Evidence of different $Λ_{\rm c}$-baryon and D-meson elliptic flow in Pb$-$Pb collisions at $\mathbf{\sqrt{\textit{s}_{\rm NN}}}$ = 5.36 TeV with ALICE at the LHC

The ALICE collaboration presents the first measurement of elliptic flow ($v_2$) for prompt $\Lambda_{\rm c}$ baryons in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 5.36$ TeV, observing a significantly larger $v_2$ for $\Lambda_{\rm c}$ compared to D$^0$ mesons that provides evidence for charm-hadron formation via quark coalescence.

The Gist

The Big Picture: A Cosmic Dance Floor

Imagine the universe, just after the Big Bang, wasn't a cold, empty void. Instead, it was a super-hot, super-dense soup of tiny particles called Quarks and Gluons. Scientists call this the Quark-Gluon Plasma (QGP). It's like a fluid so perfect that it flows without any friction, like a dancer who never trips.

To study this ancient soup, scientists at CERN smash lead atoms together at nearly the speed of light. This creates a tiny, fleeting "fireball" that mimics the conditions of the early universe. The ALICE experiment is the giant camera watching this fireball cool down and turn back into normal matter (protons and neutrons).

The Stars of the Show: The "Charm" Guests

In this experiment, the scientists are tracking two specific types of "guests" that get created in the initial smash:

1. D-mesons: These are like "charm couples" (a charm quark paired with a lighter partner).
2. Lambda-c baryons: These are "charm trios" (a charm quark paired with two other partners).

These guests are heavy and slow to react. The big question the scientists wanted to answer was: Do these heavy guests just float through the party, or do they actually join the dance?

The Dance Move: "Elliptic Flow"

When the lead atoms collide, they don't hit perfectly head-on. They graze each other, creating an oval-shaped fireball (like a football).

• The Physics: Because the fireball is oval, there is more space for particles to escape through the "short side" of the oval than the "long side."
• The Result: If the particles interact with the hot soup, they get pushed out more in the short direction. This creates a pattern called Elliptic Flow ($v_2$).

Think of it like a crowded dance floor. If the room is shaped like an oval, and everyone is bumping into each other, people will naturally drift toward the shorter sides of the room. If a heavy guest (like a D-meson) is moving with the crowd, they will show this "oval drift." If they are just floating through the air without touching anyone, they won't show the drift.

The Discovery: Who Joined the Dance?

The paper reports two major findings from these collisions at record-breaking energy levels:

1. The "Baryon vs. Meson" Split (The Trio vs. The Couple)

The scientists found that the Lambda-c baryons (the trios) showed a much stronger "oval drift" than the D-mesons (the couples), especially at medium speeds.

• The Analogy: Imagine a dance floor where people are forming groups.
  • The D-mesons are like couples holding hands.
  • The Lambda-c baryons are like groups of three friends holding hands.
  • The theory is that in this hot soup, particles form by "coalescence"—sticking together as the soup cools.
  • Because the trios are made of three people, they can "catch" more of the collective motion of the crowd than the couples can. It's like a three-person conga line picking up more momentum from the crowd than a two-person line.
• Why it matters: This proves that the heavy charm quarks aren't just floating; they are getting swept up in the collective flow of the quark-gluon plasma before they form into particles. It's evidence that the "dance" happens at the level of the individual quarks, not just the final particles.

2. The "Strange" Guest (The Ds Meson)

The scientists also looked at a specific type of D-meson called the $D_s$, which contains a "strange" quark. They noticed it seemed to drift slightly less than the regular D-mesons.

• The Analogy: Imagine the $D_s$ is a guest who is wearing a very slippery suit. They might slip out of the dance circle earlier than the others, missing some of the pushing and shoving that builds up the "drift."
• The Significance: This hints that particles with "strange" quarks might form or leave the interaction zone at a slightly different time than regular particles. It's a subtle clue about the timing of how the universe cools down.

The Verdict: The Soup is Real

The paper concludes that these heavy charm particles are indeed interacting with the Quark-Gluon Plasma. They aren't just spectators; they are active participants in the fluid dynamics of the early universe.

The fact that the "trios" (baryons) dance more vigorously than the "couples" (mesons) is the "smoking gun" that the heavy quarks are thermalizing (getting hot and moving with the crowd) and then recombining to form new particles.

In simple terms:
Scientists smashed atoms together, created a tiny drop of the universe's first soup, and watched heavy particles dance. They found that the heavy particles did dance with the crowd, and that groups of three danced harder than groups of two. This confirms our understanding of how the universe's fundamental building blocks behave in extreme heat and density.

Technical Summary

1. Problem and Scientific Context

The paper addresses the fundamental question of how heavy quarks (specifically charm quarks) interact with the Quark-Gluon Plasma (QGP), a deconfined state of matter created in ultra-relativistic heavy-ion collisions.

• The Challenge: While light-flavor hadrons exhibit strong collective flow (anisotropic flow, $v_n$) indicating thermalization with the medium, the extent to which heavy charm quarks participate in this collective motion and how they hadronize (form particles) remains a critical area of investigation.
• Key Mechanisms: The study focuses on two competing hadronization mechanisms in the QGP:
  1. Fragmentation: Dominant at high transverse momentum ($p_T$), where a quark fragments into a hadron.
  2. Recombination (Coalescence): Dominant at intermediate $p_T$, where a heavy quark coalesces with light quarks from the medium. This mechanism predicts specific mass and baryon-to-meson ordering in elliptic flow ($v_2$).
• Specific Gaps: Previous measurements established D-meson $v_2$, but there was a lack of data on:
  • Prompt $\Lambda_c^+$ baryon elliptic flow (crucial for testing baryon-meson splitting).
  • The difference between strange ($D_s^+$) and non-strange ($D^0, D^+$) D-mesons, which probes the role of strange quarks in the coalescence process and potential early kinetic freeze-out.
  • Measurements at the highest LHC energy ($\sqrt{s_{NN}} = 5.36$ TeV) with significantly improved statistics.

2. Methodology

The analysis utilizes data collected by the ALICE detector during LHC Run 3 (2023).

• Data Sample:

  • Collision System: Pb–Pb collisions at $\sqrt{s_{NN}} = 5.36$ TeV.
  • Centrality: 30–50% (semi-central collisions).
  • Statistics: $1.7 \times 10^9$ events ($\approx 1.1$ nb$^{-1}$ integrated luminosity), nearly 20 times larger than previous Run 2 datasets in the same centrality class.
  • Kinematic Range: Midrapidity ($|y| < 0.8$) and transverse momentum $0.5 < p_T < 24$ GeV/c.

• Particle Reconstruction:

  • Particles: Prompt $D^0$, $D^+$, $D_s^+$ mesons and $\Lambda_c^+$ baryons (and their antiparticles).
  • Decay Channels:
    • $D^0 \to K^-\pi^+$
    • $D^+ \to K^-\pi^+\pi^+$
    • $D_s^+ \to \phi\pi^+ \to K^-K^+\pi^+$
    • $\Lambda_c^+ \to pK^-\pi^+$
  • Detectors: Inner Tracking System (ITS2), Time Projection Chamber (TPC), and Time-Of-Flight (TOF) for tracking and Particle Identification (PID).

• Analysis Techniques:

  • Signal Selection: Machine Learning (Boosted Decision Trees - BDTs using XGBoost) was employed to suppress combinatorial background and separate prompt charm hadrons from non-prompt ones (originating from beauty decays).
  • Elliptic Flow ($v_2$) Measurement: The Scalar Product (SP) method was used. Flow vectors were constructed using the FT0C, FV0A, and TPC detectors to ensure a pseudorapidity gap ($\Delta\eta > 1.3$) from the charm candidates, suppressing non-flow correlations.
  • Extraction of Prompt $v_2$: Since $v_2$ cannot be measured candidate-by-candidate, a simultaneous fit was performed on the invariant mass distribution and the $v_2$ as a function of invariant mass.
  • Prompt Fraction Correction: A data-driven approach varying BDT selection criteria was used to estimate the non-prompt fraction ($f_{\text{non-prompt}}$). The prompt $v_2$ was then extrapolated to $f_{\text{non-prompt}} = 0$ via a linear fit.

3. Key Contributions

• First Measurement: This is the first measurement of the elliptic flow ($v_2$) of prompt $\Lambda_c^+$ baryons in Pb–Pb collisions.
• Unprecedented Precision: The analysis covers a $p_T$ range down to $0.5$ GeV/c (first time for $D^0$) and extends up to 24 GeV/c, utilizing a dataset 20 times larger than previous Run 2 measurements.
• Baryon-Meson Splitting: Provides the first evidence of a significant difference in $v_2$ between charm baryons and mesons in the heavy-flavor sector.
• Strange vs. Non-Strange: Offers new constraints on the $v_2$ difference between $D_s^+$ and $D^0$ mesons, testing sequential coalescence models.

4. Key Results

• General Behavior: All charm hadrons exhibit a positive $v_2$, increasing with $p_T$ at low momenta and decreasing at high momenta, following the trend of light hadrons (pions).
• Mass Ordering: At low $p_T$ ($< 4$ GeV/c), a clear mass ordering is observed ($v_2(\pi) > v_2(D)$), consistent with hydrodynamic expansion and radial flow effects.
• $D^0$ vs. $D^+$: The $v_2$ values for $D^0$ and $D^+$ are compatible within uncertainties across the full $p_T$ range.
• $D^0$ vs. $D_s^+$: A hint of a difference is observed in the $1 < p_T < 5$ GeV/c interval, where $D_s^+$ shows a lower $v_2$ than $D^0$. The statistical significance is 2.6$\sigma$. This suggests potential differences in hadronization timescales or early kinetic freeze-out for strange mesons, though uncertainties prevent a definitive conclusion.
• $\Lambda_c^+$ vs. $D^0$ (Major Finding): In the interval $4 < p_T < 12$ GeV/c, the $\Lambda_c^+$ baryon exhibits a significantly larger $v_2$ than the $D^0$ meson.
  • Significance: 3.7$\sigma$.
  • Interpretation: This "baryon-meson splitting" is strong evidence for quark coalescence (recombination) as the dominant hadronization mechanism at intermediate $p_T$. In this model, the $v_2$ of a baryon (3 quarks) is the sum of its constituent quarks' $v_2$, leading to a higher value than a meson (2 quarks) and a shift of the $v_2$ peak to higher $p_T$.
• High $p_T$ ($> 10$ GeV/c): All species show similar non-zero $v_2$, attributed to path-length-dependent energy loss (jet quenching) affecting high-momentum partons similarly.

5. Significance and Theoretical Comparison

• Partonic Origin: The observation of baryon-meson splitting in the charm sector confirms that collective flow develops at the partonic level (quark-gluon plasma) and that charm quarks participate in this collective motion before hadronizing.
• Model Validation: The results were compared with various transport models (TAMU, Catania, LBT-PNP, POWLANG, EPOS4HQ, Langevin).
  • TAMU provided the best overall quantitative agreement with the data across different species.
  • Most models qualitatively reproduce the trends but struggle with precise quantitative descriptions of the $v_2$ peak and the magnitude of the baryon-meson splitting.
• Implications: These measurements constrain the spatial diffusion coefficient of heavy quarks in the QGP and the relaxation time required for charm quarks to reach thermal equilibrium. The results support the view that charm quarks are strongly coupled to the medium and that hadronization via coalescence is a dominant process in the intermediate $p_T$ region.

In summary, this paper provides definitive experimental evidence that charm quarks participate in the collective flow of the QGP and hadronize via quark coalescence, fundamentally shaping our understanding of heavy-flavor dynamics in extreme nuclear matter.