A comparative study of $T_{cc}$ versus $X(3872)$ production in $pp$ collisions at $\sqrt{s}=$ 7 TeV

This paper utilizes the PACIAE and DCPC models to compare $T_{cc}$ and $X(3872)$ production in 7 TeV $pp$ collisions, revealing significant differences in transverse momentum spectra between compact tetraquark and molecular states that can serve as experimental criteria for distinguishing their internal structures.

The Gist

Imagine the universe as a giant, high-speed particle collider, like a cosmic race track where tiny building blocks of matter crash into each other at incredible speeds. When these collisions happen, they sometimes create rare, exotic "creatures" made of quarks (the fundamental pieces of matter). Two of these creatures are the X(3872) and the Tcc.

Scientists have been arguing about what these creatures actually are. Are they tight, compact balls of four quarks stuck together (like a solid marble)? Or are they loose, fluffy clouds of two separate particles orbiting each other (like a double-star system)?

This paper is like a detective story where the authors use a computer simulation to figure out which of these two descriptions is correct. Here is how they did it, explained simply:

The Simulation: A Cosmic Kitchen

The researchers used a virtual kitchen called PACIAE (a model that simulates how particles collide and cook up new matter). They set the temperature to the equivalent of a 7 TeV collision (a very high-energy crash, similar to what happens at the Large Hadron Collider).

In this kitchen, they tried to bake the X(3872) and Tcc in two different ways:

1. The "Compact" Recipe: Mixing four ingredients (quarks) together all at once to form a tight ball.
2. The "Molecular" Recipe: First baking two separate cakes (mesons), and then gently sticking them together to form a pair.

The Findings: What the Simulation Told Them

1. The "Double Trouble" Problem (Yields)
The simulation showed that making the Tcc (which needs two heavy charm quarks) is much harder and rarer than making the X(3872) (which only needs one charm and one anti-charm).

• Analogy: Imagine trying to bake a cake that requires two rare, expensive gold eggs versus a cake that only needs one. The gold-egg cake will naturally be much harder to find in the bakery.
• Result: The X(3872) was produced much more often than the Tcc, regardless of whether it was a "compact" ball or a "loose" pair.

2. The Speed Test (Transverse Momentum)
The researchers looked at how fast these particles were moving sideways when they were born.

• Analogy: Imagine two groups of runners. One group is running as a tight, single unit (the compact ball), and the other is running as a pair holding hands loosely (the molecule).
• Result: The simulation showed that the "tight ball" version and the "loose pair" version move differently. If you measure their speeds carefully, you can tell them apart. The "tight ball" tends to have a different speed distribution than the "loose pair."

3. The Mirror Test (Asymmetry)
The Tcc comes in two flavors: a positive version ($T^+_{cc}$) and a negative version ($T^-_{cc}$). The researchers checked if the kitchen produced equal amounts of both.

• Analogy: Imagine a factory that makes left-handed and right-handed gloves. If the factory is perfectly balanced, it makes 50/50. But if the machinery is biased, it might make more left-handed gloves.
• Result: The simulation found a big difference in how many positive vs. negative Tcc particles were made, depending on whether they were "tight balls" or "loose pairs."
  • At low speeds, the "loose pair" showed a bigger imbalance between positive and negative versions.
  • At high speeds, the "tight ball" showed a bigger imbalance.
  • This difference acts like a fingerprint to identify which structure is real.

4. The "Glue" Factor (Coalescence Parameters)
Finally, they calculated a "glue parameter." This measures how close the ingredients need to be to stick together.

• Analogy: Think of it as the "stickiness" required to make the particle. If the ingredients need to be very close (a small room) to stick, it's a compact ball. If they can be far apart (a large room) and still stick, it's a loose molecule.
• Result: The simulation showed that as the particles move faster, the "room" they need to stick together gets smaller. This helps scientists understand the size of the source where these particles are born.

The Bottom Line

The paper concludes that by looking at how fast these particles are moving, how many of them are made, and whether there are more positive or negative versions, scientists can tell the difference between a "tight ball" of quarks and a "loose pair" of particles.

The authors suggest that future experiments should use these specific "speed" and "counting" clues to solve the mystery of what the Tcc and X(3872) really are inside. They also plan to look at these particles in heavy-ion collisions (even bigger crashes) in the future to see if the results hold up.

Technical Summary

Technical Summary: A Comparative Study of $T_{cc}$ versus $X(3872)$ Production in $pp$ Collisions at $\sqrt{s} = 7$ TeV

Problem Statement
The internal structure of exotic hadrons remains a subject of significant debate within Quantum Chromodynamics (QCD). While the quark model successfully classifies conventional baryons and mesons, the discovery of "XYZ" states, such as $X(3872)$ and the doubly charmed tetraquark $T_{cc}(3875)$, challenges this framework. These states are hypothesized to exist either as compact tetraquarks or as loosely bound hadronic molecules. Despite numerous theoretical interpretations, distinguishing between these configurations experimentally is difficult. This paper addresses the need for observable criteria to differentiate between compact tetraquark and molecular configurations for $T_{cc}$ ($cc\bar{u}\bar{d}$) and $X(3872)$ ($c\bar{c}u\bar{u}$ or $c\bar{c}d\bar{d}$) in proton-proton ($pp$) collisions.

Methodology
The authors employ a two-step simulation framework combining the Parton and Hadron Cascade Model (PACIAE) with the Dynamically Constrained Phase-Space Coalescence (DCPC) model.

1. PACIAE: Used to simulate $pp$ collisions at $\sqrt{s} = 7$ TeV. The process is divided into four stages: initial parton generation (via PYTHIA with hadronization disabled), parton rescattering (using LO-pQCD cross-sections), hadronization, and hadronic rescattering. The model parameters were tuned to ALICE data for $D^0$ and $D^+$ yields at $\sqrt{s} = 2.76$ TeV.
2. DCPC: Applied to form the exotic states from the constituents generated by PACIAE.
   • Compact Tetraquark Scenario: Formed at the partonic level (Partonic Final State, PFS) via the coalescence of four constituent quarks ($c, \bar{c}, q, \bar{q}$).
   • Loose Molecular Scenario: Formed at the hadronic level (Hadronic Final State, HFS) via the coalescence of two mesons ($D$ and $D^*$).
   • Constraints: The models enforce component, coordinate, and momentum constraints. For tetraquarks, the radius $R_0$ is set $< 1.0$ fm (pointlike), while for molecules, $1.0 < R_0 < 10.0$ fm. Invariant mass windows are strictly defined based on experimental values.

Key Contributions and Results
The study simulates 600 million events for molecular states and 18.6 million for tetraquark states to analyze yields, transverse momentum ($p_T$) spectra, production asymmetry, and coalescence parameters.

• Production Yields: The simulation predicts that molecular states are more likely to be produced than compact tetraquark states. However, the yield of $X(3872)$ is significantly higher than that of $T_{cc}$ in both configurations. This disparity is attributed to the statistical abundance of $c\bar{c}$ pairs compared to $cc$ or $\bar{c}\bar{c}$ pairs required for $T_{cc}$ formation.
• Transverse Momentum ($p_T$) Spectra: Both configurations exhibit a steep decline in $p_T$ spectra. Crucially, the paper identifies a significant discrepancy in the shape of the $p_T$ distributions between compact and molecular states. The ratio of tetraquark to molecular yields decreases as $p_T$ increases, with a more pronounced drop observed for $X(3872)$ compared to $T_{cc}$.
• Production Asymmetry ($A$): The asymmetry between $T_{cc}^+$ and $T_{cc}^-$ is defined as $A = (N_{T_{cc}^-} - N_{T_{cc}^+}) / (N_{T_{cc}^-} + N_{T_{cc}^+})$. The results show distinct behaviors for the two models: at low $p_T$, the tetraquark state exhibits smaller asymmetry than the molecular state, while at high $p_T$, the tetraquark state shows larger asymmetry. This $p_T$-dependent behavior is proposed as a discriminator.
• Coalescence Parameters: The coalescence parameters ($B_2$ for molecules, $B_4$ for tetraquarks) are extracted. Both parameters show a rising trend with increasing $p_T$. Since a larger coalescence parameter corresponds to a smaller correlation volume (a more compact source), this trend implies that the correlation volume decreases as $p_T$ increases.

Significance and Claims
The paper claims that the calculated distributions—specifically the transverse momentum spectra, the production asymmetry between charged $T_{cc}$ states, and the coalescence parameters—serve as valuable criteria for distinguishing between compact tetraquark and molecular configurations in future experimental measurements. The authors suggest that high-statistics experiments can utilize these kinematic differences to investigate the internal structures of these exotic hadrons. The study does not propose new experimental setups but rather provides theoretical benchmarks for interpreting existing or future data from facilities like the LHC.

Future Outlook
The authors note that heavy-ion collisions may offer an advantage in producing abundant charmed and doubly charmed exotic states. Consequently, they state their intention to extend this research framework to heavy-ion collision environments to further explore the production and properties of these states.