Search for $\Xi^0p$, $\Omega^- p$, and $\Omega^- n$ dibaryons in $\Upsilon(1S)$ and $\Upsilon(2S)$ decays at Belle

Using data from 102 million $\Upsilon(1S)$ and 158 million $\Upsilon(2S)$ decays collected by the Belle detector, researchers found no evidence for $\Xi^0p$, $\Omega^-p$, or $\Omega^-n$ dibaryon states and established the first 90% confidence-level upper limits on their production branching fractions at the level of $O(10^{-7})$–$O(10^{-6})$.

The Gist

The Big Picture: Hunting for "Double-Decker" Particles

Imagine the universe is built out of tiny Lego bricks called baryons (like protons and neutrons). Usually, these bricks stick together in groups of three to form atoms, or they fly around alone. But physicists have long wondered: What if two of these bricks could stick together to form a tiny, double-decker "dibaryon" molecule?

Specifically, this paper looks for three special types of these double-decker molecules made of "strange" bricks (particles containing strange quarks):

1. $\Xi^0p$: A "strange" brick paired with a proton.
2. $\Omega^-p$: A very heavy "strange" brick paired with a proton.
3. $\Omega^-n$: A very heavy "strange" brick paired with a neutron.

Why do we care? Because understanding how these bricks stick together helps scientists figure out what happens inside neutron stars—the incredibly dense, crushed cores of dead stars. If these bricks can stick together easily, it changes our math for how neutron stars behave.

The Experiment: The "Cosmic Collision Course"

To find these rare molecules, the researchers used the Belle detector at the KEKB accelerator in Japan. Think of this machine as a giant, high-speed racetrack where they smash electrons and positrons (anti-electrons) together.

When these particles collide, they sometimes create a heavy, unstable particle called $\Upsilon$ (Upsilon). This particle is like a "glue factory." It is full of energy and, when it breaks apart, it spits out a shower of new particles. The researchers hoped that occasionally, this shower would accidentally snap two strange bricks together into one of the dibaryon molecules they were hunting for.

They looked at two different types of collisions:

• $\Upsilon(1S)$: 102 million collisions.
• $\Upsilon(2S)$: 158 million collisions.

That's a lot of collisions! It's like watching 260 million fireworks displays, hoping to spot one specific, rare color combination.

The Search: Looking for a Shadow

The researchers didn't just look for the molecules directly; they looked for the "footprints" they would leave behind.

• Bound States (The "Glued" Version): If the two bricks are stuck together tightly (bound), they act like a single, slightly heavier brick that decays slowly.
• Unbound States (The "Near-Miss" Version): If they are just barely touching or about to fly apart, they act like two separate bricks that are very close together.

The team used a sophisticated computer filter to sift through the data. They looked at the "invariant mass" (a way of measuring the total weight of the debris) to see if there was a pile-up of particles at a specific weight that matched their predictions.

The Analogy: Imagine you are looking for a specific type of rare coin in a massive pile of sand. You have a metal detector (the computer analysis) that beeps when it finds metal. You scan the whole pile, looking for a beep at the exact frequency of your rare coin.

The Results: The Silence of the Lab

After scanning all 260 million collisions, the metal detector never beeped for the rare coins.

• No Signal Found: There were no significant spikes in the data that indicated the existence of these $\Xi^0p$, $\Omega^-p$, or $\Omega^-n$ dibaryons.
• Setting Limits: Since they didn't find them, the paper sets a "limit." Think of this as saying: "If these molecules exist, they are so rare that we would have seen them at least once in 10 million tries. Since we didn't, they must be rarer than that."
  • They calculated that the chance of these molecules being created in these collisions is less than about 1 in 10 million to 1 in 1 million.

Why This Matters (According to the Paper)

Even though they didn't find the molecules, the paper is important because it provides new rules for the game.

1. Ruling Out Theories: Some computer models (like "Lattice QCD") suggested these molecules might be too weak to stick together. Other models (like "Soft-core potential") suggested they might stick together easily. By saying "we didn't see them," the researchers are telling the theorists: "Your models that predict these are common are likely wrong. You need to adjust your math."
2. Neutron Star Clues: Since these particles are relevant to neutron stars, knowing they don't form easily in these specific conditions helps scientists refine their models of what happens inside those dense stars.
3. First of Its Kind: This is the first time anyone has looked for these specific three types of dibaryons in this specific way (using Upsilon decays).

Summary

The researchers acted like cosmic detectives, sifting through 260 million high-energy collisions looking for a specific, rare type of "double-particle" molecule. They found nothing. While this might sound like a "failed" experiment, in science, a negative result is powerful: it tells us what doesn't exist, which helps us narrow down the search for how the universe is built. They have now set a strict "speed limit" on how often these molecules can appear, forcing theorists to update their blueprints of the subatomic world.

Technical Summary

Technical Summary: Search for $\Xi^0p$, $\Omega^-p$, and $\Omega^-n$ Dibaryons in $\Upsilon(1S)$ and $\Upsilon(2S)$ Decays

Problem and Motivation
Multistrange baryon-baryon interactions are critical for modeling dense matter in neutron stars, yet they remain poorly constrained experimentally. Theoretical frameworks, including lattice QCD and chiral effective field theory, suggest moderately attractive interactions in the $\Xi N$ system, though these are often insufficient to predict bound states. Conversely, phenomenological models and recent femtoscopy measurements by ALICE indicate stronger attractive interactions in the $\Omega N$ system, potentially sufficient to form weakly bound dibaryon states. This paper addresses the need for experimental data to discriminate among these theoretical descriptions by searching for $\Xi^0p$, $\Omega^-p$, and $\Omega^-n$ dibaryon states near their respective baryon-pair thresholds.

Methodology
The analysis utilizes data collected by the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. The dataset comprises 102 million $\Upsilon(1S)$ decays and 158 million $\Upsilon(2S)$ decays, corresponding to integrated luminosities of 5.75 fb$^{-1}$ and 24.9 fb$^{-1}$, respectively. Background estimation relies on 79.4 fb$^{-1}$ of data collected at a center-of-mass energy of 10.52 GeV.

The search strategy involves reconstructing specific decay chains for both bound-state and unbound (near-threshold) hypotheses:

• $\Xi^0p$ Channel: Reconstructed via $\pi^0 \Lambda p$. A bound-state hypothesis assumes a direct three-body decay, while the unbound hypothesis assumes a two-body configuration ($\Xi^0 \to \pi^0 \Lambda$).
• $\Omega^-p$ Channel: The bound-state hypothesis assumes a strong decay to $\Xi^0 \Lambda$ (reconstructed via $\Xi^0 \to \pi^0 \Lambda$), while the unbound hypothesis is reconstructed directly as $\Omega^- p$ (via $\Omega^- \to K^- \Lambda$).
• $\Omega^-n$ Channel: Reconstructed as $\Xi^- \Lambda$ (via $\Xi^- \to \pi^- \Lambda$) for the bound-state hypothesis. The unbound near-threshold configuration is not reconstructed due to the lack of direct neutron detection.

Selection criteria include kinematic fits, particle identification (proton, kaon, pion efficiencies $\sim$95%), and topological constraints (e.g., flight distances, vertex quality). The analysis combines $\Upsilon(1S)$ and $\Upsilon(2S)$ samples, justified by their similar hadronization dynamics via three-gluon intermediate states and the significant feed-down from $\Upsilon(2S) \to \pi\pi\Upsilon(1S)$.

Invariant-mass spectra are modeled using unbinned extended maximum likelihood fits. Signal shapes are defined by Gaussian functions (for bound $\Xi^0p$), Breit–Wigner convolved with Gaussians (for bound $\Omega$ states), and double-sided Crystal Ball functions (for unbound hypotheses). Backgrounds are modeled with polynomials or Argus-like threshold functions. Systematic uncertainties, totaling 4.6%–6.1%, are evaluated regarding fit models, reconstruction efficiencies, particle identification, and luminosity.

Key Contributions and Results
This work presents the first search for $\Xi^0p$, $\Omega^-p$, and $\Omega^-n$ dibaryons in $\Upsilon(1S)$ and $\Upsilon(2S)$ decays.

• Observation: No statistically significant signals consistent with dibaryon production were observed in any of the five analyzed final states across the scanned mass ranges (from 30 MeV below to 30 MeV above the baryon-pair thresholds).
• Upper Limits: In the absence of a signal, 90% confidence-level (CL) upper limits were set on the branching fractions of $\Upsilon(1S)$ and $\Upsilon(2S)$ decays to these dibaryon systems. The limits range from $O(10^{-7})$ to $O(10^{-6})$, depending on the specific channel and the assumed mass difference from the threshold.
• Sensitivity: The achieved sensitivity is comparable to previous dibaryon searches and is benchmarked against the measured branching fraction for antideuteron production in $\Upsilon$ decays.

Significance
The paper claims that these results provide new experimental constraints on the formation of multistrange dibaryons in gluon-rich bottomonium decays. By probing mass regions near thresholds with high statistics, the study complements existing searches in hadronic, nuclear, and heavy-ion environments. The null results help constrain theoretical models of baryon-baryon interactions, particularly regarding the strength of attractive forces in the $\Xi N$ and $\Omega N$ systems required to form weakly bound states.