Hyperon Polarization along the Beam Direction Relative to the Second and Third Harmonic Event Planes in Isobar Collisions at $\sqrt{{s}_{NN}}=200\text{ }\text{ }\mathrm{GeV}$

Hyperon Polarization along the Beam Direction Relative to the Second and Third Harmonic Event Planes in Isobar Collisions at $\sqrt{s_{N N}} = 200 GeV$

M. I. Abdulhamid et al. (STAR Collaboration)

Phys. Rev. Lett. 131, 202301 – Published 14 November 2023

Abstract

The polarization of $Λ$ and $\bar{Λ}$ hyperons along the beam direction has been measured relative to the second and third harmonic event planes in isobar $Ru + Ru$ and $Zr + Zr$ collisions at $\sqrt{s_{N N}} = 200 GeV$ . This is the first experimental evidence of the hyperon polarization by the triangular flow originating from the initial density fluctuations. The amplitudes of the sine modulation for the second and third harmonic results are comparable in magnitude, increase from central to peripheral collisions, and show a mild $p_{T}$ dependence. The azimuthal angle dependence of the polarization follows the vorticity pattern expected due to elliptic and triangular anisotropic flow, and qualitatively disagrees with most hydrodynamic model calculations based on thermal vorticity and shear induced contributions. The model results based on one of existing implementations of the shear contribution lead to a correct azimuthal angle dependence, but predict centrality and $p_{T}$ dependence that still disagree with experimental measurements. Thus, our results provide stringent constraints on the thermal vorticity and shear-induced contributions to hyperon polarization. Comparison to previous measurements at RHIC and the LHC for the second-order harmonic results shows little dependence on the collision system size and collision energy.

Received 16 March 2023
Revised 7 July 2023
Accepted 3 October 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.202301

Physics Subject Headings (PhySH)

Collective flow Polarization phenomena Relativistic heavy-ion collisions

Nuclear Physics

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Vol. 131, Iss. 20 — 17 November 2023

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Figure 1
Sketches illustrating the initial geometry, (a) elliptical shape and (b) triangular shape, viewed from the beam direction in heavy-ion collisions. Solid arrows denote flow velocity indicating stronger collective expansion in the direction of the event plane angle $Ψ_{n}$ ; open arrows indicate vorticities.
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Figure 2
$⟨ \cos θ_{p}^{*} ⟩^{sub}$ of $Λ$ and $\bar{Λ}$ as a function of hyperon azimuthal angle relative to the second- (left panel) and the third-order (right panel) event planes, $n (ϕ - Ψ_{n})$ , in 20%–60% central isobar collisions at $\sqrt{s_{N N}} = 200 GeV$ . The sign of the data for $\bar{Λ}$ is flipped as indicated by $sgn (α_{H})$ . The solid lines are fit functions used to extract the parameters indicated in the label where $p_{1}$ corresponds to the $n$ th-order Fourier sine coefficient. Note that the results presented in these figures are not corrected for the event plane resolution.
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Figure 3
Centrality dependence of the second- and the third-order Fourier sine coefficients of $Λ + \bar{Λ}$ polarization along the beam direction in isobar $Ru + Ru$ and $Zr + Zr$ collisions at $\sqrt{s_{N N}} = 200 GeV$ . Open boxes show systematic uncertainties. Solid bands show calculations from the hydrodynamic model [27] including contribution from the shear-induced polarization (SIP) based on Ref. [43] by Becattini-Buzzegoli-Palermo (BBP) or Ref. [44] by Liu-Yin (LY) in addition to that due to thermal vorticity $ω_{th}$ . The model calculations with a nearly zero shear viscosity (“ideal hydro”) are also shown.
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Figure 4
Transverse momentum dependence of the second- and third-order Fourier sine coefficients of $Λ + \bar{Λ}$ polarization along the beam direction for 20%–60% central isobar $Ru + Ru$ and $Zr + Zr$ collisions at $\sqrt{s_{N N}} = 200 GeV$ , compared to the second-order measurements in $Au + Au$ collisions [3]. Open boxes show systematic uncertainties. The results for the third-order event plane measurements in isobar collisions are slightly shifted for a better visibility. Solid bands present calculations from the hydrodynamic model [27] (see Fig. 3 caption).
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Figure 5
Comparison of the second Fourier sine coefficients of the $Λ + \bar{Λ}$ polarization component along the beam direction among isobar and $Au + Au$ collisions at $\sqrt{s_{N N}} = 200 GeV$ [3] and $Pb + Pb$ collisions at $\sqrt{s_{N N}} = 5.02 TeV$ [4] as a function of centrality. Open boxes show systematic uncertainties. The inset presents the same data plotted as a function of average number of participants $⟨ N_{part} ⟩$ . Note that the data points for $Pb + Pb$ collisions are rescaled to account for the difference in the decay parameter $α_{Λ}$ used in the $Pb + Pb$ analysis.
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Physical Review Letters

Hyperon Polarization along the Beam Direction Relative to the Second and Third Harmonic Event Planes in Isobar Collisions at sNN=200 GeV

M. I. Abdulhamid et al. (STAR Collaboration)

Phys. Rev. Lett. 131, 202301 – Published 14 November 2023

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Hyperon Polarization along the Beam Direction Relative to the Second and Third Harmonic Event Planes in Isobar Collisions at $\sqrt{s_{N N}} = 200 GeV$