Probing the nature of the $\chi_{c1}(3872)$ state using radiative decays

Using proton-proton collision data from the LHCb detector, this study observes the radiative decay $\chi_{c1}(3872)\rightarrow\psi(2S)\gamma$ for the first time and measures a branching ratio that challenges the interpretation of the $\chi_{c1}(3872)$ as a pure $D^0\bar{D}^{*0}$ molecule, strongly suggesting it contains a significant compact charmonium or tetraquark component.

The Gist

The Mystery of the "Ghost Particle"

Imagine you are a detective trying to figure out what a very strange, elusive object is made of. You have a suspect: a particle called $\chi_{c1}(3872)$.

For over 20 years, scientists have been arguing about this particle's identity. It's like a chameleon that changes its appearance depending on how you look at it.

• Theory A (The Molecular Theory): Some scientists think it's a "loose couple." Imagine two distinct houses (particles called $D^0$ and $D^{*0}$) standing next to each other in a field, barely holding hands. They are far apart, forming a "molecule."
• Theory B (The Compact Theory): Other scientists think it's a "tight-knit family." Imagine four people (quarks) huddled together in a tiny room, tightly bound. This could be a "tetraquark" or a standard "charmonium" particle.

The problem is that the particle looks like both. It's too heavy to be just a standard particle, but it's produced too easily to be just a loose couple.

The Experiment: A Flash of Light

To solve this mystery, the LHCb collaboration (a team of scientists using a giant particle detector at CERN) decided to watch how this particle "dies" or decays. Specifically, they looked at what happens when the particle emits a flash of light (a photon, $\gamma$).

Think of the $\chi_{c1}(3872)$ as a glowing firework. When it explodes, it can turn into two different types of fireworks:

1. Type 1: A standard firework called $J/\psi$.
2. Type 2: A larger, heavier firework called $\psi(2S)$.

The scientists asked a simple question: Which one does it prefer? Does it mostly make the standard firework, or does it surprisingly make the larger one?

The Discovery

Using data from billions of proton collisions (equivalent to 9 years of data collection), the team did two major things:

1. First Observation: They spotted the $\chi_{c1}(3872)$ turning into the larger firework ($\psi(2S)$) plus a photon for the very first time. Before this, they had only seen hints of it. Now, they have a confirmed sighting.
2. The Ratio: They counted how many times it made the small firework versus the large one. They found that the particle makes the large firework ($\psi(2S)$) about 1.67 times more often than the small one.

The Verdict: What is it made of?

This ratio is the "smoking gun" that solves the mystery.

• If it were a "Loose Couple" (Molecule): Theoretical calculations say a loose couple would almost never make the large firework. It would be like a loose couple trying to lift a heavy piano; they just don't have the strength. The prediction was that the large firework should be extremely rare (less than 1% of the time).
• If it were a "Tight Family" (Compact): Theoretical calculations say a tight family is strong enough to make the large firework frequently. The prediction was that the large firework should be common (more than 1 time for every small one).

The Result: The scientists found the large firework was made 1.67 times as often as the small one.

The Conclusion

The paper concludes that the "Loose Couple" theory is highly unlikely. The particle is too "strong" and "compact" to be just two distant houses holding hands.

Instead, the data strongly suggests that the $\chi_{c1}(3872)$ contains a significant "compact" component. It is likely a tight-knit group of quarks (a tetraquark) or a standard charmonium particle, perhaps mixed with a little bit of the "loose couple" behavior, but the core of it is definitely a tight, compact structure.

In short: The particle isn't a flimsy, distant relationship; it's a tightly bound, compact family. The "molecule" idea, if it exists at all, is only a small part of the story.

Technical Summary

Technical Summary: Probing the nature of the $\chi_{c1}(3872)$ state using radiative decays

Problem and Motivation
The internal structure of the $\chi_{c1}(3872)$ state (also known as $X(3872)$) remains one of the most significant open questions in hadron spectroscopy. While its mass is extremely close to the $D^0\bar{D}^{*0}$ threshold and its quantum numbers are $J^{PC} = 1^{++}$, its exact nature is debated. The proximity to the threshold and a large coupling to the $D^0\bar{D}^{*0}$ system support the interpretation of the state as a loosely bound $D^0\bar{D}^{*0} + \bar{D}^0 D^{*0}$ molecular state. However, the observed production cross-section in high-energy hadron collisions is significantly larger than theoretical predictions for a pure molecular object, suggesting a substantial compact component, such as a conventional charmonium ($\chi_{c1}(2P)$), a tetraquark ($c\bar{c}q\bar{q}$), or a mixture.

To distinguish between these hypotheses, the ratio of partial radiative decay widths, $R_{\psi\gamma} \equiv \Gamma(\chi_{c1}(3872) \to \psi(2S)\gamma) / \Gamma(\chi_{c1}(3872) \to J/\psi\gamma)$, serves as a critical diagnostic. Theoretical predictions for this ratio vary widely depending on the assumed structure: pure charmonium models predict $R_{\psi\gamma} \gtrsim 1$, while pure molecular models predict $R_{\psi\gamma} \ll 1$ (typically $< 0.5$), unless specific assumptions regarding coupling constants are made. Previous experimental measurements have yielded conflicting results, with BaBar and LHCb reporting values consistent with charmonium-like behavior, while Belle and BESIII reported upper limits or non-observations consistent with molecular interpretations.

Methodology
This study utilizes proton-proton collision data collected by the LHCb detector at center-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of 9 fb$^{-1}$ (Run 1 and Run 2). The analysis focuses on the decay chain $B^+ \to \chi_{c1}(3872)K^+$, followed by the radiative decays $\chi_{c1}(3872) \to \psi\gamma$, where $\psi$ represents either the $J/\psi$ or $\psi(2S)$ meson. The $\psi$ mesons are reconstructed via their dimuon decay modes ($\mu^+\mu^-$).

The event selection involves:

1. Reconstruction: Identification of muon and kaon candidates, and reconstruction of photons from electromagnetic calorimeter clusters.
2. Kinematic Selection: Requirements on transverse momentum ($p_T$) for muons and kaons, and transverse energy ($E_T$) for photons. The dimuon mass is constrained to the known $J/\psi$ or $\psi(2S)$ mass.
3. Background Suppression: A kinematic fit constrains the $B^+$ candidate to originate from the primary vertex and the dimuon mass to the known $\psi$ mass. Candidates with masses consistent with direct $B^+ \to \psi K^+$ decays are rejected.
4. Multivariate Analysis: A Multilayer Perceptron (MLP) classifier is trained separately for the $J/\psi\gamma$ and $\psi(2S)\gamma$ channels using simulated signal samples and data-driven or simulated background samples to further suppress combinatorial and physics backgrounds.

Signal yields are determined using extended unbinned maximum-likelihood fits to the two-dimensional distributions of the $\psi\gamma$ and $\psi\gamma K^+$ masses. The fit models include signal components parameterized by modified Gaussian functions (with power-law tails or bifurcated Gaussians) and various background components (combinatorial, partially reconstructed $B$ decays, and random combinations).

Key Contributions and Results
The primary contribution of this work is the first observation of the $\chi_{c1}(3872) \to \psi(2S)\gamma$ decay. The statistical significance of the signal is found to be 4.8$\sigma$ for Run 1 and 6.0$\sigma$ for Run 2.

The ratio of branching fractions, interpreted as the ratio of partial decay widths $R_{\psi\gamma}$, is measured by combining the results from Run 1 and Run 2, accounting for correlated systematic uncertainties. The final result is:
$$R_{\psi\gamma} = 1.67 \pm 0.21 \text{ (stat)} \pm 0.12 \text{ (syst)} \pm 0.04 \text{ (BF)}$$
where the third uncertainty arises from the branching fractions of the $\psi(2S)$ and $J/\psi$ mesons into dilepton final states.

The measured value of $R_{\psi\gamma} \approx 1.67$ is:

• In good agreement with previous measurements by BaBar and LHCb (Run 1).
• Consistent with theoretical predictions for a conventional charmonium $\chi_{c1}(2P)$ state, a compact tetraquark, or a molecular state mixed with a sizeable compact component.
• In tension with the upper limits set by the BESIII collaboration ($R_{\psi\gamma} < 0.59$) and the predictions for a pure $D^0\bar{D}^{*0}$ molecular state, which generally expect $R_{\psi\gamma} \ll 1$.

Significance
The paper concludes that the large measured value of $R_{\psi\gamma}$ makes the interpretation of the $\chi_{c1}(3872)$ as a pure $D^0\bar{D}^{*0} + \bar{D}^0 D^{*0}$ molecular state questionable. Instead, the result strongly indicates the presence of a sizeable compact component (either charmonium or tetraquark) within the wave function of the $\chi_{c1}(3872)$ state. This measurement provides a decisive constraint on theoretical models, favoring those that incorporate a compact core over those relying solely on a loosely bound molecular structure.