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Observation of the centrality-dependent difference in directed flow between charged kaons and $K^{*0}$ resonances in Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 14.6, 19.6 and 27 GeV

This paper presents the first measurement of the rapidity-odd directed flow ( $v_1^{\text{odd}}$ ) for $K^{*0}$ resonances in Au+Au collisions at 14.6, 19.6, and 27 GeV, revealing a centrality-dependent difference between charged kaons and $K^{*0}$ that provides crucial insights into the interplay between early-stage partonic collectivity and late-stage hadronic rescattering effects.

Original authors: The STAR Collaboration

Published 2026-07-14

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: The STAR 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 a giant, high-speed dance party where two massive crowds of gold atoms smash into each other. When they collide, they create a super-hot, super-dense soup of tiny particles called a "quark-gluon plasma." As this soup cools down, it freezes into a swarm of new particles, some of which are very short-lived "resonances" that pop into existence and vanish almost instantly.

Scientists at the STAR experiment are trying to figure out how these particles move. They are looking at a specific dance move called "directed flow" (specifically the v^odd₁), which is like a sideways push that happens right after the crash. Think of it as the crowd leaning to the left or right depending on how the two groups of atoms hit each other.

The team studied three types of dancers in gold-on-gold collisions at three different energy levels: 14.6, 19.6, and 27 GeV. They compared:

Charged Kaons: The "steady" dancers who live long enough to see the whole party.
Phi mesons: The "long-livers" who stick around so long they barely notice the chaos.
K*0 resonances: The "flash-in-the-pan" dancers. They live for only about 4 femtometers per second (a tiny fraction of a second) and decay right in the middle of the dense, crowded dance floor.

The Big Discovery
The researchers found a surprising difference in how these dancers leaned.

The charged kaons and phi mesons leaned in the same direction, and this didn't change much whether the collision was a gentle bump (peripheral) or a hard smash (central).
The K*0 resonances, however, did something weird. In gentle collisions, they leaned one way. But in the hardest, most central collisions, they suddenly leaned the opposite way!

Why Did the Short-Lived Dancers Change Their Minds?
The paper suggests this flip isn't because the K*0 dancers started with a different move. Instead, it's because they got bumped around after they were born.

Imagine the K0 is a fragile balloon that pops the moment it's released. In a crowded room (a central collision), the pieces of the popped balloon (the decay daughters) immediately run into other people in the crowd. These collisions push the pieces in a way that messes up the original direction the balloon was flying. Because the K0 decays so fast, it happens right in the middle of this dense, chaotic crowd, making it very sensitive to these late-stage bumps.

In contrast, the phi mesons live so long (about 46 femtometers per second) that they survive the entire party and only decay after the crowd has thinned out. They don't get bumped around, so their dance move stays consistent.

What the Data Rules Out
The scientists ran computer simulations to test their ideas. They compared two scenarios:

A simulation where the particles just fly freely after the crash, with no extra bumps. In this version, the difference between the K*0 and the kaons was almost zero.
A simulation that included a "hadronic afterburner" (UrQMD model), which adds the extra bumps and collisions that happen in the dense crowd. This version showed a difference that looked a lot like what the scientists actually measured.

The paper explicitly states that the idea of "no hadronic scattering" (no extra bumps) is ruled out with 99.4% confidence. In other words, the data proves that the K*0 particles must be getting hit by other particles in the late stages of the collision.

How Sure Are They?
The team measured this effect directly in real collisions. They found that the difference in the "lean" between the K*0 and the charged kaons grows larger as the collisions get more central (more crowded). While they can't say exactly how the particles interact at a microscopic level without more data, the measurements strongly suggest that the late-stage interactions are the cause. The results are consistent with models that include these messy, late-stage collisions, but the paper stops short of calling it a solved mystery, noting that it's crucial for understanding how much of the flow comes from the early "partonic" stage versus the later "hadronic" stage.

In short, the K*0 particles aren't just showing us how the party started; they are showing us how the crowd got in the way of the dancers before the music stopped.

Technical Summary: Centrality-Dependent Directed Flow of $K^{*0}$ Resonances vs. Charged Kaons

Problem Statement
In high-energy heavy-ion collisions, the evolution of the created medium involves a transition from a deconfined quark-gluon plasma (QGP) to a hadronic phase. While anisotropic flow observables, particularly the rapidity-odd directed flow ( $v_1^{odd}$ ), are sensitive to early-time partonic dynamics, short-lived resonances like the $K^{*0}$ (lifetime $\sim 4$ fm/c) decay within the dense hadronic medium. Their decay daughters ( $K\pi$ ) are subject to re-scattering and regeneration, which can alter the reconstructed yield and flow signals. It remains unclear to what extent the measured $v_1^{odd}$ of such resonances reflects genuine early-stage partonic collectivity versus late-stage hadronic interactions and reconstruction artifacts. Specifically, hydrodynamic models suggest that asymmetric modifications of the $K^{*0}$ yield relative to the event plane, driven by late-stage rescattering, could distort the observed flow.

Methodology
The STAR Collaboration analyzed Au+Au collisions at center-of-mass energies $\sqrt{s_{NN}} = 14.6, 19.6,$ and $27$ GeV using minimum-bias data from the Beam Energy Scan (BES-II) program. The dataset comprises approximately 500, 900, and 400 million events at the respective energies.

Particle Reconstruction: $K^{*0}$ ( $\bar{K}^{*0}$ ) and $\phi$ mesons were reconstructed via their hadronic decay channels ( $K^{*0} \to K^\pm \pi^\mp$ and $\phi \to K^+ K^-$ ) using the Time Projection Chamber (TPC) and Time-of-Flight (TOF) detectors. Particle identification relied on $dE/dx$ and $1/\beta$ measurements.
Flow Measurement: The rapidity-odd directed flow ( $v_1^{odd}$ ) was calculated using the event plane method. The first-order event plane ( $\Psi_{EP}^1$ ) was reconstructed using the Event Plane Detector (EPD) covering $2.1 < |\eta| < 5.1$ . The large pseudorapidity gap between the EPD and the TPC suppresses non-flow contributions.
Signal Extraction: The $v_1^{odd}$ was extracted from the invariant mass distribution of opposite-charge pairs. The signal yield was isolated by subtracting a combinatorial background estimated via a pair-rotation method. The flow of the signal was derived by fitting the $v_1$ of the combined signal and background as a function of invariant mass.
Analysis Scope: Measurements were performed for charged kaons, $\phi$ mesons, and $K^{*0}$ resonances across various centrality classes (0–80%), with a focus on the slope of $v_1^{odd}$ vs. rapidity ( $dv_1^{odd}/dy$ ) and the average integrated flow $\langle v_1^{odd} \rangle$ as a function of the number of participating nucleons ( $\langle N_{part} \rangle$ ).

Key Contributions
This work presents the first measurement of the rapidity-odd directed flow ( $v_1^{odd}$ ) for $K^{*0}$ resonances in heavy-ion collisions. It provides a direct comparison of flow observables between short-lived resonances ( $K^{*0}$ ), long-lived mesons ( $\phi$ ), and stable charged kaons across multiple collision energies and centralities.

Results

Centrality Dependence of Slope: In peripheral collisions (40–80%), the $v_1^{odd}$ slope ( $dv_1^{odd}/dy$ ) is negative for all particle species ( $K^{*0}$ , charged kaons, and $\phi$ ). However, in mid-central collisions (10–40%), the $K^{*0}$ slope becomes positive, while the slopes for charged kaons and $\phi$ mesons remain negative.
Transverse Momentum Dependence: For mid-central collisions at $\sqrt{s_{NN}} = 19.6$ GeV, the $v_1^{odd}$ of $K^{*0}$ becomes positive at low transverse momentum ( $p_T < 1$ GeV/c), whereas it remains negative for $\phi$ mesons in the same centrality class.
Average Flow Difference: The average directed flow $\langle v_1^{odd} \rangle$ for $K^{*0}$ exhibits a sign change from negative to positive as collisions become more central. In contrast, $\langle v_1^{odd} \rangle$ for charged kaons and $\phi$ mesons remains negative across all centralities.
Model Comparison: The difference in $\langle v_1^{odd} \rangle$ $⟨ v_{1}^{o dd} ⟩$ between $K^{*0}$ $K^{* 0}$ and charged kaons increases with centrality. When compared to hydrodynamic calculations:
- Models without a hadronic afterburner predict a difference close to zero.
- Models incorporating a hadronic afterburner (UrQMD) reproduce a positive difference, though the magnitude is slightly weaker than the experimental data in central collisions.
- The data exclude the scenario of "no hadronic scattering effects" at a 99.4% confidence level when integrated over 0–80% centrality.

Significance
The paper concludes that the observed centrality-dependent difference in directed flow between charged kaons and $K^{*0}$ resonances is likely driven by late-stage hadronic rescattering. Specifically, the re-scattering of $K^{*0}$ decay daughters in the dense hadronic medium leads to an asymmetric modification of the reconstructed $K^{*0}$ yield relative to the first-order event plane. This finding highlights that the directed flow of short-lived resonances is a sensitive probe of the hadronic phase and demonstrates that realistic hadronic scattering "afterburners" are essential for reliably interpreting collective flow observables in terms of partonic collectivity. The results challenge the interpretation of $v_1^{odd}$ in short-lived resonances as a pure signature of early-stage dynamics without accounting for late-stage interactions.

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