RHIC Beam Energy
Scan and Vorticity
TCHoU meeting
2023/6/27
Kosuke Okubo

Heavy ion collisions experiment• Understand the properties of quark-gluon
plasma(QGP)• Map out QCD phase diagram• Beam energy scan program

2Kosuke Okubo

RHIC-STAR experiment
Solenoidal Tracker At RHIC (STAR)

Relativistic Heavy Ion Collider (RHIC)

TOF
BBCTPCZDC‣ Time Projection Chamber (TPC)• Brookhaven National Lab. (NY)•- Main tracking detector, |η|<1.0, full azimuth

sNN = 7.7 - 200 GeV for A+A
p+p, p+Au, Au+Au, Cu+Cu,Cu+Au…

‣ Time-Of-Flight (TOF)- Particle identification, |η|<0.9, full azimuth‣ Beam-Beam Counters (BBC)- Event plane reconstruction , 3.3<|η|<5.0‣ Zero Degree Calorimeters (ZDC)- Event plane reconstruction using spectator neutrons,|η|>6.3
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Kosuke Okubo

Vorticity and magnetic field✦In non-central collisions…
‣ The created matter should exhibit strong vorticity.
-Z.-T.Liang and X.-N. Wang, PRL94, 102301‣ The strong magnetic field would appear in the initialstate.
-D. Kharzeev, L. McLerran, and H. Warring, Nucl.Phys.A803, 227 (2008)-McLerran and Skokov, Nucl. Phys. A929, 184 (2014)

BL

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Kosuke Okubo

Global polarization
antiparticleparticle‣ Large orbital angular momentum transfers to the spin degrees of freedom:- Quarks and anti-quarks’ spins are aligned with the angular momentum.
‣ Spin alignment by magnetic field:- Quarks and anti-quarks get aligned in the opposite direction due to theopposite signs of their magnetic moments.
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Kosuke Okubo

How to measure the global polarization?
✦Parity-violating decay of hyperon• Daughter proton preferentially decays alongthe Λ’s spin (opposite for anti-Λ).

Λ → p + π−

(BR:63.9%, cτ~7.9cm)• Polarization can be measured via the distributionof the azimuthal angle of the daughter proton(in the hyperon rest frame).
✦Projection onto the transverse plane

8 ⟨sin(Ψ1 − ϕ*p )⟩PH =παHRes(Ψ1)- STAR, PRC76, 024915(2007)

αH : decay parameter (αΛ = 0.732 ± 0.014)
Ψ1 : 1st-order event planeϕ*p : azimuthal angle of the daughter
proton in the Λ’s rest frame

6P.A. Zyla et al. (PDG),
Prog. Theor. Exp. Phys.2020, 083C01 (2020).

Kosuke Okubo

Collision energy dependence of PH
J. Adams et al. (STAR), PRC98, 14910 (2018)• Positive polarization signals are observed.
Becattini, Karpenko, Lisa, Upsal, and Voloshin,PRC95.054902 (2017)1 ω μΛ B±PΛ(Λ) ≃2 TT
ω = (PΛ + PΛ)kBT/ℏ ∼ 1021s −1μΛ : magnetic momentαΛ =0.642

T : temperature at thermal equilibrium(=160 MeV)

• Polarization increases with decreasing
collision energy.
• No significant difference between Λ andanti-Λ.

7Kosuke Okubo

Collision energy dependence of PHPH [%]Global polarization of Λ hyperons in Pb+Pb collisions atsNN = 2.76, 5.02 TeV.

8STAR Au+Au 20%-50%

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PRC76.024915 (2007)Λ
Λ

Nature548.62 (2017)ΛΛ

Phys. Rev. C 98 (2018)ΛΛSTAR prelim.
Λ +ΛΛ

2.76 TeV

PΛ( % ) = 0.08 ± 0.10(stat.)± 0.04(syst.)ΛPΛ( % ) = − 0.05 ± 0.10(stat.)± 0.03(syst.)

ALICE PRC101.044611 (2020)

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Λ

Λ

Pb+Pb 15-50%AMPT, Λprimary

2primary+feed-down

UrQMD+vHLLE, Λ
primary
primary+feed-down

5.02 TeV

PΛ( % ) = − 0.13 ± 0.11(stat.)± 0.04(syst.)PΛ( % ) = 0.14 ± 0.12(stat.)± 0.03(syst.)

0α Λ = -α =0.732
Λ−210102

310sNN [GeV]✓Global polarization continue to decrease at higher energies.

8Kosuke Okubo

Vorticity at low energy

X.-G. Deng et al., PRC101.064908 (2020)

UrQMD model• Angular momentum is the largest at3 GeV.
• Vorticity disappears at 2mN GeV.
➡Global polarization is expected to be thelargest at 2mN ≈ 1.9 < sNN < 7.7 GeV.

9Kosuke OkuboPH [%]

Global polarization in low energies
STAR Au+Au 20%-50%

STAR preliminary

5Nature548.62 (2017)

ΛΛ

PRC76.024915 (2007)

ΛΛ

PRC98.014910 (2018)

ΛΛ

PRC104.L061901 (2021)

ΛSTAR prelim.
Λ+Λ

Λ

Λ

ALICE PRC101.044611 (2020)
ΛΛ

Pb+Pb 15-50%

HADES prelim. SQM2021
Λ Au+Au 10-40%
Λ Ag+Ag 10-40%

0AMPT, Λprimary

primary+feed-down

α Λ = -α =0.732

UrQMD+vHLLE, Λ
primary
primary+feed-down

10Λ3102

10sNN [GeV]• HADES experiment has measured in Au+Au at 2.4 GeV and Ag+Ag at 2.55 GeV.
• STAR experiment has measured in Au+Au at 3.0, 7.2 GeV.
➡Global polarization increases with decreasing collision energy to 2.4 GeV.

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Kosuke Okubo

Centrality dependence of PH
AMPT model

Y.Jiang et al.,PRC94,044910(2016)• In most central collision, no initial angularmomentum.
arXiv：1805.04400• The polarization decrease in more centralcollisions.

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Kosuke Okubo

Rapidity dependence of PH• Polarization is expected to depend on rapidity but the prediction is different
among the models.
Z.T.Liang et al., Chin.Phys.C 45 (2021) 1, 014102

D.X.Wei, W.T.Deng and X.G.Huang, PRC99.014905 (2019)

AMPT

geometrical model

W.-T.Deng and X.G.Huang:PRC93,064907

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Kosuke Okubo

Rapidity dependence of PH• Polarization does not show significant
rapidity dependence within acceptance.
arXiv：1805.04400• Polarization in large rapidity region can be
explored in the future forward upgrade.

13Kosuke Okubo

Transverse momentum dependence of PH

One might expect…
• Decrease at low pT due to the smearing
effect caused by scattering at the laterstage of the collisions.
• Decrease at high pT due to jet
fragmentation.

arXiv：1805.04400

No significant pT dependence within
uncertainties.

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Kosuke Okubo

Global polarization of Ξ and Ω
P. A. Zyla et al. (Particle Data Group), Prog. Theor. Exp. Phys. 2020, 083C01 (2020)

Global polarization measurement of the other particles.
• Different spin and magnetic moments• Less feed-down in Ξ and Ω compared to Λ
• Could be different freeze-out• Different valence s-quarks• Less statistics of Ξ and Ω compared to ΛW.-T. Deng and X.-G. Huang, PRC93.064907 (2016)
15Kosuke OkuboΞ and Ω polarization measurement at 200 GeV• Global polarization of Ξ and Ω in Au+Au
collisions at 200 GeV⟨PΛ⟩ = 0.24 ± 0.03(stat.)± 0.03(syst.) [%]J, Adam et al. (STAR), PRL126, 162301 (2021)⟨PΞ⟩ = 0.47 ± 0.10(stat.)± 0.23(syst.) [%]⟨PΩ⟩ = 1.11 ± 0.87(stat.)± 1.97(syst.) [%]• Ξ and Ω polarization could be larger
than that of Λ
• Consistent with AMPT model calculation
within uncertainties.
• Naive expectation- Lighter particles could be morepolarized ( Ξ<Λ )- Earlier freeze-out leads to larger
polarization ( Ξ>Λ )- Feed-down effect : ~15-20% reduction
for primary Λ PH
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Kosuke OkuboΞ polarization at 27 and 54.4 GeV• Global polarization have measured in Au+Au collisions at 27 and 54.4 GeV- Consistent with AMPT model within uncertainties- Ξ polarization is consistent with Λ polarization within uncertainties.

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Kosuke Okubo

Centrality dependence of Ξ polarization

J, Adam et al. (STAR), PRL126, 162301 (2021)• Ξ polarization increases in more central
collisions as well as Λ polarization.
• Ξ polarization could be larger in peripheral
collisions.

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Kosuke Okubo

Global polarization in isobar collisions• Global polarization in Zr+Zr and Ru+Ru- The mass number is the same but the proton
number is different.
- Initial magnetic field different (~10%)- Verification of the magnetic contribution
S. Shuzhe et al., Phys.Lett.B 788 (2019) 409-413• System size dependence of the PH- AMPT model expects global polarization islarger in Cu+Cu than Au+Au collisions.
- The timing of the Λ production depends onthe collision system.
(Cu+Cu < Cu+Au < Au+Au)

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Kosuke Okubo

Global polarization in isobar collisions
Global polarization of Λ(Λ̄) hyperons in Au+Au collisions at 200 GeV• Significant global polarization are observed, PΛ and PΛ̄ increase with centrality.
• No significant difference between PΛ and PΛ̄ in Ru+Ru and Zr+Zr collisions.
• PΛ+Λ̄ are consistent between Ru+Ru and Zr+Zr collisions.
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Kosuke Okubo

Comparison with isobar and Au+Au collisions• Global polarization of Λ and Λ̄ are consistent between isobar and Au+Au collisionsystem, no collision system dependence is observed.

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Kosuke Okubo

Polarization along the beam direction : Pz
• Stronger flow in in-plane than in out-of-plane
cloud make local polarization along beam axis
• Longitudinal component, Pz, can be expressedwith ⟨cos θ*p⟩arXiv:2303.09074

αH :decay parameterθ*p :θof daughter proton in Λ rest frame
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Kosuke Okubo

Centrality dependence of Pz
J, Adam et al. (STAR), PRL123, 132301 (2019)
ALICE SQM2021

αΛ = 0.750

αΛ =0.642• Local polarization is larger in peripheral collisions.
- v2 is large in peripheral collisions- v2 has finite values due to the initial density fluctuations in most central collisions
but Pz is zero within the uncertainty.
- Consistent with BW model but AMPT model predicts opposite trend

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Kosuke Okubo

Centrality dependence of Pz

n=2

n=3

arXiv:2303.09074• Hydrodynamic model with shear-induced contribution can describe the result
vorticity :shear :

• No strong collision system and energy dependence- v2 in 5.02 TeV Pb+Pb is ~60% larger than that in 200 GeV isobar
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Kosuke Okubo

Summary and outlook
Summary• Global and local polarization of hyperons has been observed in heavy-ion
collisions- Most vortical fluid created in heavy-ion collisions (ω ∼ 1021s −1)- Differential dependence of global/local polarization has been measured- Ξ and Ω global polarization
BUR2020, STAR Note SN0755

Outlook• High statistics data ob BES-II 7.7 - 19.6 GeV
and FXT 3 - 7.7 GeV• Polarization in large rapidity region can be
explored in the future forward upgrade

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Kosuke OkuboBack up

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Kosuke Okubo

Feed-down effect✓観測されるΛ粒子のうち約60%が重い粒子の崩壊によって生成される。
✓親粒子の偏極は娘粒子(Λ粒子)に引き継がれる。
CAB : 粒子AからBへのスピン伝達係数
SR : 親粒子のスピンfΛR : ラムダ粒子のうち粒子Rの崩壊によって生成されるラムダ粒子の割合
μR : 粒子Rの磁気モーメント✓ラムダ粒子のグローバル偏極は15 - 20 %程度抑制される。

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Kosuke Okubo

Time dependence of vorticity

X.-G. Deng et al., PRC101.064908 (2020)

28Kosuke Okubo

Vorticity and directed flow

✓The slope of the directed flow at mid-rapidity is likely correlated with thevorticity.
- Global polarization and the negative slope of directed flow of pions have a similar
collision energy dependence.
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Kosuke Okubo