated events.
• Analysis Strategy:
  • Events are classified using a probabilistic ternary classifier based on kinematic variables ($E_{e^+}$, $E_{\gamma\gamma}$, $\theta_{e^+-\gamma\gamma}$) to distinguish between Free Proton Decay, Bound Proton Decay, and Atmospheric Neutrino Background.
  • Sensitivity is projected using a Bayesian framework, calculating the 90% credible lower limit on the proton lifetime ($\tau$) for Hyper-Kamiokande.

3. Key Contributions

• Consistent Modeling: The first study to apply a single, unified transport model (GiBUU) to both the proton decay signal and the atmospheric neutrino background, eliminating inconsistencies found in previous factorized approaches.
• Quantification of SRC Impact: A rigorous evaluation of how Short-Range Correlations (via the CdA model) affect the search sensitivity, a factor often treated simplistically or ignored in previous background estimates.
• Systematic Uncertainty Breakdown: A detailed decomposition of systematic uncertainties into categories: Fermi Motion/SRCs, Pion FSIs, Neutrino Interactions, Flux, and Reconstruction.
• Secondary Interaction Analysis: Explicit inclusion of secondary hadronic interactions in water for atmospheric neutrino backgrounds, which can mimic proton decay signatures.

4. Key Results

• Signal Efficiency & Background Rates:
  • The total signal detection efficiency is estimated at ~38% (comparable to SK's reported ~38%), with a breakdown of 21.6% for the "Lower" momentum region ($<100$ MeV/c) and 17.4% for the "Upper" region ($100-250$ MeV/c).
  • The background rate without neutron tagging is 1.60 events/(Mton·years), consistent with SK predictions.
• Impact of Nuclear Models (LFG vs. CdA):
  • Signal Efficiency: The choice of Fermi momentum distribution (LFG vs. CdA) causes a moderate change in signal efficiency (~8% variation).
  • Background Rate: The CdA model (with high-momentum tails) induces a significant increase (~70%) in the estimated atmospheric neutrino background rate compared to LFG. This is because high-momentum nucleons allow neutrino interactions to produce low-recoil events that mimic the signal region.
• Impact of FSIs:
  • Pion FSIs cause a moderate uncertainty in signal efficiency (3-5%) but are the dominant source of uncertainty for the background rate (16%).
  • FSIs significantly distort the kinematic distributions (invariant mass and total momentum), causing bound proton decay events to migrate into the atmospheric background region.
• Sensitivity Projections:
  • The projected 90% confidence level sensitivity for Hyper-Kamiokande after 10 years is ~$10^{35}$ years.
  • The results are largely consistent with previous estimates (within 7-10%), but the study highlights that the systematic uncertainty on the background rate is dominated by the choice of the nucleon momentum distribution (SRCs), a factor not fully accounted for in previous SK analyses.

5. Significance

• Refining Future Limits: As experiments move into the $10^{35}$ year regime, statistical errors will decrease, making systematic uncertainties the limiting factor. This paper demonstrates that the treatment of nuclear effects (specifically SRCs and FSIs) is critical for accurate sensitivity projections.
• Methodological Advancement: By using GiBUU, the authors provide a framework that can rigorously consider correlations between signal and background systematic uncertainties, which are currently neglected in experimental analyses.
• Guidance for Future Searches: The study suggests that future proton decay searches must incorporate high-momentum tails (SRCs) in their background models to avoid underestimating the background rate. It also calls for a multi-probe approach (combining electron scattering, neutrino scattering, and proton decay data) to constrain nuclear models more tightly.

In conclusion, this work validates the sensitivity of next-generation detectors while providing a crucial correction to the understanding of systematic uncertainties, emphasizing that the choice of nuclear momentum distribution is the dominant systematic uncertainty in the search for proton decay.