Search for proton decay via $p \to e^{+}\pi^{0}\pi^{0}$ and $p \to \mu^{+}\pi^{0}\pi^{0}$ in 0.401 megaton-years exposure of Super-Kamiokande I-V

Using 0.401 megaton-years of data from Super-Kamiokande I-V, this study conducted the first search for the proton decay modes $p \to e^{+}\pi^{0}\pi^{0}$ and $p \to \mu^{+}\pi^{0}\pi^{0}$, finding no significant signal above background and establishing new lower limits on their lifetimes that exceed previous experimental results by more than an order of magnitude.

The Gist

Imagine the universe is built out of tiny, indestructible LEGO bricks. For decades, physicists have believed that the most fundamental brick of all—the proton (which makes up the core of every atom in your body, the stars, and everything you see)—is eternal. It was thought to be the one thing in the universe that never breaks down.

But what if that brick does crumble?

This paper is the report from a massive, high-stakes treasure hunt conducted by the Super-Kamiokande experiment in Japan. Their goal? To catch a proton in the act of decaying (falling apart) into something else. Specifically, they were looking for a very rare and messy breakup where a proton turns into a positron (or an antimuon) and two neutral pions.

Here is the story of their hunt, explained simply.

1. The Giant Fish Tank

To catch a proton decay, you need a detector so huge that it can watch trillions of protons at once, waiting for one to finally give up.

Imagine a giant, cylindrical swimming pool buried deep underground in a Japanese mine. This is Super-Kamiokande. It holds 50,000 tons of ultra-pure water.

• The Walls: The tank is lined with over 11,000 giant, super-sensitive eyes (photomultiplier tubes).
• The Job: These eyes are waiting to see a flash of blue light called Cherenkov radiation. This light is like the "sonic boom" of light that happens when a particle zips through water faster than light can travel in water.

2. The Theory: Why Look for This?

For a long time, scientists only looked for the "clean" breakup of a proton: turning into a positron and one pion. It's like looking for a car crashing into a single tree.

However, new theories suggested that protons might also break into a "messier" pile: a positron and two pions. Think of it like a car crashing into two trees at once.

• Why it matters: If we find this "messy" crash, it proves that the universe's rules (specifically Grand Unified Theories) are even more complex and exciting than we thought. It would be a massive discovery, rewriting our understanding of how the universe began and how it might end.

3. The Challenge: The Noise in the Room

The hardest part of this experiment isn't building the tank; it's ignoring the noise.

Imagine you are trying to hear a single whisper in a stadium filled with cheering fans.

• The Whisper: The proton decay (the event we want).
• The Fans: Atmospheric neutrinos. These are ghostly particles raining down on Earth from space. They pass through the detector constantly, creating flashes of light that look almost exactly like a proton decaying.

The team had to filter out billions of "fan cheers" to find that one "whisper." They used a series of digital filters (cuts) to eliminate anything that didn't look exactly right:

• Was the event inside the "safe zone" (fiducial volume) of the tank?
• Did it have the right number of light rings?
• Did it have the right energy?

4. The Hunt: 0.401 Megaton-Years

The researchers didn't just look for a few days. They analyzed data collected over 25 years (from 1996 to 2020), covering five different phases of the detector's operation.

To put the scale in perspective: They watched 401,000 tons of water for a full year. That is equivalent to watching a mountain of water the size of a small city for a year, just to see if one single atom inside it decided to vanish.

5. The Results: The "Almost" Moments

After crunching the numbers, here is what they found:

• The Positron Search: They found one event that looked like a proton decaying into a positron and two pions.
• The Antimuon Search: They found one event that looked like a proton decaying into an antimuon and two pions.

But here is the twist: When they checked the math, these two events were perfectly consistent with the "noise" (the atmospheric neutrinos). It's like hearing a whisper in the stadium, but realizing it was just a fan dropping a soda can. It could have been the whisper, but it's more likely just background noise.

Conclusion: They did not find a proton decaying.

6. The Silver Lining: Setting the Record

Even though they didn't find the decay, they didn't come up empty-handed. In science, proving something doesn't happen is just as important as proving it does.

Because they watched so much water for so long and found nothing, they can now say with 90% confidence:

"If a proton does decay this way, it must be incredibly rare. It will take at least 72,000,000,000,000,000,000,000,000,000,000,000,000,000 years (7.2 × 10³³) for one to happen."

To put that in perspective: The universe is only about 13.8 billion years old. This new limit is trillions of times older than the universe itself.

Summary

The Super-Kamiokande team built a massive underwater eye to watch for the universe's most fundamental brick falling apart. They watched for decades, filtering out billions of false alarms. They found two suspicious events, but they turned out to be just background noise.

The takeaway: Protons are even more stubborn than we thought. They are holding together for longer than anyone predicted. While this means the universe is stable for a very, very long time, it also means the physicists have to keep building bigger, better detectors to find the one crack in the foundation that might finally explain how everything works.

Technical Summary

1. Problem Statement and Motivation

• Theoretical Context: Grand Unified Theories (GUTs) predict baryon number violation, implying that protons are unstable and can decay. While the dominant decay mode in many GUTs (e.g., SU(5), SO(10)) is assumed to be $p \to e^+\pi^0$ or $p \to \mu^+\pi^0$, theoretical studies suggest that three-body decays involving two neutral pions ($p \to \ell^+\pi^0\pi^0$) could have rates comparable to the two-body modes.
• Research Gap: Prior to this study, the IMB-3 experiment had searched for these modes but with limited sensitivity ($\sim 10^{32}$ years). There was no dedicated search for these specific three-body decay channels in the Super-Kamiokande (SK) detector, which has significantly larger exposure and better reconstruction capabilities.
• Objective: To perform the first search for proton decay into a charged anti-lepton ($e^+$ or $\mu^+$) and two neutral pions ($\pi^0\pi^0$) using the full dataset of Super-Kamiokande's pure water phases (SK-I through SK-V).

2. Methodology

Detector and Dataset

• Detector: Super-Kamiokande is a 50-kiloton cylindrical water Cherenkov detector located in Japan. It consists of an Inner Detector (ID) with 11,129 20-inch PMTs and an Outer Detector (OD) for vetoing cosmic rays.
• Exposure: The analysis utilized data from SK-I (1996–2001) through SK-V (2019–2020), covering a total exposure of 0.401 megaton-years.
• Fiducial Volume (FV): Events were selected from the "Fully Contained" (FC) region, defined as being at least 2 meters away from the ID wall, corresponding to a target mass of 22.5 kilotons ($\approx 7.5 \times 10^{33}$ protons).

Simulation and Background Modeling

• Signal Simulation: Monte Carlo (MC) samples were generated for both decay modes. The simulation accounted for:
  • Three-body decay kinematics.
  • Final state interactions (FSI) of pions within oxygen nuclei (absorption, scattering, charge exchange) using the NEUT package.
  • Distinctions between free protons (hydrogen) and bound protons (oxygen), the latter suffering from Fermi motion and binding energy effects.
• Background Modeling: The primary background is atmospheric neutrinos ($\nu_{atm}$). Simulations used the Honda flux model and NEUT for neutrino interactions, with detector response simulated via GEANT3. 500 years of MC background events were generated per phase and scaled to the actual livetime.

Event Selection Criteria

A "single-box" method was employed (as opposed to the "two-box" method used in previous two-body searches) because a significant fraction of free-proton signal events exceeded the momentum threshold used in the two-box split. The selection criteria (C1–C7) included:

1. Fully Contained (FC): All visible particles within the ID; vertex in FV; no hits in OD.
2. Ring Multiplicity: 3, 4, or 5 reconstructed Cherenkov rings.
3. Particle Identification (PID):
   • For $p \to e^+\pi^0\pi^0$: All rings must be "showering" (electron-like).
   • For $p \to \mu^+\pi^0\pi^0$: Exactly one ring must be "non-showering" (muon-like).
4. Michel Electron Tagging: No tagged Michel electrons for the electron mode; exactly one for the muon mode.
5. Neutron Tagging (SK-IV/V): No tagged neutrons (using 2.2 MeV $\gamma$ from H-capture) to suppress backgrounds.
6. Invariant Mass ($M_{rec}$): Reconstructed between 800 and 1050 MeV/c².
7. Total Momentum ($P_{rec}$): Reconstructed less than 200 MeV/c.

Systematic Uncertainties

Uncertainties were evaluated separately for each SK phase and included:

• Physics Models: Pion FSI in oxygen (dominant), Fermi momentum, correlated decay.
• Detector/Reconstruction: Fiducial volume definition, ring counting, PID efficiency, energy scale, and neutron tagging efficiency.
• Background: Neutrino flux, interaction cross-sections, and energy scale uncertainties.

3. Key Contributions

• First Search in SK: This is the inaugural search for $p \to e^+\pi^0\pi^0$ and $p \to \mu^+\pi^0\pi^0$ in the Super-Kamiokande detector.
• Expanded Dataset: It incorporates the full SK-I through SK-V dataset (0.401 Mton$\cdot$yr), significantly increasing statistical power over previous experiments.
• Methodological Refinement: The adoption of a "single-box" momentum cut and the use of neutron tagging (in SK-IV/V) optimized the sensitivity for these specific three-body topologies, which differ kinematically from the standard two-body decays.

4. Results

Observations

• Candidate Events:
  • $p \to e^+\pi^0\pi^0$: 1 candidate event observed (in SK-II).
  • $p \to \mu^+\pi^0\pi^0$: 1 candidate event observed (in SK-IV).
• Background Expectation:
  • Expected atmospheric neutrino background: 0.49 events for the electron mode and 0.90 events for the muon mode across all phases.
• Statistical Significance:
  • The observed events are consistent with the expected background.
  • Poisson probabilities for observing $\ge 1$ event given the background are 38.7% (electron mode) and 59.4% (muon mode).
  • Conclusion: No significant excess of signal events was found.

Lifetime Limits

Using a Bayesian method to combine results from all five SK phases, the study set the following lower limits on the partial proton lifetime at 90% Confidence Level (C.L.):

• $\tau/B(p \to e^+\pi^0\pi^0) > 7.2 \times 10^{33}$ years
• $\tau/B(p \to \mu^+\pi^0\pi^0) > 4.5 \times 10^{33}$ years

5. Significance

• Improved Sensitivity: These limits represent an improvement of more than one order of magnitude (approximately 50 times) compared to the previous best limits set by the IMB-3 experiment ($\sim 10^{32}$ years).
• Theoretical Constraints: The results provide the most stringent constraints to date on GUT models that predict significant three-body proton decay rates involving two neutral pions.
• Future Prospects: The analysis demonstrates the capability of Super-Kamiokande to probe complex multi-body decay modes. The upcoming SK-Gd phase (with Gadolinium loading) will further enhance neutron tagging efficiency, potentially lowering background rates and improving sensitivity in future searches.