Search for sub-GeV dark particles in $\eta\to\pi^0+\rm{invisible}$ decay

Using a sample of approximately 10 million $J/\psi$ events collected by the BESIII detector, this study reports the first search for the decay $\eta\to\pi^0S\to\pi^0\chi\bar{\chi}$ involving a dark scalar and invisible dark matter, finding no significant signal and setting stringent new limits on branching fractions and dark-matter-nucleon scattering cross sections that improve upon previous constraints by five orders of magnitude.

The Gist

The Big Picture: Hunting for the "Ghost" in the Machine

Imagine the universe is a giant, bustling city. We know that most of the "stuff" in this city (about 84% of it) is made of Dark Matter. It's like the invisible architecture holding the city together; we can't see it, we can't touch it, and it doesn't talk to light. We only know it's there because of how it pulls on the visible buildings (stars and galaxies) with gravity.

For decades, scientists have tried to catch this "ghost" by setting up giant traps underground, waiting for a dark matter particle to bump into an atom in their detector. But for sub-GeV dark matter (which is very light, like a feather compared to a bowling ball), these traps are useless. The ghost is too light to knock the atoms hard enough to trigger the alarm.

The New Strategy: Instead of waiting for the ghost to walk into a trap, the scientists at the BESIII experiment (a giant particle collider in China) decided to look for the ghost's footprints in a very specific, quiet corner of the city: the decay of a particle called the Eta ($\eta$).

The Plot: The "Magic Trick" of the Eta Particle

Think of the Eta particle as a magician. Usually, when this magician performs a trick, it splits into two visible things: a Neutral Pion ($\pi^0$) and some other standard particles. We can see the Pion clearly; it's like a bright flash of light.

The scientists asked a simple question: "What if, sometimes, the magician pulls a rabbit out of a hat, but the rabbit is invisible?"

In this scenario:

1. The Eta particle splits into a visible Pion (the flash of light).
2. It also splits into a Dark Scalar Boson ($S$), which is a new, invisible particle.
3. This invisible Boson immediately splits into two Dark Matter particles ($\chi$), which fly away unseen.

The result? The detector sees a Pion and... nothing else. It's like seeing a magician's hat, a flash of light, and then realizing the rest of the hat is empty, but the math says something must be missing.

The Investigation: How They Did It

The team used a massive dataset of 10 billion particle collisions (specifically $J/\psi$ events) collected by the BESIII detector. It's like reviewing 10 billion hours of security camera footage to find one specific, weird event.

The Process:

1. The Tag: They first identified the "magician" (the Eta particle) by looking at its partners (Kaons) in the collision.
2. The Search: They looked for cases where the Eta turned into a Pion (which they could see) and nothing else.
3. The Math: They calculated the "missing mass." If the Pion has less energy than the Eta should have given it, the difference must be the invisible Dark Matter.

The Results: The Ghost Remains Elusive (For Now)

After sifting through all that data, the scientists found no significant signal. They didn't see the "invisible rabbit."

However, in science, a "null result" is still a huge victory. Here is what they learned:

• Setting the Boundaries: Even though they didn't find the particle, they proved that if it does exist, it can't be too common. They set strict "speed limits" and "weight limits" on how often this invisible decay can happen.
• The New Record: They improved the constraints on how Dark Matter interacts with normal matter by 5 orders of magnitude (that's 100,000 times better than previous experiments).
  • Analogy: Imagine previous experiments could only detect a ghost if it was shouting. This experiment was sensitive enough to hear a ghost whispering. Even though they didn't hear the whisper, they proved the ghost isn't whispering that loudly.

Why This Matters

This paper is a game-changer for a few reasons:

1. New Hunting Ground: It proves that particle colliders (like the one in Beijing) are excellent places to hunt for light Dark Matter, a job usually reserved for underground detectors.
2. The "Flavor" Connection: The study suggests that if this invisible particle exists, it might interact with "up" quarks (a type of building block of matter) in a very specific way. This gives theorists new clues on how to build their models.
3. Future Hope: While they didn't find the particle, they cleared the path. Future experiments (like REDTOP or HIAF) will have even more data. If the "invisible rabbit" is hiding in this specific spot, these new, bigger experiments might finally catch it.

The Bottom Line

The BESIII team looked for a ghost in the machine by watching a particle magician perform a trick. They didn't see the ghost, but they proved that if the ghost is there, it's much quieter and more elusive than we thought. This narrows down the search for the universe's missing mass and brings us one step closer to understanding what 84% of our universe is actually made of.

Technical Summary

1. Problem Statement

Dark matter (DM) constitutes approximately 84% of the universe's matter content, yet its fundamental nature remains unknown within the Standard Model (SM). While direct detection experiments have established strong constraints on GeV-scale DM, sub-GeV DM (masses below 1 GeV) remains elusive.

• The Challenge: Sub-GeV DM particles have non-relativistic velocities, resulting in nuclear recoil energies below the detection thresholds of traditional direct detection experiments.
• The Opportunity: Collider experiments offer a model-independent approach to search for sub-GeV DM by looking for "invisible" decays of mesons. Specifically, the decay $\eta \to \pi^0 S \to \pi^0 \chi \bar{\chi}$ (where $S$ is a dark scalar mediator and $\chi$ is invisible dark matter) represents a promising channel. This process is theoretically linked to DM-nucleon scattering, allowing collider searches to constrain the same interaction parameters as direct detection experiments but with different systematic uncertainties.

2. Methodology

Data Source and Dataset:

• Experiment: BESIII detector at the BEPCII collider.
• Dataset: $(10087 \pm 44) \times 10^6$ $J/\psi$ events collected at a center-of-mass energy of $\sqrt{s} = 3.097$ GeV.
• Production Channel: The analysis utilizes the $J/\psi \to \phi \eta$ process, chosen for its low background and high production yield.

Event Selection Strategy:

1. Tagging ($\eta$ Inclusive Decay Tag - IDT):

   • Select $J/\psi \to \phi \eta$ events where $\phi \to K^+ K^-$.
   • Identify $K^+ K^-$ pairs with an invariant mass in the $\phi$ region $[1.00, 1.04]$ GeV/$c^2$.
   • The $\eta$ meson is identified inclusively via the recoil mass of the $K^+ K^-$ system ($0.45 < M_{\text{recoil}}^{KK} < 0.65$ GeV/$c^2$).
   • A kinematic fit constrains the recoil mass to the nominal $\eta$ mass.
   • Resulting Sample: $N_{\text{IDT}} = (2185.3 \pm 3.4) \times 10^3$ $\eta$ mesons.

2. Signal Search ($\eta \to \pi^0 S$):

   • Search for $\eta \to \pi^0 S$ where $\pi^0 \to \gamma\gamma$ and $S$ decays invisibly to $\chi\bar{\chi}$.
   • Selection Criteria:
     • Exactly two charged tracks (the $K^+ K^-$ from the tag).
     • At least two photon candidates forming a $\pi^0$ ($M_{\gamma\gamma} \in [0.115, 0.150]$ GeV/$c^2$).
     • Kinematic fit constraining $M_{\gamma\gamma}$ to the $\pi^0$ mass.
     • Background Suppression:
       • Total energy of extra photons ($E_{\text{tot}}^{\text{oth.}\gamma}$) $< 0.1$ GeV.
       • Recoil angle of $K^+ K^- \pi^0$ ($\cos \theta_{\text{recoil}}$) restricted to $[-0.7, 0.7]$.
       • Invariant mass $M_{K^+ K^- \pi^0}$ optimized using the Punzi method to maximize signal-to-noise. Three distinct mass ranges for $S$ ($m_S$) were analyzed with specific $M_{K^+ K^- \pi^0}$ cuts:
         • Type I ($0 \le m_S < 165$ MeV/$c^2$): $M < 2.7$ GeV/$c^2$.
         • Type II ($165 \le m_S < 305$ MeV/$c^2$): $M < 2.15$ GeV/$c^2$.
         • Type III ($305 \le m_S \le 400$ MeV/$c^2$): $M < 2.0$ GeV/$c^2$.

3. Signal Extraction:

   • The signal yield is extracted via an unbinned extended maximum likelihood fit to the squared missing mass distribution ($M_{\text{miss}}^2$).
   • $M_{\text{miss}}^2 = (E_{\text{c.m.}} - \sum E_i)^2/c^4 - (\sum \vec{P}_i)^2/c^2$, where $i$ represents the $K^+, K^-, \pi^0$.
   • Signal significance is calculated as $\sqrt{2 \ln(L/L_0)}$.

4. Systematic Uncertainties:

   • Key sources include IDT yield extraction (0.7%), photon detection (0.5% per photon), kinematic fit requirements, and fitting strategy variations.
   • Total systematic uncertainty ranges from 2.1% to 2.5% depending on the $m_S$ hypothesis.

3. Key Contributions

• First Search: This is the first search for sub-GeV dark particles in the specific decay channel $\eta \to \pi^0 S \to \pi^0 \chi \bar{\chi}$ with an on-shell scalar mediator $S$.
• Model Framework: The analysis adopts a flavor-specific scalar model where the dark scalar $S$ couples to the first-generation SM quarks ($u, d$) and the Dirac fermion DM $\chi$. This allows for a direct translation of the branching fraction limits into constraints on the coupling strength $g_u$ (or $g_d$) and the DM-nucleon scattering cross-section.
• Complementarity: The study demonstrates that collider searches for meson decays can provide constraints on DM-nucleon interactions that are independent of astrophysical DM flux models, complementing direct detection experiments like PandaX-4T.

4. Results

• Observation: No significant signal excess was observed over the background for $m_S$ ranging from 0 to 400 MeV/$c^2$. The maximum signal significance was found to be less than $2\sigma$ (at $m_S = 240$ MeV/$c^2$).
• Branching Fraction Limits: Upper limits (ULs) on the branching fraction $\mathcal{B}(\eta \to \pi^0 S)$ were set at the 90% confidence level (CL).
  • Range: $(1.8 \sim 5.5) \times 10^{-5}$.
• Coupling Strength Limits: Based on the flavor-specific model, upper limits on the coupling strength between the scalar $S$ and up-quarks ($g_u$) were derived.
  • Range: $(1.3 \sim 3.2) \times 10^{-5}$.
• Comparison with Other Experiments:
  • The constraints on $g_u$ are 3.3 to 18.3 times stronger than previous limits from the PandaX-4T direct detection experiment (which measured DM-nucleon scattering mediated by $S$).
  • The results improve upon constraints from $K^+ \to \pi^+ + \text{invisible}$ searches (NA62, E949) in specific mass regions.
• Dark Matter-Nucleon Cross-Section:
  • The derived limits on the DM-nucleon scattering cross-section ($\bar{\sigma}_n$) improve the sensitivity of current direct detection experiments by approximately 5 orders of magnitude for sub-GeV DM masses (assuming $m_S = 300$ MeV/$c^2$ and $g_\chi = 1$).
  • The analysis also probes the "thermal relic" parameter space, excluding regions for $g_\chi = 0.1$.

5. Significance

• Probing New Physics: The results provide stringent constraints on light scalar mediators and sub-GeV dark matter, exploring parameter spaces that are inaccessible to traditional nuclear recoil experiments due to energy threshold limitations.
• Validation of BESIII Capabilities: The study highlights the unique potential of the BESIII experiment to study invisible decays due to its low-background environment and high statistics of $J/\psi$ events.
• Future Outlook: While current $\eta$ factories (like REDTOP) may struggle with background levels for such searches, the results suggest that future super tau-charm facilities (planning to collect $10^{12}$ $J/\psi$ events) could significantly extend the sensitivity to even smaller coupling strengths. Additionally, the strategy can be extended to $\eta' \to \pi^0 S$ to probe masses up to ~800 MeV/$c^2$.

In conclusion, this paper establishes a new, highly sensitive frontier for searching for sub-GeV dark matter using meson decays, effectively bridging the gap between collider physics and direct detection constraints.