Observation of the decay $\chi_{c1}(3872)\rightarrow J\mskip -3mu/\mskip -2mu\psi \mu^+\mu^-$

Using 9 fb$^{-1}$ of proton-proton collision data from the LHCb detector, this paper reports the first observation of the $\chi_{c1}(3872)\rightarrow J/\psi \mu^+\mu^-$ decay with a significance of 6.5$\sigma$ and measures its branching fraction relative to the $\chi_{c1}(3872)\rightarrow J/\psi \pi^+\pi^-$ mode to be $(1.68\pm 0.32\pm 0.05)\times10^{-3}$.

The Gist

The Great Particle Hunt: Finding a Ghost in the Machine

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful particle smasher. It shoots protons together at nearly the speed of light, creating a chaotic explosion of subatomic debris. Most of this debris is boring and predictable, but sometimes, hidden in the chaos, are rare, exotic particles that don't fit the standard rulebook of physics.

This paper reports on the LHCb experiment's successful hunt for one such rare event: a specific "ghost" decay of a particle called $\chi_{c1}(3872)$.

The Mystery Particle: $\chi_{c1}(3872)$

Think of the $\chi_{c1}(3872)$ as a mysterious guest at a party. We know it exists, and we know its name, but scientists are still arguing about what it actually is.

• Is it a standard "charmonium" particle (a heavy quark and its anti-quark holding hands)?
• Is it a "tetraquark" (four quarks stuck together)?
• Is it a "molecule" made of two other particles loosely bound together?

To solve this mystery, scientists need to watch how this particle behaves when it breaks apart. The more ways we can see it decay, the better we can understand its true nature.

The New Discovery: A Rare Breakup

For a long time, scientists knew that the $\chi_{c1}(3872)$ often breaks up into a $J/\psi$ (a heavy particle) and two pions (light particles). This is like the particle breaking a vase into a heavy pot and two small pebbles. It happens frequently.

However, this paper announces the first time anyone has seen the $\chi_{c1}(3872)$ break up into a $J/\psi$ and two muons (heavy cousins of electrons).

• The Analogy: Imagine you have a toy that usually breaks into a heavy block and two small marbles. You have seen this happen thousands of times. But suddenly, you see it break into a heavy block and two heavy bowling balls instead. It's the same toy, but a much rarer, stranger way of breaking.

The team analyzed data from 2011 to 2018 (about 9 "inverse femtobarns" of data, which is a fancy way of saying "a massive amount of collision records"). They found 60 of these rare events. The statistical certainty that this wasn't just random noise is 6.5 sigma. In the world of particle physics, 5 sigma is the gold standard for a "discovery," so 6.5 is a very confident "Yes, we saw it!"

How They Found It (The Detective Work)

Finding these rare events is like finding a specific needle in a haystack the size of a city, where the needle looks almost exactly like a piece of straw.

1. The Filter (Trigger): The computer system acts like a bouncer at a club, letting in only events that look promising (like having two muons).
2. The Detective (BDT): The team used a "Boosted Decision Tree" (BDT), which is essentially a super-smart computer algorithm trained to spot patterns. It was taught to distinguish between real muons and pions that pretended to be muons (a common trick in particle physics).
   • Analogy: Imagine a security guard who has to tell the difference between a real diamond and a piece of glass that looks like a diamond. The BDT is the guard who has studied thousands of diamonds and knows exactly how the light reflects off the real one.
3. The Comparison: To measure how rare this event is, they compared it to the common "pebble" decay ($J/\psi$ + pions). They found that for every 1,000 times the particle breaks into pebbles, it breaks into bowling balls (muons) about 1.7 times.

What This Means

The paper concludes that this rare decay happens with a branching fraction of roughly $1.68 \times 10^{-3}$ relative to the common decay.

• The Prediction Check: Before this experiment, a theoretical paper predicted this decay would happen about 4 times out of 100,000. The new measurement is roughly 7 times out of 100,000. While not an exact match, the new result is close enough to the prediction to say, "Okay, our current theories aren't totally wrong, but we need to look closer."

The Bottom Line

This paper doesn't claim to have solved the mystery of what the $\chi_{c1}(3872)$ is yet. Instead, it has opened a new door. By proving that this particle can decay into muons, scientists now have a new tool to study it.

The authors suggest that with even more data in the future, they might be able to see how the decay happens—whether it's driven by a "virtual photon" (a fleeting burst of light) or by the creation of other particles like the $\omega$ meson. This could finally help them decide if the $\chi_{c1}(3872)$ is a compact tetraquark, a loose molecule, or something else entirely.

In short: They found a very rare, strange way a mysterious particle breaks apart, confirming it exists and giving physicists a new clue to solve the 20-year-old mystery of what this particle really is.

Technical Summary

Technical Summary: Observation of the decay $\chi_{c1}(3872) \to J/\psi\mu^+\mu^-$

Problem and Motivation
Over the last two decades, the nature of the $\chi_{c1}(3872)$ state (formerly $X(3872)$) has remained a subject of intense debate within the field of hadron spectroscopy. While its existence and quantum numbers ($J^{PC} = 1^{++}$) are well-established, its internal structure is disputed, with hypotheses ranging from a compact tetraquark to a loosely bound $D^{*0}D^0$ molecule or a mixture of charmonium and molecular components. To elucidate this nature, further studies of its decay modes are required.

The decay $\chi_{c1}(3872) \to J/\psi\mu^+\mu^-$ is of particular interest as it involves a dimuon pair. Theoretical considerations suggest that at low dimuon masses, the decay is dominated by a virtual photon pole, while at higher masses, contributions from real $\rho^0$ and $\omega$ mesons are expected. The $\omega$ meson couples more strongly to the dimuon pair than the $\rho^0$, potentially making the $\omega$ contribution more prevalent in the $J/\psi\mu^+\mu^-$ mode compared to the analogous $J/\psi\pi^+\pi^-$ mode. Prior to this work, this decay channel had received little attention, with only a single theoretical estimate predicting a branching fraction of $(4.2 \pm 1.7) \times 10^{-5}$ based on Dalitz decay contributions. Additionally, the potential presence of the $\chi_{c0}(3915)$ state in the dimuon invariant-mass spectrum above the $\omega$ threshold was noted as a factor requiring consideration in background modeling.

Methodology
The analysis utilizes proton-proton collision data collected by the LHCb detector between 2011 and 2018, corresponding to an integrated luminosity of $9 \text{ fb}^{-1}$ (3 $\text{fb}^{-1}$ at $\sqrt{s} = 7, 8$ TeV and 6 $\text{fb}^{-1}$ at 13 TeV). The study focuses on displaced $\chi_{c1}(3872)$ candidates originating from the decay of long-lived beauty hadrons.

• Selection: The analysis selects $J/\psi \to \mu^+\mu^-$ candidates that are displaced from the primary interaction vertex. These are combined with a pair of oppositely charged tracks identified as muons (for the signal) or pions (for the normalization mode, $\chi_{c1}(3872) \to J/\psi\pi^+\pi^-$).
• Background Suppression: To reject background from pions misidentified as muons in the signal mode, a Boosted Decision Tree (BDT1) classifier is trained using simulation and validated with the control mode $\chi_{c1}(1P) \to J/\psi\mu^+\mu^-$. A second BDT (BDT2) is employed to reduce combinatorial background from random $J/\psi$ and muon combinations.
• Mass Modeling: The signal yield is extracted via an extended unbinned maximum-likelihood fit to the $J/\psi\mu^+\mu^-$ invariant mass distribution. The signal line shape is modeled by a Breit-Wigner function convolved with a double-sided Crystal Ball function. The combinatorial background is modeled by a first-order polynomial multiplied by a phase-space factor. The fit includes components for the $\chi_{c1}(3872)$ signal, combinatorial background, pion misidentification background, and a potential $\chi_{c0}(3915)$ contribution. Same-sign candidates ($J/\psi\mu^\pm\mu^\pm$) are used to constrain the background shape.
• Efficiency and Normalization: The branching fraction is measured relative to the abundant $\chi_{c1}(3872) \to J/\psi\pi^+\pi^-$ mode. Relative detection and selection efficiencies are evaluated using simulation, with corrections applied for particle identification (PID) and BDT performance differences between data and simulation.

Key Contributions and Results
The paper reports the first observation of the $\chi_{c1}(3872) \to J/\psi\mu^+\mu^-$ decay.

• Significance: The signal is observed with a statistical significance of $6.5\sigma$, including systematic uncertainties related to the mass model.
• Yields: The total fitted yield for the signal is $60 \pm 11$ events across Run 1 and Run 2. The fitted mass is $3872.58 \pm 0.83$ MeV. The yield for the $\chi_{c0}(3915)$ state is found to be $14 \pm 14$, indicating the current dataset is insufficient to draw strong conclusions about its presence in this channel.
• Branching Fraction Ratio: The ratio of branching fractions is measured as:
  $$\frac{\mathcal{B}(\chi_{c1}(3872) \to J/\psi\mu^+\mu^-)}{\mathcal{B}(\chi_{c1}(3872) \to J/\psi\pi^+\pi^-)} = (1.68 \pm 0.32 \pm 0.05) \times 10^{-3}$$
  where the first uncertainty is statistical and uncorrelated systematic, and the second is correlated systematic.
• Absolute Branching Fraction: Using the known branching fraction for the normalization mode, the absolute branching fraction is determined to be:
  $$\mathcal{B}(\chi_{c1}(3872) \to J/\psi\mu^+\mu^-) = (7.2 \pm 2.7) \times 10^{-5}$$
  This result is consistent with the theoretical prediction of $(4.2 \pm 1.7) \times 10^{-5}$ found in Ref. [15], which considers only the Dalitz contribution.

Significance of the Work
The authors state that this first observation may help elucidate the nature of the $\chi_{c1}(3872)$ state and identify potential avenues for future investigation. The paper notes that with a larger dataset, it will be possible to study the decay form factors to disentangle contributions from the virtual photon and $\rho^0$ or $\omega$ mesons. Furthermore, a larger dataset would allow for a more detailed investigation of the enhancement consistent with the $\chi_{c0}(3915)$ state to determine which states are present in this mass region. The work builds upon previous observations of similar muonic Dalitz decays of $\chi_c$ and $\chi_b$ mesons.