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Exploring the origin of D $^0$ meson elliptic flow in PbPb collisions at $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV using event shape engineering

Using event-shape engineering on 5.02 TeV PbPb collision data from the CMS detector, this study demonstrates that the elliptic flow of prompt D $^0$ mesons is strongly correlated with that of inclusive charged particles, indicating that initial-state geometry substantially influences charm-hadron flow development.

Original authors: CMS Collaboration

Published 2026-07-14

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: CMS Collaboration

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the Large Hadron Collider (CERN) as the world's most powerful particle slingshot. When scientists smash heavy lead atoms together at nearly the speed of light, they don't just make a mess; they create a tiny, fleeting drop of the hottest, densest stuff in the universe: a Quark-Gluon Plasma (QGP). Think of this plasma not as a gas, but as a super-fluid, a cosmic honey that flows with almost zero friction.

In this new study, the CMS team at CERN acted like cosmic detectives, trying to solve a mystery: Where does the "flow" of heavy particles come from?

The Mystery of the Heavy Hitters

Inside this super-hot soup, there are two types of players. First, you have the "lightweights" (like pions and protons), which are everywhere. Then, you have the "heavyweights," specifically D0 mesons. These are particles containing a "charm" quark, which is much heavier than the light stuff.

For a long time, scientists knew that the light particles flowed in a specific pattern (called "elliptic flow," or v2) because the collision wasn't a perfect circle. It was more like a football. The football shape of the collision (the initial geometry) squeezed the fluid, forcing the particles to fly out in an oval pattern.

But the heavy D0 mesons are different. Because they are so heavy, they are like bowling balls in a pool of water. You might think they would just sit there or get pushed around randomly, ignoring the shape of the pool. The big question was: Do these heavy bowling balls actually feel the shape of the collision and flow with the fluid, or do they just plow through it?

The Experiment: Sorting the Chaos

To answer this, the team looked at 0.607 nb⁻¹ of lead-lead collision data collected in 2018 at a collision energy of 5.02 TeV. That's a lot of data, but every collision is slightly different. Some collisions are perfectly head-on (central), and some are glancing blows (peripheral). Even within the "head-on" group, the atoms inside the nuclei aren't perfectly round; they wobble and jiggle, making the collision shape vary from event to event.

To handle this, the scientists used a clever trick called "Event Shape Engineering."

Imagine you have a giant bag of marbles, and you want to study how they roll. But every time you pour them out, the table is slightly tilted differently. To fix this, you measure the tilt of the table before you pour the marbles. If you only look at the marbles that rolled on tables tilted in a specific way, you can see a clear pattern.

In this experiment, the scientists measured a parameter called q2. This number tells them how "oval" or "lopsided" the energy distribution was in the forward part of the detector (far away from where the D0 mesons were measured). A high q2 meant a very oval collision shape; a low q2 meant a rounder one.

They then sorted their collisions into groups based on this q2 number. This allowed them to compare D0 mesons from "very oval" collisions against those from "rounder" collisions, while keeping everything else the same.

The Discovery: A Strong Connection

Here is what they found:

The Heavy Follow the Light: They measured the flow (v2) of the heavy D0 mesons and compared it to the flow of the light, inclusive charged particles in the exact same collisions.
The Linear Link: They discovered a strong linear correlation. When the light particles flowed strongly (because the collision was very oval), the heavy D0 mesons also flowed strongly. When the light particles flowed weakly, the D0 mesons did too.
The Numbers: This correlation held true for D0 mesons with transverse momentum (pT) in the range of 2–30 GeV. Specifically, for the 10–40% centrality range (the middle-ground collisions), the correlation was very strong for low momentum D0 mesons (2–10 GeV).

This suggests that the initial-state geometry—the shape of the collision at the very beginning—is the main driver for how these heavy charm particles move. The heavy D0 mesons aren't just plowing through; they are interacting with the fluid so much that they get swept up in its collective dance.

What About the Models?

The team also checked their results against a computer simulation called the PHSD model (Parton-Hadron-String-Dynamics).

The Good News: For slower D0 mesons (pT < 4 GeV), the model matched the data pretty well.
The Bad News: The model seemed to underestimate how well the charm quarks were "thermalized" (how well they mixed with the fluid) at these low speeds. The real data showed a stronger connection to the fluid than the simulation predicted.
The High-Speed Twist: When they looked at very fast D0 mesons (pT > 10 GeV), the linear connection started to get weaker. The paper suggests this might be because these super-fast particles lose energy as they travel through the medium, a process that depends on how far they have to go (path-length dependent energy loss).

The Bottom Line

The paper doesn't claim to have solved the entire mystery of the universe, but it provides compelling evidence for a specific idea: The shape of the collision at the very start dictates how heavy charm particles flow.

By using the q2 parameter to sort events, the team showed that the heavy D0 mesons are deeply connected to the collective motion of the Quark-Gluon Plasma. They aren't just bystanders; they are participants in the fluid's dance, proving that even the heavyweights can be swept up by the initial geometry of the crash.

The authors measured this directly in the lab using real data, not just simulations, and found that the correlation is strong enough to suggest that the initial shape is the dominant factor in creating this flow. While some computer models get close, they still need to be tweaked to fully explain how well these heavy particles mix with the cosmic soup.

Technical Summary: Exploring the Origin of D0 Meson Elliptic Flow in PbPb Collisions at $\sqrt{s_{NN}} = 5.02$ TeV using Event Shape Engineering

Problem Statement
Relativistic heavy ion collisions create a quark-gluon plasma (QGP), a state of matter behaving as a near-ideal fluid where initial spatial geometry is transformed into final-state momentum anisotropies. While the elliptic flow ( $v_2$ ) of light-quark hadrons is well-established as a hydrodynamic response to initial-state eccentricity, the behavior of heavy quarks (charm) remains a critical probe for understanding the QGP's properties. Specifically, it is necessary to determine if the collective flow observed in charm hadrons, such as $D^0$ mesons, is driven primarily by the initial-state geometry or if other mechanisms (e.g., path-length dependent energy loss) dominate, particularly at high transverse momentum ( $p_T$ ). Standard centrality-based measurements average over event-by-event fluctuations in the initial geometry, potentially obscuring the direct correlation between initial eccentricity and final flow.

Methodology
This analysis utilizes a lead-lead (PbPb) data sample collected by the CMS detector at the CERN LHC in 2018, corresponding to an integrated luminosity of 0.607 nb $^{-1}$ at $\sqrt{s_{NN}} = 5.02$ TeV. The study employs an event-shape engineering technique to isolate collisions with similar initial-state geometries within fixed centrality classes.

Event Selection and Geometry Characterization:
- Events are classified by centrality (0–10% to 40–50%).
- An asymmetry parameter, $q_2$ , is calculated using transverse energy ( $E_T$ ) deposits in the forward hadron calorimeters (HF, $3.0 < |\eta| < 5.2$ ). This parameter serves as a proxy for the initial-state eccentricity.
- To minimize centrality bias, events within 10% centrality bins are further subdivided into ten $q_2$ -based event-shape classes.
Signal Reconstruction:
- Prompt $D^0$ mesons are reconstructed via the decay channels $D^0 \to K^-\pi^+$ and $D^0 \to K^+\pi^-$ in the mid-rapidity region ( $|y| < 1$ ).
- A Boosted Decision Tree (BDT) algorithm optimizes signal significance, distinguishing prompt $D^0$ mesons from non-prompt backgrounds (from $b$ -hadron decays) using impact parameter significance and vertex quality. A selection of decay length $< 0.0085$ cm ensures a 95% prompt purity.
- Signal yields are extracted by fitting invariant mass distributions with a combination of Gaussian functions and background polynomials.
Flow Measurement:
- The elliptic flow coefficient ( $v_2$ ) is measured for both prompt $D^0$ mesons ( $2 < p_T < 30$ GeV) and inclusive charged particles ( $1 < p_T < 3$ GeV) using the scalar product (SP) method.
- The SP method utilizes subevents in different pseudorapidity regions to avoid autocorrelations: HF towers for the reference flow vectors and the central tracker for the particles of interest.
- The $v_2$ of inclusive charged particles is used as a data-driven proxy for the event-by-event initial eccentricity.
Correlation Analysis:
- The study examines the correlation between $D^0$ meson $v_2$ and inclusive charged particle $v_2$ within common $q_2$ intervals.
- Pearson correlation coefficients ( $r$ ) and linear fit slopes/intercepts are calculated to quantify the linearity of this relationship.
- Results are compared against the Parton-Hadron-String-Dynamics (PHSD) model.

Key Contributions and Results

Strong Linear Correlation: For $D^0$ mesons with $p_T$ in the range of 2–10 GeV and centrality classes 10–40%, a strong linear correlation is observed between the $D^0$ meson $v_2$ and the inclusive charged particle $v_2$ . The Pearson correlation coefficients are consistent with unity, and the slopes of the linear fits are consistent with one.
Initial-Geometry Dominance: The linear relationship suggests that the elliptic flow of prompt $D^0$ mesons in this kinematic region is primarily driven by the initial-state geometry of the collision, similar to the behavior of light-quark hadrons.
High- $p_T$ and Centrality Dependence:
- For the most central events (0–10%) and at higher $p_T$ ( $> 10$ GeV), the linear correlation weakens.
- In the 40–50% centrality class, the correlation is also weaker.
- These deviations from linearity at high $p_T$ may indicate the onset of path-length dependent energy loss mechanisms for charm quarks traversing the QGP.
Model Comparison: The PHSD model predictions generally agree with data at low $p_T$ ( $< 4$ GeV) but underestimate the degree of charm-quark thermalization, as evidenced by lower slopes in the scatter plots for central events at higher $p_T$ .

Significance
This work provides compelling evidence that the initial-state geometry substantially impacts the development of charm-hadron flow in heavy ion collisions. By utilizing event-shape engineering, the analysis isolates the geometric contribution to flow, demonstrating that prompt $D^0$ mesons participate in the collective expansion of the QGP medium. The observed linear correlation validates the hydrodynamic response of heavy quarks to initial eccentricity at low to intermediate $p_T$ . Furthermore, the observed deviations at high $p_T$ and in extreme centrality classes offer new constraints on theoretical models regarding the thermalization and energy loss mechanisms of heavy quarks in the QGP. The results reinforce the utility of heavy-flavor hadrons as probes of the QGP's collective properties.

The Mystery of the Heavy Hitters

The Experiment: Sorting the Chaos

The Discovery: A Strong Connection

What About the Models?

The Bottom Line

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