Search for the lepton number violating decay $η\to π^+π^+e^-e^- + c.c.$ via $J/ψ\toϕη$

Using a sample of $(10.087\pm 0.044)\times 10^{9}$ $J/\psi$ events collected by the BESIII detector, this study reports the first search for the lepton number violating decay $\eta\to \pi^+\pi^+ e^-e^- + \text{c.c.}$, finding no signal and setting an upper limit on its branching fraction of $4.6 \times 10^{-6}$ at the 90% confidence level.

The Gist

Imagine the universe as a giant, incredibly complex rulebook. For decades, physicists have been trying to read every page of this book, known as the Standard Model, to understand how the smallest building blocks of reality behave. One of the most sacred rules in this book is the Law of Conservation of Lepton Number.

Think of "Lepton Number" like a cosmic currency. Electrons and neutrinos are the "coins." The rule says: You can't create or destroy coins out of thin air. If you start with zero coins, you must end with zero coins. If you have a positive coin, you must balance it with a negative one.

The Big Question: Is the Rulebook Wrong?

For a long time, scientists suspected there might be a hidden loophole. They wondered: What if these coins can actually be their own opposites? If a particle called a Majorana neutrino exists, it could break the rule, allowing two "negative" coins to appear where there were none before. This would be a massive discovery, proving that the universe has a secret way of creating matter from nothing, which could explain why we exist at all instead of just empty space.

The Experiment: The Great Cosmic Hunt

The paper you shared describes a massive hunt for this "forbidden" event. The scientists, working at the BESIII detector in Beijing (a giant, high-tech camera for subatomic particles), decided to look for a specific, impossible reaction:

The Target: They wanted to see an Eta meson (a short-lived particle) spontaneously turn into two positive pions and two negative electrons.

• The Problem: In the standard rulebook, this is impossible. It's like watching a perfectly balanced scale suddenly tip because two heavy weights appeared on one side without any source.
• The Method: They didn't just wait for an Eta meson to appear. They used a "factory" called the J/ψ particle. Think of the J/ψ as a heavy delivery truck. When it crashes, it often drops off an Eta meson and a Phi particle (which quickly turns into two K-mesons).

The "Blind" Search

To ensure they didn't cheat or get lucky by guessing where to look, the scientists used a Blind Analysis.

• The Analogy: Imagine a detective searching a dark room for a specific, rare coin. They set up their search grid and rules before they turn on the light. They don't look at the floor until the rules are locked in. This prevents them from accidentally "finding" what they want to see just because they were hoping for it.

The Result: Silence is Golden

After analyzing over 10 billion J/ψ collisions (that's a lot of truck crashes!), they looked at the data.

• What they expected: If the "Majorana neutrino" loophole exists, they should have seen a few events where the Eta meson broke the rules.
• What they found: Zero. Not a single event. The scale remained perfectly balanced. The "forbidden" decay did not happen.

The Conclusion: Setting a New Limit

Since they didn't find the "magic" event, they didn't give up. Instead, they set a new speed limit for how rare this event could possibly be.

• The Metaphor: Imagine you are looking for a needle in a haystack. You dig through a haystack the size of a mountain and find nothing. You can't say the needle doesn't exist, but you can say, "If it is there, it must be so rare that it's less than 1 in 200,000,000."
• The Paper's Finding: They calculated that if this forbidden decay happens at all, it occurs less than 4.6 times in every 1 million Eta mesons.

Why Does This Matter?

Even though they didn't find the "smoking gun," this is a huge victory for science.

1. Ruling Out Possibilities: It tells theorists, "Hey, if you are building a new theory about the universe, you can't make the rules too loose. Your theory must respect this new limit."
2. Refining the Search: It's like narrowing down the search area for a lost ship. We know it's not in this specific ocean; now we know where to look next.
3. The Quest Continues: The hunt for the Majorana neutrino and the secrets of the universe's matter-antimatter imbalance is still wide open. This paper just drew a very precise line in the sand, saying, "We haven't crossed it yet."

In short: The BESIII team took a giant, high-tech snapshot of 10 billion particle collisions, looking for a magical rule-breaking event. They didn't find it, but by proving how rare it is, they helped the rest of the physics world write a more accurate version of the universe's rulebook.

Technical Summary

1. Problem and Motivation

The Standard Model (SM) of particle physics conserves total lepton number ($L$). However, the observation of neutrino oscillations implies that neutrinos have mass, which suggests the possibility of Lepton Number Violating (LNV) processes.

• Theoretical Context: If neutrinos are Majorana particles (their own antiparticles), LNV processes with a change in lepton number of two ($|\Delta L| = 2$) are expected. Such processes are crucial for understanding the origin of neutrino mass (via the seesaw mechanism) and could explain the baryon-antibaryon asymmetry in the universe.
• The Gap: While extensive searches have been conducted at high-energy colliders (LHCb, CMS, ATLAS) and in nuclear experiments (neutrinoless double beta decay), no significant LNV signal has been found.
• Specific Goal: This paper presents the first experimental search for the LNV decay of the $\eta$ meson into two pions and two electrons: $\eta \to \pi^+\pi^+e^-e^-$ (and its charge conjugate). This decay is strictly forbidden in the SM.

2. Methodology

Data Sample and Detector

• Dataset: The analysis utilizes a sample of $(10.087 \pm 0.044) \times 10^9$ $J/\psi$ events collected by the BESIII detector at the BEPCII collider.
• Production Mechanism: The search focuses on the decay chain:
  $$J/\psi \to \phi \eta, \quad \phi \to K^+K^-, \quad \eta \to \pi^+\pi^+e^-e^-$$
• Blind Analysis: To avoid bias, a blind analysis technique was employed. The signal region was defined and the analysis procedure fixed using Monte Carlo (MC) simulations before unblinding the data.

Event Selection and Reconstruction

• Track Requirements: Events were required to have at least six charged tracks ($K^+, K^-, \pi^+, \pi^+, e^-, e^-$) consistent with the hypothesis $e^+e^- \to K^+K^-\pi^+\pi^+e^-e^-$.
• Particle Identification (PID): Charged tracks were identified using specific ionization energy loss ($dE/dx$) in the MDC, time-of-flight (TOF), and energy deposition in the EMC. Confidence levels were calculated for electron, kaon, and pion hypotheses.
• Kinematic Fit: A 4-constraint (4C) kinematic fit was applied, constraining the total four-momentum to the initial $e^+e^-$ collision energy. The optimal $\chi^2_{4C}$ cut was determined to be $< 20$ for the signal channel.
• Signal Region: A 2D signal region was defined based on invariant masses:
  • $M_{\pi^+\pi^+e^-e^-} \in [0.530, 0.564] \, \text{GeV}/c^2$ (around the $\eta$ mass).
  • $M_{K^+K^-} \in [1.008, 1.031] \, \text{GeV}/c^2$ (around the $\phi$ mass).

Normalization Strategy

To minimize systematic uncertainties associated with the branching fraction of the production process $B(J/\psi \to \phi\eta)$, the analysis used a relative measurement against a reference channel:

• Reference Channel: $J/\psi \to \phi\eta, \phi \to K^+K^-, \eta \to \gamma\gamma$.
• Formula: The branching fraction of the signal is calculated as:
  $$B(\eta \to \pi^+\pi^+e^-e^-) = B(\eta \to \gamma\gamma) \times \frac{N_{\text{net}}^{\pi^+\pi^+e^-e^-}}{N_{\text{net}}^{\gamma\gamma}} \times \frac{\epsilon_{\gamma\gamma}}{\epsilon_{\pi^+\pi^+e^-e^-}}$$
  Where $N_{\text{net}}$ represents the net yield and $\epsilon$ represents the detection efficiency.

Background Estimation

• Inclusive MC: An inclusive MC sample was used to estimate backgrounds from other $J/\psi$ decays.
• Result: Only two background events were found in the inclusive MC, and both were located well outside the defined signal region. No background events were observed in the actual data within the signal region.

3. Key Contributions

1. First Search: This is the world's first experimental search for the LNV decay $\eta \to \pi^+\pi^+e^-e^-$.
2. High-Precision Normalization: By normalizing to the well-measured $\eta \to \gamma\gamma$ channel, the analysis effectively cancels out the large uncertainty (approx. 11%) associated with the $J/\psi \to \phi\eta$ branching fraction.
3. Comprehensive Systematics: The study provides a rigorous evaluation of systematic uncertainties, including tracking, PID, kinematic fitting, photon detection, and MC modeling, resulting in a total systematic uncertainty of 7.5%.

4. Results

• Signal Observation: No signal events were observed in the signal region of the data.
• Upper Limit Calculation: Using a frequentist method with an unbounded profile likelihood treatment (assuming Poisson background fluctuations and Gaussian efficiency/systematic uncertainties), the upper limit on the signal yield was set to $N_{\text{up}} = 17.81$ at the 90% Confidence Level (CL).
• Branching Fraction Limit: The resulting upper limit on the branching fraction is:
  $$B(\eta \to \pi^+\pi^+e^-e^-) < 4.6 \times 10^{-6} \quad (\text{at } 90\% \text{ CL})$$

5. Significance

• New Physics Constraints: This result provides the first experimental constraint on LNV processes specifically within the $\eta$ meson sector.
• Complementarity: The limit complements constraints from other experiments (like neutrinoless double beta decay and searches in $K$ and $D$ mesons), helping to narrow down the parameter space for Majorana neutrino masses and other Beyond-Standard-Model (BSM) theories.
• Future Impact: While no LNV was found, the methodology establishes a benchmark for future searches in light hadrons. A future observation of this decay would be a definitive discovery of physics beyond the Standard Model, potentially confirming the Majorana nature of neutrinos.