Influence of strangeness on the anisotropic flow of prompt D$^\pm_\mathrm{s}$ mesons in PbPb collisions at $\sqrt{s_\mathrm{NN}}$ = 5.02 TeV

Using CMS data from PbPb collisions at 5.02 TeV, this study measures the azimuthal anisotropy of prompt D$^\pm_\mathrm{s}$ mesons and finds their flow coefficients to be consistent with those of D$^0$ mesons, indicating that the strangeness content does not significantly alter the mesons' interaction with the quark-gluon plasma within the measured transverse momentum range.

The Gist

Imagine a giant, high-speed game of billiards, but instead of a table, you have two massive lead atoms smashing into each other at nearly the speed of light. When they collide, they don't just bounce off; they melt. For a tiny fraction of a second, the matter inside them turns into a super-hot, super-dense soup called Quark-Gluon Plasma (QGP).

Think of this soup not as a liquid you can drink, but as a thick, sticky honey made of the fundamental building blocks of the universe (quarks and gluons) that usually live locked inside protons and neutrons.

The Experiment: Dropping Heavy Balls in Honey

In this experiment, scientists at CERN's CMS detector wanted to see how "heavy" particles move through this sticky honey. Specifically, they looked at a type of particle called a $D_s$ meson.

To understand what makes a $D_s$ meson special, let's use an analogy:

• Imagine a $D^0$ meson is like a heavy bowling ball made of a "charm" brick and a "up/down" brick.
• Imagine a $D_s$ meson is a similar heavy bowling ball, but one of the bricks is a "strange" brick.

In the normal world (like in a proton-proton collision), "strange" bricks are rare. But in the super-hot QGP soup, the heat is so intense that it creates a flood of these "strange" bricks. The big question was: Does having a "strange" brick change how the heavy ball moves through the soup?

The Flow: Dancing in a Crowd

When the lead atoms collide, they don't hit perfectly head-on. They usually glance off each other, creating an oval-shaped explosion rather than a perfect circle.

As the QGP soup expands, it flows outward. Because the collision was oval-shaped, the soup flows faster in some directions than others. This is called anisotropic flow.

• $v_2$ (Elliptic Flow): Think of this as the particles dancing in an oval pattern, squeezing through the "short" side of the oval faster than the "long" side.
• $v_3$ (Triangular Flow): Imagine the collision wasn't just an oval, but a bit lumpy or triangular. The particles then flow in a wavy, triangular pattern.

Scientists measure how well the heavy particles (the bowling balls) join this dance. If they move with the crowd, they have "flow." If they just plow through the soup without caring about the shape, they have no flow.

The Big Discovery: The "Strange" Brick Doesn't Matter

The scientists measured the dance moves ($v_2$ and $v_3$) of the $D_s$ mesons (with the strange brick) and compared them to the $D^0$ mesons (without the strange brick).

The Result: The two types of particles danced exactly the same way.

This is a huge deal because it tells us two important things about the universe:

1. The Soup is the Boss: The heavy charm quark (the main weight of the bowling ball) interacts with the QGP soup so strongly that it forgets about the specific type of light brick (strange vs. non-strange) attached to it. The soup's flow dominates the movement.
2. Rebuilding the Particle: When the soup cools down and the particles stop moving, they have to "rebuild" themselves into solid particles. The fact that the $D_s$ and $D^0$ flow the same way suggests that when the heavy charm quark grabs a light quark to become a meson, it doesn't matter if that light quark is "strange" or not. The heavy quark's journey through the soup dictates the final result, not the flavor of the partner it picks up at the end.

Why This Matters

Think of it like a runner in a marathon.

• Scenario A: The runner is wearing a heavy backpack (the charm quark) and a red hat (the strange quark).
• Scenario B: The runner is wearing the same heavy backpack but a blue hat (the non-strange quark).

If the wind (the QGP) is blowing hard, both runners will be pushed in the same direction, regardless of their hat color. This experiment proved that for heavy particles in this extreme environment, the "hat color" (strangeness) doesn't change how the wind pushes them.

The Bottom Line

This paper confirms that the Quark-Gluon Plasma is a very efficient mixer. It treats heavy particles with "strange" ingredients and those without them almost identically. This helps physicists understand the rules of the universe at its most extreme temperatures, proving that the heavy charm quark is the main character in the story, and the strange quark is just a supporting actor that doesn't change the plot.

Technical Summary

1. Problem and Motivation

The study addresses a fundamental question in heavy-ion physics: How does the presence of a strange quark affect the interaction of heavy charm quarks with the Quark-Gluon Plasma (QGP)?

• Context: In ultrarelativistic heavy-ion collisions, a QGP is formed. Heavy quarks (charm and bottom) are produced early in the collision and traverse this medium. Their subsequent motion is characterized by anisotropic flow ($v_n$), specifically elliptic flow ($v_2$) and triangular flow ($v_3$).
• The Gap: While the flow of non-strange charm mesons (like $D^0$) has been extensively studied, the behavior of strange charm mesons ($D^\pm_s$, containing a charm and a strange quark) was less constrained.
• Scientific Question: Does the "strangeness content" of the $D^\pm_s$ meson alter its flow compared to the $D^0$ meson?
  • Hypothesis 1: If the QGP exhibits strangeness enhancement (an increased fraction of strange quarks compared to proton-proton collisions), $D^\pm_s$ mesons might form via coalescence with thermalized strange quarks, potentially inheriting different flow characteristics than $D^0$ mesons formed with light (up/down) quarks.
  • Hypothesis 2: If the flow is dominated by the parent charm quark's interaction with the medium (via energy loss or thermalization) regardless of the light quark it eventually pairs with, the flow coefficients should be identical for $D^\pm_s$ and $D^0$.

2. Methodology

Data Sample and Detector:

• Experiment: CMS detector at the CERN LHC.
• Collision System: Lead-Lead (PbPb) collisions at a nucleon-nucleon center-of-mass energy of $\sqrt{s_{NN}} = 5.02$ TeV.
• Dataset: 2018 data corresponding to an integrated luminosity of 0.58 nb$^{-1}$ (approx. 4.27 billion minimum bias events).
• Centrality Classes: Analyzed in three centrality bins: 0–10% (central), 10–30% (mid-central), and 30–50% (mid-peripheral).

Reconstruction and Selection:

• Decay Channel: Prompt $D^\pm_s$ mesons were reconstructed via the decay chain:
  $$D^\pm_s \to \phi(1020) + \pi^\pm \to (K^+ + K^-) + \pi^\pm$$
• Track Selection: Charged tracks required $p_T > 1.5$ GeV and $|\eta| < 2.4$. Strict quality cuts were applied (e.g., $\chi^2/\text{dof}/N_{\text{layers}} < 0.18$).
• Vertexing: Candidates were required to have a decay length significance and pointing angle consistent with a displaced vertex.
• Background Suppression:
  • Combinatorial Background: A Boosted Decision Tree (BDT) algorithm (using TMVA) was trained to distinguish signal from background based on kinematic and topological variables (decay length, pointing angle, vertex probability).
  • Non-Prompt Contamination: A cut on the distance of closest approach (DCA) to the primary vertex ($< 0.01$ cm) was applied to enhance the prompt fraction. The residual non-prompt contribution (from $b$-hadron decays) was estimated and subtracted using a template fit method.

Flow Measurement:

• Method: The Scalar Product (SP) method was used to extract $v_2$ and $v_3$.
• Reference Particles: Event plane orientation was estimated using three subevents:
  1. Forward Hadronic Calorimeter (HF) at negative $\eta$ ($-5 < \eta < -3$).
  2. Forward Hadronic Calorimeter (HF) at positive $\eta$ ($3 < \eta < 5$).
  3. Tracker region ($|\eta| < 0.75$).
  • This configuration ensures a large pseudorapidity gap ($\Delta\eta > 3$) between the $D^\pm_s$ candidate and reference particles to suppress non-flow correlations.
• Signal Extraction: Since the invariant mass ($m_{\text{inv}}$) distribution contains significant background, a simultaneous fit was performed on the $m_{\text{inv}}$ spectrum and the $v_n(m_{\text{inv}})$ distribution. This allowed the extraction of the flow coefficient for the pure signal ($v_n^{\text{Sig}}$) separate from the background ($v_n^{\text{Bkg}}$).

3. Key Contributions

1. First Precision Measurement of $D^\pm_s$ Flow: This paper presents the first detailed measurement of $v_2$ and $v_3$ for prompt $D^\pm_s$ mesons over a wide transverse momentum range ($4 < p_T < 40$ GeV for $v_2$ and $4 < p_T < 20$ GeV for $v_3$).
2. Direct Comparison with $D^0$: It provides a direct, high-precision comparison between strange ($D^\pm_s$) and non-strange ($D^0$) charm mesons within the same experimental setup and centrality classes.
3. Validation of Hadronization Mechanisms: The results test theoretical models regarding how heavy quarks hadronize in the QGP (recombination vs. fragmentation) and whether the flavor of the light quark partner influences the final flow.

4. Results

• Elliptic Flow ($v_2$):

  • Positive $v_2$ values were observed for $D^\pm_s$ in all centrality classes with a significance $>1\sigma$.
  • The $v_2$ peaks at low $p_T$ ($4–6$ GeV) and decreases as $p_T$ increases.
  • A clear centrality dependence is observed: $v_2$ is largest in the 30–50% (peripheral) class and smallest in the 0–10% (central) class.
  • Comparison: The $v_2$ coefficients for $D^\pm_s$ are consistent with those previously measured for $D^0$ mesons within the precision of the measurement across the entire $p_T$ range.

• Triangular Flow ($v_3$):

  • Significant and positive $v_3$ values were observed for $D^\pm_s$ in the 10–30% centrality class for $4 < p_T < 10$ GeV.
  • Comparison: The $v_3$ values for $D^\pm_s$ are consistent with those of $D^0$ mesons.

• Systematic Uncertainties: The total systematic uncertainties range from 0.7% to 2.5% for $v_2$ and 0.8% to 1.3% for $v_3$, dominated by efficiency corrections and non-prompt contributions.

5. Significance and Conclusion

The primary conclusion of the paper is that the strangeness content of the $D^\pm_s$ meson does not significantly alter its azimuthal anisotropy compared to the non-strange $D^0$ meson within the measured $p_T$ range.

• Implication for QGP Physics: This suggests that the anisotropic flow of heavy charm mesons is dominated by the evolution of the parent charm quark within the QGP medium, rather than the specific flavor of the light quark it coalesces with during hadronization.
• Mechanism Insight: Whether the charm quark thermalizes and recombines with a light quark (at low $p_T$) or loses energy via path-length dependent mechanisms (at high $p_T$), the resulting flow is insensitive to whether the light quark is strange or non-strange.
• Theoretical Impact: These results constrain theoretical models of heavy-flavor transport in the QGP, indicating that the "strangeness enhancement" in the QGP does not lead to a distinct flow signature for strange charm mesons compared to non-strange ones in this kinematic regime.

This measurement provides a crucial benchmark for understanding the degree of thermalization of heavy quarks and the details of the hadronization process in the extreme conditions of the early universe.