Search for the decays $X(3872)\to K_{S}^{0}K^{\pm}\pi^{\mp}$ and $K^*(892)\bar{K}$ at BESIII

Using a 10.9 fb$^{-1}$ data sample from the BESIII detector, researchers searched for the charmless decays $X(3872) \to K_{S}^{0}K^{\pm}\pi^{\mp}$ and $K^*(892)\bar{K}$ via the radiative process $e^+e^- \to \gamma X(3872)$ but found no significant signal, resulting in the establishment of upper limits on their relative branching fractions.

The Gist

The Mystery of the "Exotic" Particle: A Cosmic Detective Story

Imagine you are a master chef, and you’ve spent your whole life making perfect, standard recipes. You know exactly how a cake is made (flour, eggs, sugar) and how a loaf of bread is made (flour, water, yeast). But one day, you encounter a mysterious dish that looks like a cake, smells like bread, but has a texture that shouldn't exist according to any recipe book you’ve ever read.

In the world of particle physics, scientists have found a "dish" like this called the X(3872).

The Main Character: The X(3872)

Most particles in our universe are made of simple combinations of "quarks" (the tiny building blocks of matter). Usually, they come in predictable pairs or triplets. However, the X(3872) is a rebel. It doesn't fit the standard "recipe." Some scientists think it’s a "hadronic molecule"—essentially two separate particles hugging each other so tightly they act like one—while others think it’s a "tetraquark"—a single, complex structure made of four quarks.

Because we don't know its true "recipe," we have to study how it "breaks apart" (decays) to figure out what it’s made of.

The Mission: Searching for the "Charmless" Clues

The researchers at the BESIII experiment (a massive, high-tech microscope in China) decided to look for a very specific way this particle might break apart.

They were looking for "charmless" decays.

Think of it this way: The X(3872) is a heavy, complex meal that usually contains "charm" (a specific type of quark). Most of the time, when it breaks down, it leaves behind "charm" in the leftovers. The scientists wanted to see if the X(3872) could ever break down into something completely different—something made only of "light" particles (like kaons and pions) with no charm at all.

If they found these "charmless" leftovers, it would be like finding a chocolate cake that, when sliced, turns into nothing but strawberries and cream. That would tell us a huge amount about the "secret ingredients" inside the cake.

The Experiment: The High-Speed Camera

To do this, they used a giant particle collider to smash electrons and positrons together at incredibly high speeds. This creates a burst of energy that can "summon" the X(3872) particle into existence.

They then used the BESIII detector—a massive, multi-layered machine—to act like a high-speed camera, capturing the "shrapnel" left behind after the particle decays. They were specifically looking for two patterns of shrapnel:

1. A specific combination of kaons and pions.
2. A combination involving a "vector" particle (a more energetic type of particle).

The Result: A "Silent" Discovery

After scanning through a massive amount of data (equivalent to a huge digital library of collisions), the scientists had to deliver some surprising news: They found nothing.

They didn't see any significant signal of these "charmless" decays. In science, "finding nothing" is actually a very important result. It’s like a detective searching a room for a specific footprint and coming up empty. It doesn't mean the detective failed; it means they have successfully ruled out one possibility.

Why Does This Matter? (The "Upper Limit")

Because they didn't find the signal, they couldn't say exactly how often this decay happens. Instead, they set an "Upper Limit."

Imagine you are looking for a rare bird in a forest. You don't see it, but after searching for ten hours, you can say, "I can say with 90% certainty that there are fewer than five of these birds in this area."

That is what the scientists did. They said, "We didn't see the charmless decay, but we can say with 90% confidence that it happens less than X% of the time."

The Big Picture

This "nothing" result is actually a huge clue for theorists. It acts as a constraint. It tells the scientists who are writing the "math recipes" for the universe: "Your recipe for the X(3872) must be one where these charmless decays are extremely rare."

By narrowing down what the X(3872) cannot do, we are getting much, much closer to understanding what it actually is. We are slowly uncovering the secret recipe of one of the universe's most mysterious ingredients.

Technical Summary

Technical Summary: Search for the Decays $X(3872) \to K^0_S K^\pm \pi^\mp$ and $K^*(892) \bar{K}$ at BESIII

1. Problem and Motivation

The $X(3872)$ is a prominent candidate for an exotic hadron (such as a hadronic molecule, tetraquark, or a mixture of charmonium and exotic states) due to its proximity to the $D^0 \bar{D}^{*0}$ threshold and significant isospin violation in its decay modes. While many of its observed decay channels involve charm quarks (e.g., $J/\psi \pi^+ \pi^-$), investigating charmless decays—decays that do not contain charm quarks in the final state—is crucial for understanding its internal substructure.

This study specifically targets two charmless decay modes:

• $X(3872) \to K^0_S K^\pm \pi^\mp$: A light hadron decay.
• $X(3872) \to K^*(892) \bar{K}$: A vector-pseudoscalar ($VP$) decay.

Theoretical models, particularly those treating $X(3872)$ as a $\bar{D}D^*$ molecular state, predict specific branching fractions for these $VP$ modes based on intermediate meson loops. Measuring these provides a way to constrain model parameters (such as the cutoff scale $\alpha$).

2. Methodology

The analysis was performed using the BESIII detector at the BEPCII collider, utilizing a $10.9\text{ fb}^{-1}$ data sample collected at center-of-mass energies between $4.16$ and $4.34\text{ GeV}$.

• Production Process: The $X(3872)$ was searched for via the radiative process $e^+e^- \to \gamma X(3872)$.
• Event Selection:
  • Charged Tracks: Required exactly one identified kaon and three pion candidates with a total charge of zero. Particle identification (PID) utilized $dE/dx$ and Time-of-Flight (TOF) information.
  • $K^0_S$ Reconstruction: Reconstructed from $\pi^+\pi^-$ pairs with a secondary vertex fit and invariant mass constraints.
  • $K^*(892)$ Reconstruction: For the $VP$ mode, $K^*(892)$ candidates were identified through $K^\pm \pi^\mp$ or $K^0_S \pi^\pm$ invariant mass windows.
  • Kinematic Fitting: A four-constraint (4C) kinematic fit was applied to enforce energy-momentum conservation, significantly suppressing backgrounds.
  • Background Suppression: Specific vetoes were applied to suppress $\pi^0$ backgrounds (using recoil mass squared $M^2_{\text{recoil}}$) and non-radiative processes.
• Signal Extraction: An extended unbinned maximum likelihood fit was performed on the invariant mass distributions. The signal shape was modeled by convolving a Monte Carlo-derived shape with a Gaussian to account for detector resolution.

3. Key Contributions

• First Search in these Channels: This paper provides a dedicated search for these specific charmless decay modes of the $X(3872)$ in $e^+e^-$ collisions.
• Constraint on Molecular Models: By not finding a signal, the study establishes stringent upper limits that directly constrain the parameter space of theoretical models involving intermediate charmed meson loops.
• Systematic Rigor: The study provides a comprehensive breakdown of systematic uncertainties, distinguishing between additive (signal extraction) and multiplicative (efficiency, luminosity, etc.) sources.

4. Results

No significant signal for the $X(3872)$ was observed in either decay channel. Consequently, the collaboration established the following upper limits at the 90% confidence level (CL):

• Relative Branching Fractions:
  • $\mathcal{B}[X(3872) \to K^0_S K^\pm \pi^\mp] / \mathcal{B}[X(3872) \to \pi^+ \pi^- J/\psi] < 0.07$
  • $\mathcal{B}[X(3872) \to K^*(892) \bar{K}] / \mathcal{B}[X(3872) \to \pi^+ \pi^- J/\psi] < 0.10$
• Absolute Branching Fraction:
  • $\mathcal{B}[X(3872) \to K^*(892) \bar{K}] < 0.60 \times 10^{-2}$

The paper also reports upper limits on the product of the production cross-section and the branching fractions at various energy points (detailed in Table I of the paper).

5. Significance

The results have two major implications for hadron physics:

1. Theoretical Constraints: The upper limit for the $K^*(892) \bar{K}$ mode falls within the lower end of the range predicted by the $\bar{D}D^*$ molecular model. This provides a meaningful constraint on the model's parameter $\alpha$, helping to refine our understanding of whether $X(3872)$ is a molecule.
2. Charmonium Interpretation: The results are also consistent with the conventional charmonium interpretation ($\chi_{c1}(2P)$), as the calculated limits are of the same order of magnitude as the expected branching fractions for standard charmonium decays. This keeps the debate regarding the exact nature of the $X(3872)$ open but narrows the possibilities.