Measurement of Kaon Directed Flow in Au+Au Collisions in the High Baryon Density Region

Rapidity-odd directed flow $v_1$ measurements are presented for $K^{\pm}$ and $K^0_S$ in Au$+$Au collisions at $\sqrt{s_{\text{NN}}}$ = 3.0, 3.2, 3.5, and 3.9 GeV with the STAR experiment. For comparison, $v_1$ of $π^{\pm}$, protons, and $Λ$ from the same collisions are also discussed. The mid-rapidity $v_1$ slope $\text{d}v_1/\text{d}y|{y=0}$ for protons and $Λ$ is positive in these collisions. On the other hand, $v_1$ slope of kaons exhibits a strong $p\text{T}$ dependence: negative at $p_\text{T} <$ 0.6 GeV/$c$ and positive at higher $p_\text{T}$. A similar $p_\text{T}$ dependence is also evident for the $v_1$ slope of charged pions. Compared to the spectator-removed calculations in Au$+$Au collisions at $\sqrt{s_{\text{NN}}} =$ 3.0-3.9 GeV, the JAM model demonstrates a pronounced shift of the $v_1$ slopes of mesons towards the negative direction. It suggests that the shadowing effect of the spectators plays an important role in the observed kaon anti-flow at low $p_\text{T}$ in the high baryon density region of non-central collisions.

💡 Research Summary

The STAR Collaboration reports the first systematic measurement of rapidity‑odd directed flow (v₁) for charged kaons (K⁺, K⁻) and neutral kaons (K⁰_S) in Au+Au collisions at √sₙₙ = 3.0, 3.2, 3.5 and 3.9 GeV, covering the high‑baryon‑density region of the QCD phase diagram (μ_B ≈ 630–720 MeV). Using the Fixed‑Target (FXT) mode of RHIC, the experiment recorded data with the Time Projection Chamber (TPC), inner TPC, Time‑of‑Flight (TOF) and the Event Plane Detector (EPD). Charged particle tracking required a distance of closest approach (DCA) < 3 cm and at least 15 TPC space points; particle identification combined dE/dx and TOF information, achieving >95 % purity for pions and protons and >90 % for kaons. Weak‑decay reconstruction (Kalman Filter) was employed for K⁰_S and Λ.

The first‑order event plane was determined from three sub‑events in the EPD and TPC, yielding a resolution R₁ of 0.65–0.75 for 10–40 % centrality. Directed flow was obtained as v₁ = ⟨cos(ϕ − Ψ₁)⟩/R₁ and the rapidity dependence was fitted with a third‑order polynomial v₁(y)=F·y+F₃·y³ over –1 < y < 0. The slope at mid‑rapidity, dv₁/dy|_{y=0}, quantifies the odd component.

Key findings:

• Protons and Λ hyperons exhibit a positive dv₁/dy, indicating a net sideward push consistent with early pressure gradients.
• Pions are mostly positive, with π⁻ showing a slight negative region near y ≈ –0.5 to 0.
• Kaons display a striking transverse‑momentum dependence: for p_T < 0.6 GeV/c the dv₁/dy is negative (anti‑flow), while for p_T > 0.6 GeV/c it becomes positive. Charged and neutral kaons differ at forward rapidities, suggesting a transported‑quark effect.
• The magnitude of v₁ decreases with increasing √sₙₙ for all species; for K⁰_S a 5.4 σ difference is observed between 3.0 and 3.9 GeV.

To interpret the results, the JAM (Jet AA Microscopic Transport) model was employed in two configurations: a pure cascade (binary collisions only) and a baryonic mean‑field (BMF) mode that includes a density‑ and momentum‑dependent nuclear potential (κ = 210 MeV). Both calculations reproduced the proton v₁ trend, but the cascade underestimates K⁰_S v₁, while the BMF overestimates it. Importantly, when spectators are removed in the model, meson v₁ shifts further negative, highlighting the role of spectator shadowing in generating the low‑p_T kaon anti‑flow. This effect is analogous to the previously observed negative elliptic flow at similar energies and is consistent with transport‑model predictions that attribute anti‑flow of pions and nucleons to spectator interactions.

Systematic uncertainties were evaluated by varying track quality cuts (DCA, nHitsFit), PID selections (nσ_TPC, TOF mass‑squared windows) and the reference event plane. The Barlow method was used to combine contributions, resulting in total systematic errors ranging from ~1 % for protons to >30 % for kaons at the highest energy, reflecting the small absolute v₁ values for mesons.

The study demonstrates that in the high‑baryon‑density regime, directed flow of strange mesons is not governed solely by the kaon‑nucleon potential; instead, the geometry and timing of the spectator matter play a decisive role, especially at low transverse momentum. These measurements provide new constraints on the equation of state (EoS) at high density, on kaon mean‑field potentials, and on transport‑model implementations of spectator effects. Future work with larger data sets, finer centrality bins, and comparisons to other transport frameworks (e.g., SMASH, PHSD) will further elucidate the interplay between the EoS, strangeness dynamics, and spectator shadowing in the quest to map the QCD phase diagram.