「高エネルギー原子核衝突で生成される渦と偏極」

Vorticity and polarization in heavy-ion collisions
Takafumi Niida

Heavy Ion Pub #31 (online)
September 28, 2020

Outline•

Introduction•

Initial orbital angular momentum, magnetic field, global polarization…

Global polarization measurements• Experimental results and Discussion•••

Global polarization•

Global spin alignment•

Local polarization along the beam direction•

and more if time permits…

Outlook and Summary* Slides are prepared in English just in case…
T. Niida, HI-Pub 20202

Important features in non-central heavy-ion collisions
Orbital angular momentum L

L

L=r⇥p
p
⇠ bA sN N<latexit sha1_base64="lbSX2W8qHLlkH8BQbEZuS9l9Is0=">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</latexit>b : impact parameter(vector connecting the center of two nuclei)
A : mass numberpparticipants

L ⇠ bA sN N

⇠ 10 (fm) ⇥ 197 ⇥ 200 (GeV)

reaction plane3= 2 ⇥ 10 ⇥ 197 (fm · GeV)(~c ⇠ 197 MeV · fm)

spectators

6<latexit sha1_base64="i5uBnN8irL2TJU6pIR6WgTpdLFg=">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</latexit>

T. Niida, HI-Pub 2020

⇠ 10 ~

Z.-T. Liang and X.-N. Wang, PRL94, 102301 (2005)
3

Important features in non-central heavy-ion collisions
D. Kharzeev, L. McLerran, and H. Warringa,
Nucl.Phys.A803, 227 (2008)
McLerran and Skokov, Nucl. Phys. A929, 184 (2014)

Initial magnetic field B

B L

Approx. Biot-Savart law for a point charge
2
q
1
r̂
q
r̂
E=
⇠
(at
t
⇠
0)
2 sin2 ✓)3/2 |r|2
4⇡✏0 (14⇡✏0 |r|2
1
B = 2v ⇥ Ecqµ0 v ⇥ r̂2
B⇠
⇠ (Z↵~/e)( /r )2
4⇡ |r|++++++
participants/r [1/fm ] (assume r ⇠ 10 fm,

2
⇠ m⇡

13

⇠ ~Z↵

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T. Niida, HI-Pub 2020

2

eB ⇠ ~Z↵

reaction plane

spectators

2

B ⇠ 10<latexit sha1_base64="teL0EWjjPkYZBE5PDWmrXu3rYNg=">AAACAHicbVDLSsNAFJ3UV42vqAsXbgaL4KpkVNBlqRuXFfqCJpbJdNIOnUnCzEQoIS78FTcuFHHrZ7jzb5y0XWjrgQuHc+7l3nuChDOlXffbKq2srq1vlDftre2d3T1n/6Ct4lQS2iIxj2U3wIpyFtGWZprTbiIpFgGnnWB8U/idByoVi6OmniTUF3gYsZARrI3Ud47suqeYgMi9z9BF/ph5UsBmbvedilt1p4DLBM1JBczR6Dtf3iAmqaCRJhwr1UNuov0MS80Ip7ntpYommIzxkPYMjbCgys+mD+Tw1CgDGMbSVKThVP09kWGh1EQEplNgPVKLXiH+5/VSHV77GYuSVNOIzBaFKYc6hkUacMAkJZpPDMFEMnMrJCMsMdEmsyIEtPjyMmmfV5FbRXeXlVp9HkcZHIMTcAYQuAI1cAsaoAUIyMEzeAVv1pP1Yr1bH7PWkjWfOQR/YH3+AEtGlOw=</latexit>⇠ 106.58)

T4

Important features in non-central heavy-ion collisions
D. Kharzeev, L. McLerran, and H. Warringa,
Nucl.Phys.A803, 227 (2008)
McLerran and Skokov, Nucl. Phys. A929, 184 (2014)

Initial magnetic field B

B L

magnetar, wikipedia

+
+
+
++
+

typical magnet

participants
reaction planesurface on magnetar
HI (200 GeV)B ⇠ 0.1

spectators**
T. Niida, HI-Pub 2020

11

T

13

T

B ⇠ 10B ⇠ 10<latexit sha1_base64="CCd8hal6imkY2/PtuWehiHGW2Og=">AAACNHicdZDLSgMxFIYzXmu9jbp0EyyKG8vEC7osdSO4qdAbdMaSSdM2NJkZkoxQhvGd3PggbkRwoYhbn8H0omirBwI//3cOJ+f3I86Udpwna2Z2bn5hMbOUXV5ZXVu3NzarKowloRUS8lDWfawoZwGtaKY5rUeSYuFzWvN75wNeu6FSsTAo635EPYE7AWszgrWxmvZlEe65igno5NGBkz+5TVwpYDl13ewXQc51glD6Hzn6Jk075+SdYcFpgcYiB8ZVatoPbisksaCBJhwr1UBOpL0ES80Ip2nWjRWNMOnhDm0YGWBBlZcMj07hrnFasB1K8wINh+7PiQQLpfrCN50C666aZAPzL9aIdfvMS1gQxZoGZLSoHXOoQzhIELaYpETzvhGYSGb+CkkXS0y0yTlrQkCTJ0+L6mEemcSvjnOF4jiODNgGO2AfIHAKCuAClEAFEHAHHsELeLXurWfrzXoftc5Y45kt8Kusj08SK6b2</latexit>

0.5 T

Lifetime of B-field is likely short (<0.5 fm/c), depending on conductivity
Rotating charged fluid also produces the field5

Important features in non-central heavy-ion collisions
B L
Strong magnetic fieldB ⇠ 1013

Orbital angular momentum

T

L=r⇥p
p
6
⇠ bA sN N ⇠ 10 ~2(eB ⇠ m⇡ (⌧ ⇠ 0.2 fm))<latexit sha1_base64="M57Jw2SWFxvE8peHZsYuobPdjBA=">AAACL3icbVDLSgMxFM34rPVVdekmWJR2U2aqoMtSQVxW6As60yGTZtrQZGZIMkIZpl/kxl/pRkQRt/6F6UPQ1gOBwznncnOPFzEqlWm+GmvrG5tb25md7O7e/sFh7ui4KcNYYNLAIQtF20OSMBqQhqKKkXYkCOIeIy1veDv1W49ESBoGdTWKiMNRP6A+xUhpyc3dVeGFLSmHltlNrMt0nNiCw3pq29kC+fG4m9gRTbvlccFWKJ5pZqk8z/o8LRbdXN4smTPAVWItSB4sUHNzE7sX4piTQGGGpOxYZqScBAlFMSNp1o4liRAeoj7paBogTqSTzO5N4blWetAPhX6BgjP190SCuJQj7ukkR2ogl72p+J/XiZV/4yQ0iGJFAjxf5McMqhBOy4M9KghWbKQJwoLqv0I8QAJhpSvO6hKs5ZNXSbNcssyS9XCVr1QXdWTAKTgDBWCBa1AB96AGGgCDJzABb+DdeDZejA/jcx5dMxYzJ+APjK9vEKKmsA==</latexit><latexit sha1_base64="j8NBdtKEvuqQFwUZUgSjJDcDF9w=">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</latexit>

D. Kharzeev, L. McLerran, and H. Warringa,
Nucl.Phys.A803, 227 (2008)
McLerran and Skokov, Nucl. Phys. A929, 184 (2014)

Z.-T. Liang and X.-N. Wang, PRL94, 102301 (2005)

reaction plane→Chiral magnetic effectChiral magnetic wave
Particle polarization
T. Niida, HI-Pub 2020

→Chiral vortical effect→Particle polarization
6

LBNL)
his version, v5))

Predicted polarizationof the orderfromparticles in unpolarized
high energy
hadron-Global polarizationa fraction to a few percent!

orbital angular momentum along the direction opposite to the reaction plane in the early stage
energy quarks
hadron-hadro...
golarized
is shownhigh
to polarize
along the same direction due to spin-orbital coupling. Such global
sequences, such as left-right asymmetry of hadron spectra, global transverse polarization ofm the decay of polarized resonances will have azimuthal asymmetry similar to the elliptic flow.
erent hadronization scenarios and can be easilyimpact
tested.
parameterxof the high energy collision picture in which the orbital angular momentum of the
1sequencesres,an angularerratum spinis added
to the final
version interaction. In particular I discuss a
articlemomentumvia publishedsome spin-orbital
Physics- Phenomenology(hep-ph)ondary particles(e.g. hyperons)
at midrapidity (xF = 0) and at low transverse momentum. I-Nian
Wangparticle(LBNL)
heproduceddirected and elliptic flow observed in relativistic nuclear collisions.
-ibid.Lett.96:039901,2006

http://arxiv.org/abs/nucl-th/0410089

zed Quark-gluon Plasma in Non-central A+A
Z.-T. Liang and X.-N. Wang, PRL94, 102301 (2005)
S. Voloshin, nucl-th/0410089 (2004)

ondaryin unpolarized high energy hadron7 Dec 2005 (thisparticles
version, v5))

Orbital angular momentum is transferred

local relative orbital angular momentum along the direction opposite beam
to the reaction
plane in the early stage
direction
scattering is shown to polarize quarks along the same direction due to spin-orbital coupling. Suchglobaltoparticlespin
1artonzbservable
consequences, such as left-right asymmetry of hadron spectra, global transverse polarization ofsion)s. Hadrons from the decay of polarized resonances will have azimuthal asymmetry similar to the elliptic flow.
Particlesʼ and anti-particlesʼ spins are aligned
ed within different hadronization scenarios and can be easily tested.

along
angularmomentum,
L
1
1
@v
z
ate
on someconsequences
hightoenergy
collision
picturein whichthe orbital angular momentum of thepostscript
figures,
an erratumofistheadded
the final
publishedversion
!
=
(r
⇥
v)
⇡
y via some spin-orbitalyintosecondaryparticleangularspin
momentuminteraction.
2
2 @x In particular I discuss aHigh Energy Physics - Phenomenology (hep-ph)larizationof secondary particles (e.g. hyperons) at midrapidity (xF = 0) and at low transverse momentum. I
2005;
Erratum-ibid.Lett.96:039901,2006(What is MathJax?)
daxcontributeto the produced particle directedantiparticle
and elliptic flow observed in relativistic nuclear collisions.

102301

Magnetic ﬁeld align particleʼs spin

particle
Vorticity → Global Polarization

Particlesʼ and antiparticlesʼ spins are aligned in
opposite direction along B due to the opposite
sign of magnetic momentax (What is MathJax?)

9v5 for this version)for this version)L)ow, October 10-14, 2016)b)
| Disable MathJax (What is MathJax?)• Vortical or QCD spin-orbit:
T. Niida,
HI-Pub(What2020 is MathJax?)
DisableMathJaxaligned with L

S.A. Voloshin

L
Producedparticles will be “globally” polarized along L and B.
B might be studied by particle-antiparticle difference.

Lambda and Anti-Lambda spins

6/30/16, 11:20 AM

7Rotation vs. Polarization
Barnett eﬀect:
rotation→polarization

Einstein-de-Haas eﬀect:
Converse: Einstein-De Haas effectpolarization→rotation
the only experiment by Einstein
A. Einstein, W. J. de Haas, Koninklijke Akademie van Wetenschappen te Amsterdam, Proceedings, 18 I, 696-711 (1915)

Magnetization of an uncharged bodywhen spun on its axis S. Barnett, Phys. Rev. 6, 239 (1915)

Rotation of a ferromagnet originally at rest
when put into an external H field

Rotation of a ferromagnet underAn effect of angular momentum
changeconservation: in the direction/strength
spins get aligned with H (irreversibly) andof
to conserve thethis magnetic-ﬁeld
must be compensated by a on overall
orbital angular momentum
total angular momentum.

~~~
J =L+S
figure: M. Matsuo et al., Front. Phys., 30 (2015)

M=
T. Niida, HI-Pub 2020!

χ: magnetic susceptibility
γ: gyromagnetic ratio

A.Einstein, W. J. de Haas,
B.Koninklijke Akademie van Wetenschappen te Amsterdam,
C.Proceedings, 18 I, 696-711 (1915)“the only experiment by Einstein”
8How to measure the polarization?
Parity-violating weak decay of hyperons (“self-analyzing”)⇤!p+⇡(BR: 63.9%, cτ~7.9 cm)

Daughter baryon is preferentially emitted in the directionof hyperonʼs spin (opposite for anti-particle)<latexit sha1_base64="uzz/9hZ3311/KMc1QeHVWhKqWZY=">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</latexit>

θ

dN
⇤
/
1
+
↵
P
cos
✓
H
H
⇤
d cos ✓

PΛ

PH: Λ polarization
θ*: polar angle of proton relative to the polarization direction in Λ rest frame
αH: Λ decay parameter

π-

dN
dcosθ
Note: αH recently updated by BESⅢ CollaborationαΛ=0.732±0.014, αΛ- =-0.758±0.012
P.A. Zyla et al. (PDG), Prog.Theor.Exp.Phys.2020.083C01
T. Niida, HI-Pub 2020

p-1

slope=αHPH

0
cosθ

1
9

How to measure
the“global”
polarization?
Title: Globally Polarized
Quark-gluon
Plasma in Non-central A+A
Globalpolarization
Nuclear Theory[nucl-th/0410089] Polarized secondary particles in unpolarized high energy hadron-hadro...

http://arxiv.org/abs/nucl-th/0410089

Collisions
Nuclear Theory[nucl-th/0410079] Globally Polarized Quark-gluon Plasma in Non-central A+A Collisions
Authors: Zuo-Tang Liang (Shandong U), Xin-Nian Wang (LBNL)
Predicted polarization of the order from(Submitted on 18 Oct 2004 (v1), last revised 7 Dec 2005 (this version, v5))

http://arxiv.org/abs/nucl-th/041007

Title: Polarized secondary particles in unpolarized high energy hadrona fraction
to a few percent!
“global” polarization :hadron
spinalignment
alonginitialangularmomentumcollisions?
Abstract:
Producedpartonshave large local
relative orbitaltheangular momentum
along thedirection opposite to thereaction plane in the early stage
Nuclear
Theory[nucl-th/0410089]
Polarized
in unpolarizedenergy quarks
hadron-hadro...
of non-central
heavy-ionsecondary
collisions.particles
Parton scattering
is shownhigh
to polarize
along the same direction due to spin-orbital coupling. Such global

http://arxiv.org/abs/nucl-

quark
polarization
will lead to many observable consequences, such as left-right asymmetry of hadron spectra, global transverse polarization of
Authors:
SergeiA. Voloshin
thermalphotons,
dileptons and hadrons. Hadrons from the decay of polarized resonances will have azimuthal asymmetry similar to the elliptic flow.
(Submitted
on 21
Oct 2004)
Global hyperon polarization is predicted within different hadronization scenarios and can be easily tested.
x in which the orbital angular momentum of the
Abstract:
In
this
short
note
I
speculateon
someconsequences
of
the
high
energycollision
picture+sconverted
1 into!secondary
ly =figures,
1particle⇢0 colliding! ⇡hadronsy =Comments:
4⇡
pages
in be
RevTexwith
2 postscriptan angularerratum spinis added
to the final
version interaction. In particular I discussDetector
canmomentumvia publishedsome spin-orbitala
Subjects:(nucl-th);High Energy
Physics particles- Phenomenology(hep-ph)possibility toNuclear
observeTheorya non-zeropolarizationof secondary(e.g. hyperons)
at midrapidity (xF = 0) and at low transverse momentum. I
Authors:
Zuo-Tang
Liang could(ShandongU),
Xin-Nian
Wangparticle(LBNL)
speculatethat such effects
contributeto the produced
directed and elliptic flow observed in relativistic nuclear collisions.
Journalalso
reference:Phys.Rev.Lett.94:102301,2005;
Erratum-ibid.Lett.96:039901,2006(Submitted
on 18 Oct 2004 (v1), last revised 7 Dec 2005 (this version, v5))
DOI:
10.1103/PhysRevLett.94.102301
Comments: 2 pages, Latex
Report number: Abstract:
LBNL-56383
Subjects: Nuclear Theory Produced(nucl-th) partons have large local relative orbital angular momentum along the direction opposite to the reaction plane in the early stage
Cite as:+arXiv:nucl-th/0410079
ofnon-central
heavy-ioncollisions.
Partonscattering is shown to polarize quarks along the same direction due to spin-orbital coupling. Such global
0
l
=
1
!
s
=
1
Cite as:⇡ ⇡ arXiv:nucl-th/0410089
!
⇢
y
y
quark
polarization will lead toobservable consequences, such as left-right asymmetry of hadron spectra,zglobal transverse polarization of(or arXiv:nucl-th/0410079v5
formany
this version)(or arXiv:nucl-th/0410089v1
for this
Authors:
Sergeiphotons,
A. Voloshin
thermaldileptons
andversion)
hadrons. Hadrons from the decay of polarized resonances will have azimuthal asymmetry similar to the elliptic flow.

Title: Globally Polarized Quark-gluon Plasma in Non-central A+A
NuclearCollisionsTheory
Projection onto the transverse plane

Title: Polarized secondary particles in unpolarized high energy hadronhadron collisions?
(Submitted
onhyperon21 Oct polarization
2004)
Globalis predicted within different hadronization scenarios and can be easily tested.

Submission
Submission history
history

Abstract: In4 thisshortnote I speculate
on someconsequences
hightoenergy
collision
picturein which the orbital angular momentum of theComments:
pages
in RevTex
with 2 postscript
figures,
an erratumofistheadded
the final
publishedversionFrom: Xin-Nian Wang[view email]collidinghadronscanbe converted
particleangular spin momentum
From:
SergeiA.
Voloshin[view
email]
Subjects:
Nuclear
Theory(nucl-th); into
Highsecondary
Energy Physics- Phenomenology(hep-ph) via some spin-orbital interaction. In particular I discuss a[v1] Mon, 18 Oct 2004 18:54:46
GMT (34kb)
possibility
observeof secondary particles (e.g. hyperons) at midrapidity (xF = 0) and at low transverse momentum. I[v1] Fri,
Thu,2221
Oct2004
2004
19:43:03to
GMT(3kb)a non-zero polarization[v2]
Oct
02:25:19
GMT(34kb)
Journalreference:Phys.Rev.Lett.94:102301,2005;
Erratum-ibid.Lett.96:039901,2006
Whichauthorsof 2004thisare endorsers?
| Disable(What is MathJax?)
alsopaper
speculatethat(34kb)
sucheffectsMathJax
could contributeto the produced particle directed and elliptic flow observed in relativistic nuclear collisions.
[v3]
Mon,
25
Oct
18:35:22
GMT
DOI:
10.1103/PhysRevLett.94.102301[v4] Tue, 26 Apr 2005 18:42:39 GMT (37kb)
LinkWed,back 7to:arXiv,
form
interface,contact.
Reportnumber:
LBNL-56383
[v5]
Dec
2005
02:02:09
GMT(37kb)
Comments:
2 pages,
Latex
Which authors
this paper arearXiv:nucl-th/0410079
endorsers? | Disable MathJax (What is MathJax?)
Citeofas:
Subjects: Nuclear Theory (nucl-th)(or arXiv:nucl-th/0410079v5
for this version)
Link back to: arXiv, form interface,contact.

Angular momentum direction can be determined byCite as:spectator deﬂection (spectators deﬂect outwards)

arXiv:nucl-th/0410089(or arXiv:nucl-th/0410089v1
for this version)
S. Voloshin
and TN, PRC94.021901(R)(2016)

Submission history

Submission
history
From: Xin-Nian Wang[view email]2 of 2[v1] Mon, 18 Oct 2004 18:54:46 GMT (34kb)[v2] Fri,
22 Oct02:25:19
GMT(34kb)
S.A. Voloshin
SergeiA.2004
Voloshin[view
email]
page 12 From:ICPPA-2,
Moscow, October 10-14, 2016
[v3]
Mon,
25
Oct
2004
18:35:22
GMT(34kb)[v1] Thu, 21 Oct 2004 19:43:03 GMT (3kb)Ψ1: azimuthal angle of b[v4] Tue, 26 Apr 2005 18:42:39 GMT (37kb)
Whichauthors of this paper are endorsers? | Disable MathJax (What is MathJax?)[v5] Wed, 7 Dec 2005 02:02:09 GMT (37kb)*: φ of daughter proton in6/30/16,
11:20 AMφΛ restframepWhich authors of this paper are endorsers? | Disable MathJax (What is MathJax?)

8 hsin( 1
PH =
⇡↵H
Res(

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2 of 2

T. Niida, HI-Pub 2020

⇤
p )i

1)

STAR, PRC76, 024915 (2007)
6/30/16, 11:26 AM10¯ (b) in the 30–40% centrality bin for(a) and of the (p̄, π ) system for !
dashed lines show the fitting function for actual fit range, Eq. (3), with2014 data. Bold solid lines show the background distribution obtained
two different background assumptions.
by a linear fitting function, and dashed lines show the backgroundfrom mixed events. Shaded areas show the extracted signal
after theGLOBAL
POLARIZATION OF ! HYPERONS IN …
protons in the ! rest frame relative to the reaction plane.
background subtraction using the fitting function.

Signal extraction with Λ hyperons

1*〈sin(Ψ -φp)〉1*〈sin(Ψ -φp)〉

As mentioned in Sec. III A, the first-order event plane "1
6
6
STAR,
PRC98,
014910(2018)×10
×10
determinedbythespectator
fragments
was
used
in
this
analysis
−
0.001
π
Λ
the TOF detector, like in our previous publication [33]. Charged STAR
10%-80%as an estimator of40the reaction
plane.
The
sideward deflection
200
GeV
Λ
Λ Au+Au
pions and protons were selected by requiring the track toof the spectators allows us to know the direction of the initial
be within three standard deviations (3σ ) from theirpeaks
40
angular momentum.
Taking into account the experimental30
realin the normalized dE/dx distribution. If the track had BG
TOF
resolution of the event plane, the polarization projected0onto(fit)
hit information, thenpa constraint based on the square of
BG the(mix)
20 system global angular momentum can be
the direction of thereal-BG
20 wasmeasured mass was required. If the TOF informationnot (fit) obtained by [13]:10available, then an additional cut based on dE/dx was applied,
(a)
(b)#$
−0.001!
" obs
STAR 10%-80
∗
sin
"
−
φ
requiring
pions(protons)
to
be
3σ
away
from
the
proton(pion)
8
Λ
p
1
1.1
1.11
P
,
(2)
=
H
peak
normalizedINdE/dx
distribution.
GLOBAL POLARIZATION
OFin
!the
HYPERONS…
PHYSICALREVIEW
014910
1.1
1.11
1.12
1.1π α C 98,
1.12(2018)
H 1.11 Res("1)
The invariant mass, Minv , was calculated using candiMinv [GeV/c2]
Minv [GeV/c2]¯ (α!¯ ),
where
α
are
the
decay
parameters
of
!
(α
)
and
!
dates
for
the
daughtertracks.
To
reducethecombinatorial
H!
6
6
FIG. 3.the⟨sin("1 −
∗
×10
×10
=
−α
=
0.642
±
0.013
[35].
The
angle
φ
denotesαzero
BG¯
background, selection criteria based on the following
decay−! mass distributions!
p0.001 FIG.
2.
Invariant
of
the
(p,
π
)
systemfor!
¯ (b) in the 10ΛΛ(a) and !
BG of α +β Minv
STAR 10%-80%
azimuthal
angle
daughterprotonbin
infor
the ! rest frame.
+
topology 40
parameters¯ (b)ofin theΛΛ were used:) system for!
the 30–40%
centrality(a) and of the (p̄, πdashed lines show the fi
ThelinesRes("is backgroundthe resolutionof the obtained
first-order event plane.
1 ) the2014 data. Bold solid
show
distribution
two different backgrou(i)Distanceoftheclosestapproach(DCA)
between40
Two
different
techniques
were
used
to extract the polarization30
byalinearfittingfunction,anddashed
lines
show
the
backgroundreal∗
daughter tracks and the primary vertex, from0signal⟨sin("−
φinvariantmass
methodand the event
1 show
mixed events. Shaded areas
thetheextracted
signal
after
the
p )⟩:
BG (fit)¯(ii) DCA
betweenreconstructedtrajectories
of
!
(
!)
protonsin the ! replane method,both ofwhich are often used in flow
analyses
BG (mix)
backgroundsubtraction
using the fitting
function.
20
candidates and the primary vertex,
As mentioned in S
real-BG (fit)[3,37].
20(iii) DCA
between two daughter tracks, anddeterminedby the spIntheinvariantmass
method[36,37],
the
mean
value
of
negativeforanti-Λ
10(BR: (a)63.9%, cτ~7.9 cm) ¯(b)−0.001(a)(b)
the TOFdetector,in ourprevious[33]. Charged(iv) Decay length of ! (!) candidates.
STAR
10%-80%as an ofestimator
thelikesine
termin Eq.publication(2) was measured
as a function
the of thpions
and protons
wereselectedbytherequiring
the
track
to
Hcannot
H̄alloofthe spectators
1.1
1.11 invariant
1.12 mass. Since
1.1
1.11
1.12
!
particles
andbackgroundbe¯1.11candidates
1.1
1.11
1.12
1.1 ! (!)
1.12 were required to point
Furthermore
away three standard deviations
be within(3σ ) from their peaks
2
2
angular momentum
separatedonanevent-by-event
basis,
the observed
polarization
Minv [GeV/c ]Minv [GeV/c]
fromvertex. M
Cuts[GeV/con the22⇤ decay topology
in thewere
normalized dE/dx distribution. If the track had TOF
resolution of the eve
Minv [GeV/c] the primary hsin(]
signal
is
the
sum
of
the
signalandbackground:
inv
)i
8
1
p
adjusted, dependingon the collisioncentrality,
to accountfor
hit information,
thena constraint based on the square of thethe direction of the
∗
FIG.
3.
⟨sin("−
φ)⟩asafunctionoftheinvariant
mass
for
!
P
=
1
∗ the
obsTOF information
p required. If
Bg∗ Sg
Hvariation of the combinatorial
measuredmass was
was
not
the
backgroundwithcentrality.
−⟨sin("
−
φ
)⟩
=
(1
−
f
(M
))⟨sin("−φ)⟩ by [13]:1inv
1 obtainedppFIG. 2. Invariant mass distributionsof H
the (p, πRes() system 1for
!¯
¯
⇡↵
)
(a) inandthe!!(b)in thenthe 10–80%
centrality
bin for
2014
data.
Solid
and
available,anadditional
cut
based
on
dE/dx
was
applied,The
backgroundlevel
relative
to
the
!
(
!)
signalmass¯ (b) in the 30–40% centrality bin for
Bg Eq. (3), with
∗ Bg(a) and of the (p̄, π + ) system for !
dashed
lines
show
the
fittingfunctionforactualfit
range,+
f(M)⟨sin("−
φ(3)
inv(pion)1
p )⟩ ,
region falls below 30% at maximum in this analysis.requiring
Finally, !pions (protons) to be 3σ away from the proton
data.
Bold solid lines show ¯the background distribution obtained
P11
different
assumptions.
H =T. Niida, 2014
HI-Pub2020
peak
inbackgroundthe normalized
dE/dx
distribution.
and ! with 0.5 < pT < 6 GeV/c and |η| < two
1 wereanalyzed
Bg

⇤!p+⇡

↵

=

↵

C a simple rational number in all cases where the conser(38)P⇤meas = 2
f⇤R C⇤R 13 f⌃0 R C⌃0 R SR PR
vation laws fully constrain it. The polarization transfer
R
coefficients C of several important baryons decaying to ⇤s
are reported in table (I) and their calculation described
where SR is the spin of the particle R. The sums in equain detail in Appendix A.
tions (37) and (38) are understood to include terms for
Taking the feed-down into account, the measured mean
the contribution of primary ⇤s and ⌃0 s. These equations⇤ spin vector along the angular momentum direction canare readily extended to include additional multiple-step
0→Λγ, Ξ→Λπ
then be expressedas:~60%
of measured
Λ are feed-down fromΣ*→Λπ,
Σ
decay chains that terminate in a ⇤ daughter, althoughX⇥⇤ ⇤such contributions would be very small.
⇤,meas
1
S⇤=
f⇤R C⇤R 3 f⌃0 R C⌃0 R SR .
(37)
Polarizationof parent particle R is transferred
itslimit
daughterΛ
Therefore,toin theof small polarization,
the polarR
izations of measured (including primary as well as sec(Polarizationtransfer
could benegative!)
This formula accounts
for direct feed-downof a particleondary) ⇤ and ⇤ are linearly related to the mean (coCΛR : coeﬃcientof spinresonance R to a ⇤, as well as the two-step decay R !
moving) thermal vorticity
and magnetic
field transfer
accordingfrom parent R to Λ
SRand: parent
particleʼs
spin⌃0 ! ⇤; these are the only significant feed-down paths
to eq. (31) or eq. (14),these physicalquantities
may
to a ⇤. In ⇤the eq.( 37),⇤f⇤R (f⌃0 R ) is the fraction
from measurement
as: of Λ originating from parent R
S(S +of1) be extractedµfΛR : fraction

Feed-down effectS⇤ = CSR

0
B
B
@

HIN
prim
− P"

d ". Any "’s oforder ofates [37–pplied tonting forSec. VI.
n " andchemical
erent formight be

$c

1

2 2P
3

f⇤R C⇤R

hSy i /

1
0
0
3 f⌃ R C⌃ R

SR (SR + 1)

C 6 R
C=6
A 4 REVIEWP C 95, 054902 (2017)
PHYSICAL
2
1
f
C
f⌃0 R C⌃0 R SR (SR + 1)
⇤R
⇤R
3
3
Bc /T
R

TABLE I. Polarization transfer factors C [see Eq. (37)] for
important decays X → "(&)π
Decay

3

(! +
2
3

2
3

S

B)

P

f⇤R C⇤R

R

P
Rf⇤R C⇤R

μR : magnetic moment of particle R

10
0
3 f⌃ R C⌃ R

(SR + 1) µR

100
3 f⌃ R C⌃ R

(SR + 1) µR

3 10
7
7
5

B
B
@

P⇤measP⇤meas

(39)

1

C
C.
A

Becattini, Karpenko, Lisa, Upsal, and Voloshin, PRC95.054902 (2017)

C

In
the
(39),
timatesofvorticity
andmagnetic
field
based
on
exper− R stands for antibaryons that feed down
+ eq.
+
1
1
Parity conserving: /2 → /2 0
−1/3
PrimaryΛ
polarization
willbedilutedby
15%-20%into
measured⇤s.
Thepolarizationtransfer
is
the
same
imentalmeasurementsoftheglobalpolarizationof hy−−+
1
Parity conserving: 1/2 → 1/2 0
p
−
+
+
3
1
for /baryons
antibaryons (C⇤R 1/3= C⇤R ) andthe magperons, as we illustrate with an example, using sNN =2 → /2 and0
Parity conserving:(model-dependent)
3/2− → 1/2+ 0−
Parity-conserving:
netic
moment has opposite sign (µ−1/5= µR ).
19.6 GeV THERMUS feed-down probabilities. Let us asR+0.900(0 → " + π 0
This
also
that
the
polarizationofdaughterparticles
sume that thethermalvorticity
is $ = 0.1 andthe magAccording
tothe
THERMUSmodel [42],tuned
to suggests−−p+0.927( →"+πnetic field is B = 0. In this case, according to eq. (15), theat sNN =−1/3& 0 → " + γ reproduce semi-central Au+Au collisions
can
be
used
to
measurethepolarizationof
its
parent!
e.g.
Ξ,
Ω
prim
prim
primary
hyperonpolarizations
are
P
=
P
=
0.05.
19.6 GeV, fewer than 25% of measured ⇤s and ⇤s are⇤⇤
However, the measured polarizations would be P⇤meas =primary, while more than 60% may be attributed to feed12
T. Niida, HI-Pub
2020
meas
⇤
0
where P is down
the parent
particle,D theC a0.0395 and P= 0.0383. The two measured values
fromprimary⌃ daughter,, ⌃ andand⌅ baryons.

tformed. Both the sign and magnitude of the reconstructed
Hyperon spin precession!0.1%
polarization agreed with the input values within statistical
Total uncertainty (sum)105%
uncertainties.
The measurement could be affected by other systematiceffects. Most of them are similar to those present in anpolarization measurement due to detector effects is estimatedanisotropic flow analysis, with the most significant one coming
to be less than a factor of 2.
PHYSICALREVIEW
C
76,
024915(2007)
from the determination of the event plane vector and its
Takingallthesepossiblecorrection
factors
into
account
B. I. ABELEV
et al.
PHYSICAL REVIEW C 76, 024915 (2007)
resolution.
In calculating the reaction plane resolution, weand considering that our measurements are consistent with
Globalpolarization
measurement
in
Au+Au
collisions
used the random subevent technique [6], as well as the
Au+Au
√sof
= 62.4
andGeV
in 2004
NN about
zero withcollisions
statistical at
error
0.01,
our200resultssuggestmixed harmonic
method [6,10,27]
with the second-order
event12 0.1 28
0.1¯ polarizations
30
45
20
13
that theglobal!17 andstatistics!
are!0.02 in magnitude.
very
limited(~9M
events)M. Aggarwal, Z. Ahammed, B. D. Anderson, D. Arkhipkin, G. S. Averichev, Y. withBai,
J. Balewski,
plane
determinedfrom TPC
tracks. The
mixed harmonic 0.08
9
2
18
50
12
0.08
a, L. S. Barnby, J. Baudot, S. Baumgart, V. V. Belaga, A. Bellingeri-Laurikainen,40 R. Bellwied,48
method
is
known
to
be
28
9
35
19effective in30 suppressing
47 a wide 50
50o, R. R. Betts,
S.
Bhardwaj,A.
Bhasin,A.
K.
Bhati,H.
Bichsel,J.
Bielcik,
J.
Bielcikova,
0.06
0.06
3
22
2
36
28
40
26
of nonflow
effectsof
S.-L. Blyth, range
M. Bombara,
B. E.effects
Bonner,(short-range
M. Botje, correlations,
J. Bouchet, A.
V. Brandin,
T. P. Burton,2
III. CONCLUSION
11
39
50
6
9
50
6
0.04
0.04
momentumconservation[28],
sky, X. Z. Cai,
H. Caines,
M. Calderónde laetc.).
Barca Sánchez, J. Callner, O. Catu, D. Cebra,
29
38
49
43
¯ hyperon global polarization has been
,41 Z. Chajecki,
P. Chaloupka,
S. Chattopadhyay,
F. Chen,J. polarization
H. Chen,39 J. Y. 0.02
Chen,The
J. Cheng,
suppress11thecontribution 45toH.theglobal! and!
0.02 To
50
3
3
41
41
18
y,10 A. Chikanian,W.
Christie,
S.
U.
Chung,
R.
F.
Clarke,M.
J.
M.
Codrington,
J.
P.
Coffin,measurementfrom
nonflow
effects(mainlydue
tomomentummeasuredin
Au+Au
collisionsatcenter-of-massenergies
0
0 37
47
5
45
15
42√
37
M. R. Cosentino,
J.
G.
Cramer,H.
J.
Crawford,
D.
Das,
S.
Dash,
M.
Daugherity,
M.
M.
deMoura,
conservation)
the combinationof 3both east14and west forwardsNN= 62.4 22and 200 GeV with the STAR detector at RHIC.
2
3
32
17
19
M. DePhillips,
Dogra, X. Dong,-0.02 A. A. Derevschikov, L. Didenko, T. Dietel, P. Djawotho, S. M.-0.02
TPC 6event plane
vectors12 was used. The
contribution from45 An upper limitof|P¯ | ! 0.02 for the global polarization of
41
50
3
22
!,
!
berg, J. E. Draper, F. Du, V. B. Dunin, J. C. Dunlop, M. R. Dutta Mazumdar, W.
R. Edwards,-0.04¯ 23hyperons within the STAR detector acceptance is
-0.04
other
jets,
etc.)
was
12
26few-particle
5 correlations
36 (i.e., resonances,
40
18
3 ! and !
v, V. Emelianov, J. Engelage, G. Eppley, B. Erazmus, M. Estienne, P. Fachini, R. Fatemi,
1350
3 obtained41
2
estimatedby comparing
theresultsfromcorrelations
obtained.
This45 upper limit is far below the few tens of percent-0.06
A. Feng,49 P.-0.06
Filip,
E. Finch,
V. Fine,3 Y.
Fisyak,J. Fu,49 C. A.
Gagliardi,
L. Gaillard,
M. S. Ganti,
10
46
28
44
34
7⚫
Λ
200 45GeV
using
positiveornegative
particlestodeterminethereactionvaluesdiscussed
in
Ref.
[1],
but
it
falls
withinthepredicted,9 V. Ghazikhanian,P.
Ghosh,
Y.
N.
Gorbunov,
H.
Gos,
O.
Grebenyuk,D.
Grosnick,B.
Grube,
-0.08
-0.08
Λ
7
37 62.4 GeV 19
19
6
3
K. S. F. F. Guimaraes,
A. Gupta, N.
Gupta,toB.
T. J. Hallman,
A. Hamed,41region
J. W. Harris,
plane. Uncertainties
relatedtheHaag,
dependenceof tracking
from50the more realistic calculations [4] based on the-0.1Hoffman,23-0.1Henry,41 S. Heppelmann,31 B. Hippolyte,18 A. Hirsch,33¯ E. Hjort,22 A. M.
. Heinz,50 T. W.
0
10
20
30
40
50
60
70
80
-1
-0.5
0
0.5 and !
1 (!) hyperon
efficiency(inparticular,
chargedparticle
HTLmodel.
9
9
22
7
4
29
7
n,42 D. J. Hofman,
R.
S.
Hollis,M.
J.
Horner,H.
Z.
Huang,
E.
W.
Hughes,T.
J.
Humanic,
G.
Igo,
onη Λ
azimuthal
angle
σ (%)
9
22 reconstruction
17 efficiency)
112
5 were estimated, P. Jacobs, W. W. Jacobs, P. Jakl, P. G. Jones, E. G. Judd, S. Kabana,40 K. Kang,43 J. Kapitan,11
20 by comparing
12 the results
47 obtained with32 different magnetic
D. Keane, A. Kechechyan, D. Kettler, V. Yu. Khodyrev, J. Kiryluk,22 A. Kisiel,29 E. M. Kislov,12
ACKNOWLEDGMENTS
field
andD.also
with
plane
vectors
determined
44
11 Global polarization of ! hyperons as a
FIG. 26
5. V.(Color
online)FIG.
4. settings(Color 23
online)Globalpolarization
of14!M.
hyperons
as20aL. Kotchenda,
G. Knospe,50A.
Kocoloski,D.
Koetke,T.event
Kollegger,
Kopytine,
Kouchpil,26
1
18 theResults
30 of
7with
consistentzero…,
givinganinelastic
upper
limit
of PH<2%function
centrality
given
as a fractionof the total
frompositively
or32negatively
chargedparticles.
The magnitude
thankthe RHIC
Operations
Groupand hadronic
RCF
at BNL,
keys
are
same
as 12inwere
functionofV.
!I.pseudorapidity
η! . Symbol
ik,22 P. Kravtsov,
Kravtsov,
K. Krueger,
C. Kuhn,
A. I. Kulikov,
A. Kumar,P. We
Kurnadi,50
3 is multiplicity
14
3
3 keys are the same as in Fig. 3. Only statisticalcross section.
correlations
dependent,
andsov,12 M.Fig.
A. C.
J. lineM. Landgraf,
S.dataLange,
S. yields
LaPointe,
Laue,
Lauret,A. Lebedev,
andtheSymbol
NERSC
Center at LBNL for their support. This
± 3 J.its
3.ofLamont,
Anonflow
constant
fit to thesepoints
P!48=F.(2.8√Lin,50 X. Lin,uncertainties
34
12 2
3
38
48
43
49
27
−3
are
shown.
C.-H. Lee,S.
Lehocka,M.
J.
LeVine,
C.
Li,
Q.
Li,
Y.
Li,
G.
S.
J.
Lindenbaum,
contribution
toanisotropic
flow
measurement
increases
with9.6) × 10 with χ /ndf = 6.5/10 for Au+Au collisions at sNN =work
wassupported
in
part
by
the
Offices
of
NP
and
HEP
13
36
3
36
3
3
49 HI-Pub 38
49
49
Niida,
2020−3
F.T.Liu,
H.
Liu,
J.
Liu,
L.
Liu,
T.
Ljubicic,W.
J.
Llope,R.
S.
Longacre,
W.
A.
Love,
Y.
Lu,
8.0)
10reaction
200 GeV(centrality
regionThe
20–70%),
anduncertainty
P = (1.9 ±collision
centrality.
average
due
to×
the
PΛ

PΛ

First paper from STAR in 2007

First observation in BES-Ⅰ
STAR, Nature 548, 62 (2017)

Positive polarization signal at lower energies!

Au+Au 20-50%

PH looks to increase in lower energies-

Λ this study

8

Becattini, Karpenko, Lisa, Upsal, and Voloshin,Λ this study

1!
µ⇤ B
P⇤ '
+
2T
T
1!
µ⇤ B
P⇤¯ '
2T
T

Λ PRC76 024915 (2007)

6Λ PRC76 024915 (2007)

4

PRC95.054902 (2017)! = (P⇤ + P⇤¯ )kB T /~⇠ 0.02-0.09 fm

1

22⇠ 0.6-2.7 ⇥ 10 s

2

-

0

The most vortical fluid!

1μΛ: Λ magnetic moment
T: temperature at thermal equilibrium(T=160 MeV)

Hint of the difference between Λ and anti-Λ PH- Effect of the initial magnetic field? (discuss later)
10

T. Niida, HI-Pub 20202

10
sNN (GeV)
14

Fastest vorticity

Great red spot of Jupiter (picture: NASA)
6/27, 2019 by Hubble Space Telescope

Ocean surface vorticity~10-5 s-1
Jupiter’s great red spot
~10-4 s-1
Core of supercell tornado~10-1 s-1
Rotating, heated soap bubbles ~102 s-1
Superfluid helium nano droplet ~106 s-1
Matter in heavy ion collisions ~1022 s-1

Ocean surface vorticity
https://sos.noaa.gov/datasets/ocean-surface-vorticity/

R
ES E A RC| R E bubble
PO R TSvortexofHsoap

T. Muel et al., Scientiﬁc Report 3, 3455 (2013)vortex imagesalignedto x-ray
beam
in He
Fig. 3. He droplets doped with Xe atoms. (A and B) X-ray diffractionof doped
droplets,
displayedin adroplets
logarithmic intensity scale. (C) Droplet andSupercell in Oklahoma (2016)
embedded Xe clusters. Images in (A) and (B) correspond to tiltedT.and
parallelof the vortex
axes with
the incident x-ray beam,bnl.gov/newsroom
respectively.
Mueletalignmentsal., Scientiﬁc
Report3, respect
3455to(2013)
http://www.silverliningtours.com/tag/tornado/page/3/

T. Niida, HI-Pub 2020

The shapes adopted by the rotating quantumof quantum vortices. The existence of these

Perfect liquid is the most vortical fluid
olution (~3%). This observation and, in particular,
15

Precise measurements at √sNN = 200 GeV
PHYSICAL REVIEW C 98, 014910 (2018)

PH [%]

STAR, PRC98, 014910 (2018)
3
Nature548.62 (2017)
ΛΛ

PRC76.024915 (2007)
Λ

2

Λ

1

>5σ significance utilizing 1.5B events-

partly due to stronger shear flow structure in lower √sNN
because of baryon stoppingPH (⇤) [%] = 0.277 ± 0.040(stat) ±0.039
0.049 (sys)¯ [%] = 0.240 ± 0.045(stat) ±0.061
PH (⇤)
0.045 (sys)Theoretical models can describe the data wellI. Karpenko and F. Becattini, EPJC(2017)77:213, UrQMD+vHLLE
H. Li et al., PRC96, 054908 (2017), AMPTY. Sun and C.-M. Ko, PRC96, 024906 (2017), CKE
Y. Xie et al., PRC95, 031901(R) (2017), PICR
D.-X. Wei et al., PRC99, 014905 (2019), AMPTSTAR Au+Au 20%-50%
0-Λthis analysis
ΛConfirmed energy dependence with new results at 200 GeVUrQMD+vHLLE, Λ
primary+feed-down
primary
AMPT, Λprimary+feed-down
primary

10
T. Niida, HI-Pub 2020

102sNN [GeV]

16

ALICE, PRC101.044611 (2020)
F. Kornas (HADES), SQM2019
J. Adams, K. Okubo (STAR), QM2019

PH [%]

Collection of recent results
STAR Au+Au 20%-50%
Nature548.62 (2017)
ΛΛ

ALICE Pb+Pb 15-50%
Λ

PRC76.024915 (2007)
Λ
Λ

Λ

•

HADES prelim. Au+Au 10-40%

PRC98.014910 (2018)
ΛΛ

ALICE at 2.76 and 5.02 TeV•

ΛSTAR prelim. 27 GeV, 54.4 GeV

5Λ

Expected signal is of the order ofcurrent statistical uncertainty

Λ

•

•

UrQMD+vHLLE, Λ
primary
primary+feed-down
AMPT, Λprimary

HADES at 2.4 GeV•

still preliminary
hopefully reduce systematic uncertainty

primary+feed-down•

Preliminary of STAR at 27 and 54.4 GeV

0

1

10

102

3

10

sNN [GeV]
T. Niida, HI-Pub 2020

17

0.08

Collection of recent results

b=10.0 fm

0.06
0.04

〈-ϖy〉

〈-ω y〉 (fm-1)

b=8.0 fmsNN=10.0 GeV

0.06

0.06

ALICE,
PRC101.044611
0.04
0.04 (2020)
0.02
F.0.02Kornas (HADES), SQM2019
0
0
0
2
4
6 K.
8
10
12 14 16 (STAR),
18
0
2
4
6
8
10 12
J. Adams,
Okubo
QM2019t (fm)t (fm)
sNN=30.0 GeV

01STAR Au+Au 20%-50%
Nature548.62 (2017)
ΛΛ
PRC76.024915 (2007)
ΛΛ
PRC98.014910 (2018)ΛΛ

2

3 4 5 6 7 10
sNN (GeV)

20 30 40

FIG. 4. Time evolution of the mid-rapidity thermal vort
ferent energies and impact parameters in the simulatio
UrQMD model.

kinematic vorticity

ALICE
Pb+Pbkinematic
15-50%FIG.
3. Initialvorticity at mid rapidity as a function of thecollisionfor impact parameters0.12
b = 5, 8, and 10 fm.
Λ energy Λ

Au+Au

HADES prelim. Au+Au 10-40%
Λ

0.1

0.18
0.16

b=5.0 fm

thermal vorticity
0.1 (a1) Au+Au,b=5.0 fm

Au+Au 0.08

0.14

b=8.0 fm

0.12

〈-ϖy〉

PH [%]

0.02

sNN=2.0 G

b=5.0 fms =5.0 G
NN

sNN=10.0 G

b=8.0 fm

0.06

sNN=30.0 G

〈-ϖy〉

〈-ϖy〉

〈-ω y〉 (fm-1)

0.04
enough (our computation suggests a turning point around b=10.0 fm
b=10.0 fm
p
0.1
5 GeV depending on
0.02
0.06centrality), the particles
STAR prelim. 27 GeV, 54.4 GeV sNN ⇠ 3
0.08
5near the mid-rapidity are not effective
angular-momentum
0
Λ
Λ
0.06
0.04
0
2
4
6
8
10 12 14 16
t (fm)
carriers and most of the angular momenta are carried by the
0.04
0.02
particles with large rapidity (but at large rapidity the angu0.02
lar momentum may not be necessarily
manifested as fluid0FIG.
4.6 7Time evolution
of
the
0
2
3 4 5 6 7 10
20 30 40
1
2
3
4
5
20
30
40
1
10
UrQMD+vHLLE,Λ leaving the mid-rapidity region approximately
vorticity) andsNN (GeV)
ferentsNNenergies(GeV) and impact papprimary
primary+feed-down
boost invariant. With sNN growing to be very large, the
UrQMD model.
AMPT,Λ
mid-rapidity
region respects a good Bjorken scaling strucprimaryprimary+feed-down
FIG. 3.theInitialkinematic
vorticity
at midrapidityFIG.
as a5.function
the vorticity at mid rapidity as a fun
Initial ofthermalture which does not support
fluid
vorticity.
We notethat
Energyofkinematicandcollision energy for impact
parameters bdependence= 5, 8,collisionand 10 fm.
0.18
energyfor
impactparametersb = 5, 8, and 10 f
in recent preliminary results reported by HADES CollaboraAu+Au
0.16
tion [42], the ⇤ polarization indeed appears to bevery small vorticity
atthermalwith UrQMD
p0.14
sNN = 2.4 GeV. Recalling that the global ⇤X.-G.
polarization
atet al., PRC101.064908 (2020) 0.12Dengp0(ourbycomputationsuggests[1]a turning
aroundferentpoint
definition
for the origin of the time axis so th
sNN = 7.7 200 GeVenoughmeasuredSTAR Collaborationp0.1
psNN5.02⇠ 3TeV 5byGeVdependingon centrality),
thet particles
ticity at= 0 roughly corresponds
theirs at the pand at sNN = 2.76 and
ALICE
Collabora0.08
p
near
mid-rapidity
are not effectivein this sense, their results are qualitatively
consition [39] is decreasing with thesNN, our results combinedwith angular-momentum
0.06
3
and
most
the HADES:
angularare carried
bythatthealthough the initialours.
We notethermal vortic
GeV
the previous
e.g. Ref.
[40],
areofconsistent
withmomenta
the 2.0-2.4
110
102
10studies in,carriers
0.04
thermal vorticity atlate time (e.g.,
particleswith large
rapidityinterpreta(but at large monotonic,
rapidity thethe
angucurrent experimental
data
if we adopt
the vorticity
0.02
s
[GeV]
p
covered by HADES
STAR
FXT:
3-7.7
GeV
NN
fm) is roughly
a decreasing function0 of sNN ; in olar momentum may not be necessarily manifested
as fluidtion of the global ⇤ polarization.
23 4
1
and STAR FXT+BES-Ⅱ
consistentwiththemeasured⇤polarization,
thissuvorticity)
andleavingthe
mid-rapidity
regionapproximately
STAR
BES
II:
7.7-19GeV
We show the time evolution of the thermal vorticity
in
Fig.
4
p
⇤ hyperons
are mostly generated in the earlyboost given
invariant.
sNNb =
growing
be verylarge, the18 sfor two different centralities
by b =With
5 fm and
8 fm. to theT. Niida, HI-Pub 2020p

0.08

espite increasing Jcollision

A possible probe of B-field

σ average for 7.7-39GeVω= Karpenko,∼5 Lisa,% Upsal, and Voloshin,Λ Becattini,
2 T (2017)
PRC95.054902

188

primary

1!
µ⇤ B
'
+
neticP⇤field
2TT
1 !magnetonµ⇤ B
N = nuclear
P⇤¯ '
2
T
T
ositive value, 2σ average for

7-39GeVL. McLerran, V. Skokov / Nuclear Physics A 929 (2014) 184–190

McLerran and Skokov, Nucl. Phys. A929, 184 (2014)

QM17, I. Upsal (STAR)
Au+Au 20-50%

STAR preliminaryμΛ: Λ magnetic moment

B = (P⇤P⇤¯ )kB T /µN
13⇠ 5.0 ⇥ 10

[Tesla]nuclear magneton μN = -0.613μΛ
Feb. 2017

upper limit from ΔPH

Conductivity increases lifetime.

Fig. 1. Magnetic field for static medium with Ohmic conductivity, σOhm .

The decay of the
12conductivity owing to expansion of the medium can only decr
time of the magnetic field and√ thus will not be considered here. Our simulations
Au–Au collisions at energy s = 200 GeV and fixed impact parameter b= 6 fm.
show time evolution of the magnetic field in the origin x⃗ = 0 as a function of theductivity σOhm . The results show that the lifetime of the strong magnetic field (eBaffected by the conductivity, if one uses realistic values obtained in Ref. [5].

• B-field at freeze-out could be probed by Λ-antiΛ splitting• Current results are consistent with zero (except 7.7 GeV)•

The small splitting could be also due to other effects
4. Energy dependence

T. Niida, HI-Pub 202019
In the previous section, we established that for realistic values of the conductiv

But need caution for the interpretation
Λ-antiΛ PH splitting could be also due to other effects:
L. P. CSERNAI, J. I. KAPUSTA, AND T. WELLE• Effect of chemical potential, expected to be small

0.10

R. Fang et al.,, PRC94, 024904 (2016)

Rotating charged fluid produces B-field with longer lifetime
X. Guo, J. Liao, and E. Wang, PRC99.021901(R) (2019)

•

0.08
0.06

PΛ̄ − PΛ

•

(a)

0.04

Spin interaction with the meson field generated by the baryon current
0.02

L. Csernai, J. Kapusta, and T. Welle, PRC99.021901(R) (2019)

0.00

•

Different space time distributions and freeze-out of Λ and antiΛ
O. Vitiuk, L.Bravina, E. Zabrodin, PLB803(2020)135298

www.nature.com/scientificreports/

−0.02

101

www.nature.com/scientificreports√

102

sN N (GeV )

0.10

(b)

www.nature.com/scientificreports
0.08PΛ̄ − PΛ

0.06
0.04
0.02
0.00

stration of the magnetic field generated by a single swirling charged particle (left) or by a swirling
nzero charge density (right).
19−1
X. Guo, J.Figure
Liao,
and
E. ωWang,
PRC99.021901(R)(2019)
1
.
5
×
10
sec
2. Thevorticity(left,
in
unit
of
MeV
correspondingto), charge density nQ (middle,yin unit of fm−3 = 1045 m−3) and magnetic field eB (right, in unit of mπ2 corresponding to 3.3 × 1014 Tesla) as
sic mechanism is simple and generic, it has not beenpreviously
applied tobeam
a verydistinctive
fluidfunctionsof collisionalenergyunit of GeV = 109 eV ), with solid/dashed curves in each panelsNN (inT.subatomic
Niida, fluid
HI-Pub2020
hotconsistingof strongly interacting
elementary
suchestimatesas quarks,
gluonsrepresenting
an particles
upper/lower
andwith the shaded band between them giving an idea of the expected

polarizations r
baryon density
case II the fact
ing to note tha
net !’s [35] is
30 GeV. This mthe produced mis sensitive todynamics.
For compar
energy heavy
equilibrium !
which orients
netic momentnuclear Bohr mbe polarized in
calculated withof the produce
time of hadron
time t at z = 0

−0.02

101

√

102

sN N (GeV )L. Csernai, J. Kapusta, and T. ¯Welle,
FIG. 1. Difference in polarization of ! and !
hyperons, with
PRC99.021901(R)positivevalue meaning that it is (2019)
opposite to the total angular momentum of the produced matter. The top panel (a) shows case I andwhere b is th
3 fm/c, b = 7
the magnitude
irrelevant comption. Note alsosatisfied there
field. Realistic
extent of thewhich is20too

from jet fraggiven the cu
primary !
initial condi
dependence
conditions,[8,9] and thSTAR Au+Au s NN = 200 GeVUrQMD IC
20%-60%, |η|<1
1
the initial flo
initial energ
hydro, primary Λboth of whicΛ
UrQMD IC
data are closhigher thanΛGlauber+tilt IC
Figure 7
polarization
0.5
within unceat large rap
η = 0 due t
to baryon t
event-by-eve
such a depe
0
acceptance o
As menti
also related
0
1
2
3
4
the contribu
p [GeV/c]
Ref. [18], thT
with nonzer
field B (J5 ∝
¯ as
FIG.
6. Polarizationof ! and of!
a function
of
p
for
the
T
- Naive
expectation
smaller
P
due
to
√ H
that J5 point
20%–60% centrality bin in Au+Au collisions at sNN = 200 GeV.
scattering at low p , fragmented at high p
Open boxes and vertical lines showTsystematic and statistical uncer- T (where e is
- Noclear pHydrodynamic
with current
precisioneµv < 0. Sin
T dependence
tainties,
respectively.
model calculations
for ! with¯ aretial angular
two different IC are compared. Note that the data points for !
21 m
a strong pT dependence. One might expect a decrease of thepolarization at lower pT dueTto the smearing effect caused byscattering at the later stage of the collisions, and/or a decreaseof polarization at higher pT because of a larger contribution

Differential measurements: centrality and p

1

PH [%]

PH [%]

STAR, PRC98, 014910 (2018)
STAR Au+Au s NN = 200 GeV|η|<1, 0.5<p <6 GeV/c
T

Λ
Λ
0.5

0

20

40

60

80

Centrality [%]In most central collision → no initial angular momentum
The polarization decreases in more central collisions.
T. Niida, HI-Pub 2020

Differential measurements: azimuthal angle

DE-XIAN WEI, WEI-TIAN DENG, AND XU-GUANG HUA
4scaled using αΛ=0.75

0.4

PH(%)

0.2

3

φ-Ψ
1 Collaboration Preliminary DataSTAR
Py (%)

PH,J (%)

out-of-plane

in-plane2

Au+Au 20-50 %STAR 200 GeV
19.6 GeV|Y| < 162.4 GeV
200 GeV100STAR preliminary

0.6

0

0.2

0.4

0.6
0.8
20-50%

1

1.2

1.4
φΛ-ΨEP,1

0.5 1.0 1.5 2.0 2.5
φ¯ polari
FIG. 9. The azimuthal angle dependence of ! and !
Figure 5
I. Karpenko and
F. Becattini,in rapidity
region |Y EPJC(2017)77.213| < 1 for Au+Au collisions at 19.6, 62.4
Λ and Λ combined
Left: Preliminary results (108) from the STAR collaboration for the global
polarization⇤andand200ofGeV.
The
D. Wei,W. Deng,
X.experimental
Huang, data [6] is also shown.

0.4

<PH>

⇤ as a function of hyperon emission angle relative to the event plane,PRC99.014905
for mid-central Au+Au(2019)pcollisions at sN N = 200 GeV. As in figure 3, published data have been rescaled to reflect the
ettransverse
al., PR.Research1.033058 (2019)new accepted value of ↵⇤ . Right: Hydrodynamic calculations (12) of H.
PJˆ Wuin theenergy dependence. We here propose another observab
momentum plane, for the same colliding system.

0.2

0

−0.2

Au+Au 200GeV

in-plane0T. Niida, HI-Pub 2020

the smoke-loop-type vortical structure, that is the spin
coefficients at
rapidity. while- The data shows largermonicpolarization
infinite
in-plane,tion structures, in the local equilibrium picture, are more sensitive to the thermal Recall
vorticitythat the charged particle distribution can bmodelspredict
theopposite,i.e. larger
in components
out-of-planevariations as a function of space and time, many
convoluted
with flow-driven
space-momentum
composed
into different
harmonic
as in Eout-of-plane
correlations. First measurements(81) report
PJ,⇤/⇤
to beunderstoodindependent of transverse
in whichmothe harmonic coefficients reflect the respon
- Not
fully
yet
ˆ
0.5
1.5 with hydrodynamic predictions (12,thementumfor pT . 21GeV/c, in agreement
111)
when
final-state
momentum-space distribution to the iφ-ItΨwas also seen (81) to be independentanisotropy
realistic initial conditions are used.
of pseudo-in coordinate space. Similarly, we can expec
1 [rad]anisotropy
rapidity, though only a limited range, |⌘| < 1 could be explored. As we discuss thein section
5, in the vortical structure of the early or inte
22
diate stage fluid can be reflected in the harmonic coeffic
several theories suggest there is much to be learned at forward rapidity.

Differential measurements: charge asymmetry
PH [%]

STAR, PRC98, 014910 (2018)
STAR Au+Au s NN = 200 GeV 20%-60%|η|<1, 0.5<p <6 GeV/cΛ

T

Chiral Separation EffectJ5 / eµv B

D.E. Kharzeev et al. / Progress in Particle and Nuclear Physics 88 (2016) 1–28

6<latexit sha1_base64="v7C5WipLvSTheo2F84emIhuK9Wg=">AAACDXicbVC7TsMwFHXKq5RXgJHFoiAxVQkCwViVBTEViT6kJooc12mt2nFkO5WqKD/Awq+wMIAQKzsbf4PbZoCWI1k6OudeXZ8TJowq7TjfVmlldW19o7xZ2dre2d2z9w/aSqQSkxYWTMhuiBRhNCYtTTUj3UQSxENGOuHoZup3xkQqKuIHPUmIz9EgphHFSBspsE8yL4zgXR5cQi+RItECEo+nQeZJDse5MbNGHthVp+bMAJeJW5AqKNAM7C+vL3DKSawxQ0r1XCfRfoakppiRvOKliiQIj9CA9AyNESfKz2ZpcnhqlD6MhDQv1nCm/t7IEFdqwkMzyZEeqkVvKv7n9VIdXfsZjZNUkxjPD0UpgybztBrYp5JgzSaGICyp+SvEQyQR1qbAiinBXYy8TNrnNdepufcX1XqjqKMMjsAxOAMuuAJ1cAuaoAUweATP4BW8WU/Wi/VufcxHS1axcwj+wPr8ARvgm5Y=</latexit>B)field p

Λ

spin

J5

RH
LH

0.5

B-field + massless quarks + non-zero μv → axial current J5

Fig. 2. (Color online) Illustration of the chiral separation effect. To be specific, the illustration is for just one kind of right-handed (RH) quarks (with Q > 0)
and their antiquarks (with Q < 0) and for the case of µ > 0 (i.e. more quarks than antiquarks). For left-handed (LH) quarks (and anti-quarks) the LH
quarks’ current is generated in the opposite direction but their contribution to the axial current EJ5 would be the same as that of RH quarks. For µ < 0 thecurrent will flip direction.

0

E To probe the existence of such a current we turn on an arbitrarily
assume a CME-induced electric current (Qe)EJ = (Qe) 5 B.
E k B
E and examine the energy changing rate of the system. The straightforward electrodynamic
small auxiliary electric field E
RR
E
E
E · B.
E
way of computation ‘‘counts’’ the work per unit time (i.e. power) done by such an electric field P = xE J · E = xE [(Qe) 5 ]E
slope ± stat.uncert. ± syst.uncert. Alternatively for this systemof chiral fermions, the (electromagnetic) chiral anomaly suggests the generation of axial chargeschR
E·B
E with CA = (Qe)2 /(2⇡ 2 ) the universal anomaly coefficient. Now a nonzero axial chemical
at the rate dQ5 /dt = xE CA E
0.097 ± 0.041 ± 0.043 [%]potential µ5 6= 0 implies an energy cost for creating each unit of axial charge, thus the energy changing rate via anomalyR
E · B.
E These reasonings therefore lead to the following
counting would give the power P = µ5 (dQ5 /dt ) = xE [CA µ5 ]E-0.112 ± 0.045 ± 0.102 [%]identification:

A

Λ:
Λ:
−2

Slopes of Λ and anti-Λ seem to be opposite (~2σ level)

−1

0

1

Z

2

observed Ach / σA xE

T. Niida, HI-Pub 2020

dependence observed

hN+ N iµv /T /
=A
hN+ + N i

Z
Possible
contribution
from
axial
chargeor
E E
E E[(Qe) 5 ]E · B =Ex[ C A µ5 ] E · B(8)µQuark vector chemical potential
may explain the data

E field. Thus the 5 must take the universal value A 5 = Qe2 µ5 that is completely fixed by the chiralfor any ch
auxiliary E
Qe
2⇡anomaly.
Sun
and
INT20-1-c
The transport phenomenon in
Eq. (4)
bearsKo,a distinctive
feature that is intrinsically different from Eq. (7). The chiralch magnetic conductivity 5 is a T -even transport coefficient while the usual conductivity is T -odd [26]. That is, the CME
current can be generated as an equilibrium current without producing entropy, while the usual conducting current isnecessarily dissipative.
C23

d cos ✓⇤Spin alignment of vector mesons

where ✓⇤ is the polar angle of the proton emission relative to the polarization direction in the hyperon
0 and φ:CharacteristicofK*
rest frame, 1  PH  1 is the hyperon polarization, and the parameter ↵⇤ = ↵⇤¯ ⇡ 0.624. To
measure the polarization of strongly decaying particles is obviously significantly more difficult. It is
Speciesφ
K*0
not at all possible for spin 1/2 particles; for the vector mesons one can hope to measure the deviationfrom 1/3of the probability
for theof
spin
projection
be zero [8]. can
The angular
distribution (averaged
Quark content
ds
ss
Angulardistribution
thedecaytoproducts
be written
over the azimuthal distribution around the polarization direction) of the decay products in this case
with
spin
densitymatrixρnn.
2)
reads:
Mass(MeV/c896
1020
often simpler in terms of applying necessary corrections for the reaction plane resolution
anddetectordN
1
acceptance.
In
the
case
analysis,thepolarizationcanbecalculatedas:
2 of the azimuthal
2
2
2 ⇤
2 ⇤
Lifetime
/
⇢
|Y
|
+
⇢
|Y
|
+
⇢
|Y
|
/
⇢
cos
✓
+
(⇢
+
⇢
)
sin
✓
(3)
4
45
0,0 1,01,1 1, 1
1, 1 1,1
0,0
1,1
1, 1
⇤
d cos ✓
2
(fm/c)2 ⇤/ (1 8⇢0,0 ) + (3 ⇢0,0
1)
cos
✓
(4)
⇤
Spin (JP)11-PH

hsin( P=RP )i,⇡↵
H the probabilities for the particle to have spin projection on the direction
where ⇢0,0 , ⇢1,1 , and ⇢ 1, 1 are
1 +1,
8 and 1, respectively.
of polarization to be zero,
The deviation from the non-polarized state value⇤⇢00 =hcos[2( pRP )]i.
⇢0,0 = 1/3 is in this case
3 a 3second order e↵ect [8]. For example, an estimate based on Eq. 1 yields
2(5)

Decays(6)KπBranching ratio 49%~100%⇢00 = 1/[3 + (!/T ) ].
For
the global
polarization,
the analysis
has tobe performed
using
one of the
To measure
the hyperon
global polarizationor vector
meson
spin alignment
experimentally,
onefirst harmonic event⇤
caneitheranalyze
directly
thedistributions
in✓, or, incasealignment.
of the global
polarization
direction deplanes,
with thefrom
reaction(and correspondingly,
the angularmomentum)direction to be deterDeviation
1/3 inplaneρ00 indicates
spin
Theoretical
expectation for ρ00
fined
by
the
one
of
the
flow
event
planes,analyzetheazimuthal
distribution
of
the
decay
products
*
sign
of
the
polarization
cannotbedetermined.
mined by the deflection direction of the projectile spectators (which on average deflect outward of the(in the resonancerestit’sframe)
to that flow
plane. The azimuthal distribution analysis
can beTherefore
calledrelative“spin alignment
measurement”
Vorticity

KK
66%

Subhash Singha, QM 2019

collision
[9]).
For
the
spin
alignment
measurements
itispossibletouse
thesecond
order
event
plane
rather than “polarization measurement”
recombination ⇢00 < 1/3(which typically has much better resolution).
<latexit sha1_base64="e5nu2AgjJbYDmdaP1lg3+pD6++Y=">AAAB9HicbVBNSwMxEJ2tX7V+VT16CRbBU82qoAcPRS8eK9gPaJeSTdM2NJusSbZQlv4OLx4U8eqP8ea/MW33oK0PBh7vzTAzL4wFNxbjby+3srq2vpHfLGxt7+zuFfcP6kYlmrIaVULpZkgME1yymuVWsGasGYlCwRrh8G7qN0ZMG67kox3HLIhIX/Iep8Q6KWjrgeqkGE9u/LOLTrGEy3gGtEz8jJQgQ7VT/Gp3FU0iJi0VxJiWj2MbpERbTgWbFNqJYTGhQ9JnLUcliZgJ0tnRE3TilC7qKe1KWjRTf0+kJDJmHIWuMyJ2YBa9qfif10ps7zpIuYwTyySdL+olAlmFpgmgLteMWjF2hFDN3a2IDogm1LqcCi4Ef/HlZVI/L/u47D9cliq3WRx5OIJjOAUfrqAC91CFGlB4gmd4hTdv5L14797HvDXnZTOH8Afe5w9Z/JEn</latexit>

Z.-T. Liang and X.-N. Wang, PRL94.102301(2005)
Y. Yang et al., PRC97.034917(2018)

2 Results

fragmentation
Magnetic field⇢00 > 1/3
<latexit sha1_base64="GYjebL1Kuq57ghuzQx68x9TpTFY=">AAAB9HicbVBNSwMxEJ2tX7V+VT16CRbBU82qoCcpevFYwX5Au5Rsmrah2WRNsoWy9Hd48aCIV3+MN/+NabsHbX0w8Hhvhpl5YSy4sRh/e7mV1bX1jfxmYWt7Z3evuH9QNyrRlNWoEko3Q2KY4JLVLLeCNWPNSBQK1giHd1O/MWLacCUf7ThmQUT6kvc4JdZJQVsPVCfFeHLjn110iiVcxjOgZeJnpAQZqp3iV7uraBIxaakgxrR8HNsgJdpyKtik0E4Miwkdkj5rOSpJxEyQzo6eoBOndFFPaVfSopn6eyIlkTHjKHSdEbEDs+hNxf+8VmJ710HKZZxYJul8US8RyCo0TQB1uWbUirEjhGrubkV0QDSh1uVUcCH4iy8vk/p52cdl/+GyVLnN4sjDERzDKfhwBRW4hyrUgMITPMMrvHkj78V79z7mrTkvmzmEP/A+fwBdCpEp</latexit>⇢00 > 1/3
<latexit sha1_base64="GYjebL1Kuq57ghuzQx68x9TpTFY=">AAAB9HicbVBNSwMxEJ2tX7V+VT16CRbBU82qoCcpevFYwX5Au5Rsmrah2WRNsoWy9Hd48aCIV3+MN/+NabsHbX0w8Hhvhpl5YSy4sRh/e7mV1bX1jfxmYWt7Z3evuH9QNyrRlNWoEko3Q2KY4JLVLLeCNWPNSBQK1giHd1O/MWLacCUf7ThmQUT6kvc4JdZJQVsPVCfFeHLjn110iiVcxjOgZeJnpAQZqp3iV7uraBIxaakgxrR8HNsgJdpyKtik0E4Miwkdkj5rOSpJxEyQzo6eoBOndFFPaVfSopn6eyIlkTHjKHSdEbEDs+hNxf+8VmJ710HKZZxYJul8US8RyCo0TQB1uWbUirEjhGrubkV0QDSh1uVUcCH4iy8vk/p52cdl/+GyVLnN4sjDERzDKfhwBRW4hyrUgMITPMMrvHkj78V79z7mrTkvmzmEP/A+fwBdCpEp</latexit>(for neutral vector mesons)

The progress in vector spin alignments measurements was presented at this conference in talks by

T. Niida, HI-Pub 2020

24

00

00

0.01 & 0.06& 0.03] [41]. The spin alignment for vector
where ✓ is the polar angle of the protonmesons
emission
relativetothepolarization
directioninthehin heavy ion collisions could have contributions
0.3
0.3
rest frame, 1  PH  1 is the hyperon
polarization,and the[12,13],parameter↵⇤ = ↵⇤¯ fields
⇡ 0.6
from
angularmomentumelectromagnetic
0.2
0.2
Pb−Pb, sNN = 2.76 TeV
measure thepolarizationofstrongly
decaying
particles
isobviously
significantly
moredifficu[15]
andmesonic
fields
[38].
While
no
quantitative
MesonM
0.5 ≤ p < 0.8 (GeV/c)
000.4 ≤ p < 1.2 (GeV/c)
ρ00 ρ(centrality):
K* K*
vs. vs.
φ φT
00 (centrality):
s
s
T
0.1
0.1
Φ
Φ
theoretical
calculationforvectormeson
polarization
at
not
for
spin
the
vectormesons
one
can
hope
to
measurethede
3.0 ≤ p T < 5.0(GeV/c) 1/2 particles; forSTAR,(2020)
3.0 ≤ALICE,
p < 5.0PRL125.012301(GeV/c) at all possible
QM18,
QM19
T
K
K
LHC
energiestoexists,
the[8].
expectedorder of distribution
magnitude can
from
1/3
of
the
probability
for
the
spin
projection
be
zero
The
angular
(av
0.40
0.40
φ φ
QM 2018
QM 20
Event plane
Event planeALICEΚ*0 Κ*00.5
0.5
beestimatedandthemeasurementsforvectormesons
and
*0
0.36
0.36
φ
over
the
azimuthal
distribution
aroundthepolarization
direction)
of
the
decay
products
in th
K|y| < 0.5
0.8 ≤ p T < 1.2 (GeV/c)
0.35 0.35
hyperonscanberelatedinamodel
dependent
way.
3.0
≤
p
<
5.0
(GeV/
c
)
0.4
0.4
T
reads:
0.34 0.34
Considering only the angular momentum contribution
0.30 0.30
0.3
0.3
0.32 0.32 of 1dN
andrecombinationastheprocess
hadronization [13], 2
2
2
2
2 ⇤
/
⇢
|Y
|
+
⇢
|Y
|
+
⇢
|Y
|
/
⇢
cos
✓
+
(⇢
+
⇢
)
sin
0,0
1,0
1,1
1,
1
1,
1
1,1
0,0
1,1
1,
1
0.2
0.2
0.25 0.25
the ρ00 of vector mesons are related
polarization as
0.30 0.30 to quarkd cos0.5✓⇤≤ p < 0.7 (GeV/c)
2
T
ρ
¼
ð1
−
P
P
Þ=ð3þ
P
P
Þ
where
P
and
P
are
quark
2
⇤
0.1
0.1
q̄
q̄
q̄
00
q
q
q
3.0 ≤ p T /< 5.0 (GeV/(1 c)⇢0,0 ) + (3 ⇢0,0cos
00 100 100 200 200 300 300 400
0
100
0 1)
100 ✓200 200 300 300〈 N 〈〉N 〉〈 N 〈〉N polarization,〉
and antiquark
respectively. Assuming
Pu ¼
0
100
200
300
0
100
200
300
For
midcentral
collisions
P
¼
P
¼
P
and
P
¼
,
the
measuredp
integrated
ForP
midcentral
collisions〈N part〉〈N part〉
•
•
ū
s̄
d
s
T
d̄
where ⇢0,0 , ⇢1,1 , and ⇢ 1, 1 are the probabilities0for0 the particle
to
have
spin
projection
on
the
d
0
K* • ρK*<ρ1/3
φ ρ•00φPb-Pb
>ρ1/3
<%
1/3
00for
00K
00 > 1/3colli••ρvaluesandϕmesonsin
10–50%
00of polarization to be zero, +1,%and1,respectively.
The
deviationfromthenon-polarized
stat0
FIG. 3. Measurements
of
ρ
as
a
function
of
hN
i
for
K
and
sionsbycould
translate
to light quark polarization of ∼0.8and00
partLarge deviation
from
1/3,
which
cannotbeexplained
vorticity
picture
⇢
=
1/3
is
in
this
case
a
second
order
e↵ect
[8].
For
example,anestimate
based
on
Eq.
1
0,0
ϕ mesons at low and high pT in Pb-Pb collisions. The statisticalstrange quark polarization of ∼0.2. Using a thermal and
2⇢00 = 1/[3+ (!/Tas) ].bars and boxes,and systematic uncertainties
are shownnonrelativistic approach as discussed in [42], vorticity (ω)
respectively. Some data points
are shifted thehorizontally
better polarization
To measure
hyperonforglobal
or vector(T)mesonalignment
and temperatureare spin
relatedto ρ00 experimenta
and vector⇤
visibility. The deviation
1
2
in
oppositeway
between:can either analyze directly the distributions
in
✓
,
or,
in
case
of
the
globalpolarization
directmeson
polarization
(P
)
as
ρ
≃
f1
−
½ðω=TÞ
=3(g
andMean field of φ meson
may
a
role?
V
00 play3
by the one of the flow event planes,
azimuthal
distribution
ofapproach,the φ?
decay
PVDoes≃analyzeð2ω=3TÞ,therespectively.
Also
in thisthep
K* and φfinedat RHICit changefrom RHIC
to LHC
only
for%0The azimuthal distribution
%0
(in
the
resonance
restframe)
relative
to
that
flow
plane.
analysismeasured
ρ
for
K
would
correspondtoKpolarization
X.
Sheng,
L.
Oliva,andQ.
Wang,
PRD101.096005(2020)
00
LHC
and
RHIC
for
φ
and calculating the corresponding factor R. This gives
Sheng, Q.Wang,
Wang,
PRD102.056013(2020)of X.
∼0.6andthe ρ00and
forX. ϕmesonswould giveϕ meson1ΔρðRNDEPÞ
¼
Δρ
ðEPÞ
×
(R
¼
0
for
randomplane)
00
00
25
4
T. Niida, HI-Pub 2020
polarization of ∼0.3.
⇤

ρρ

Results from LHC and RHIC

*0

00

ρ
φ

00

ρ
φ

00

K*0 ρ

00

ρ

K*0 00ρρ00STAR Preliminary
TPC-EPTPC-EP
STAR Preliminary
Au+Au, Au+Au,
1.0 < p 1.0< 1.5< pGeV/c< 1.5 GeV/c54.4 GeV
54.4 GeV
T
T
200 GeV200 GeV

STAR Preliminary
STAR Preliminary
Au+Au 200
GeV,
1.2GeV,< p 1.2
< 5.4
Au+Au
200
< pGeV/c< 5.4 GeV/c
T
T
ZDC EPZDC EP

part

Subhash Singha,
QMSingha,2019 QM 2019
Subhash

part

part

15

15

part

*

convective fluid velocity field gives rise to a transverse
vorticity distribution that has a right-handed toroidal
structure (ringlike) around each beam direction. Shown~ ⊥ ðx; yÞ in thein Fig. 1 as arrows are distributions of ωtransverse plane at a spatial rapidity η ¼ 4 and a proper
time τ ¼ 3 fm=cpﬃﬃﬃ in a semiperipheral (20%–30%) Au þ Au
collision at sNN ¼ 200 GeV from the CLVisc simulations.
Yasuki Tachibana, “Collective flow induced by energetic partonsin heavy-ion
collisions”see the right-handed toroidal structureOne
can clearly(module fluctuations) around the beam direction(out of thePtransverse plane). The total net vorticity h ωy i projectedto the reaction plane is nonzero for noncentral collisions.

structure in Fig. 1 is expected to show up in thcorrelation of Λ spin polarization due to radia
which correlates the spatial azimuthal angle
cells to the azimuthal angle of final hadron’
momentum. Therefore, we propose using thelations of two Λ’s to study the vortical stru
expanding fluid in high-energy heavy-ion
Shown in Fig. 2 are the transverse and longi~ ⊥ ðϕ1 Þ · P~⊥
correlations of two Λ’s, hP
hPη ðϕ1 ÞPη ðϕ2 Þi, respectively, as functions of thangle difference jϕ1 − ϕ2 j of their momenta. I
hydrosimulations■ 1-jet traveling through a uniform fluidpﬃﬃﬃ of semicentral (20%–30%) P
lisions at
sNN ¼ 2.76 TeV, we have se(GeV)
3: flow velocity e GeV/fm
viscosity to entropy density ratio to ηv =s ¼ 0.
lines) and 0.0 (the dashed lines). As expecte
4(GeV)
verse spin correlation in azimuthal angle has
0.45
mate cosine form due to the toroidal struc2transverse vorticity around the beam direct-Mach cone structure
0.4
offset due to the global spin polarization
amplitude of the oscillation (the local polar0
the offset (the global polarization) increase wit-Vortex ring
0.35
well as with ηv =s. The longitudinal spin correl
around the passage
other hand, displays a different behavior. The o-20.3
jϕ1 − ϕ2 j is the result of vortex pairing in thplane, as illustrated in Fig. 1. The sign chan
0.25
ϕ2 j ≈ 1 indicates the typical opening angle o-4pairs from the convective radial flow due t
-4
-2
0
2
4
(fm)
geometry and fluctuations. The rise of the cx (fm)
large angles is the result of spin correlations fr
FIG. 1. Transverse (arrows) and longitudinal vorticity (contour)
vortex pairs in the transverse plane. The amp
atη ¼ 4 in semiperipheral
YT and T. Hirano, Nucl.Phys.A904-905 2013 (2013) 1023c-1026cdistributions in the transverse planelongitudinalspincorrelation
increases
slightly
p
ﬃﬃ
ﬃ
L.-G.
Pang,
H.
Peterson,
Q.
Wang,
and
X.-N.
Wang,
PRL117,
192301(2016)(20%–30%) Au þ Au collisions at sNN ¼ 200 GeV with shear
Y. Tachibana and T. Hirano,
NPA904-905(2013)
1023
but decreases slightly with ηv =s.
1026th Heavy Ion Cafe, 19 July 2014
F.
Becattini
andI.
Karpenko,
PRL120.012302(2018)
viscosity
toentropydensity
ratio
η
=s
¼
0.08.
Dashedarrowsv
B. Betz, M. Gyulassy, and G. Torrieri, PRC76.044901 (2007)
In Fig. 3, we show (a) the Λ transverse spin
indicate the radial
flow
of
hot
spots.
A
cutoffinenergydensity
S. Voloshin,
EPJ Web Conf.171, 07002 (2018)
in the rapidity range Y ∈ ½2; 3&and (b) the long3
ϵ > 0.03 GeV=fm is imposed. The direction of the beam (target)
X.-L. Xia et al., PRC98.024905 (2018)
correlation in Y ∈ ½0; 1&in semiperipheral (20%is out of plane (⊙) [into the plane (⊗)]. The orbital angularpcentral (0%–5%) Au þ Au collisions at
momentum of the collision is along −ŷ.

Local vorticity

Vortexinducedbyinduced
jetCollectiveflow
by 1-jetLocal vorticity induced by collective flow

T. Niida, HI-Pub 2020

(fm)

jet

y (fm)

Vorticity by inhomogene

192301-3

26

Polarization along the beam direction
S. Voloshin, SQM2017
F. Becattini and I. Karpenko, PRL120.012302 (2018)

z

dN
1
⇤
=
(1
+
↵
P
·
p
)
H
H
p
d⌦⇤
4⇡
Z
dN
⇤
⇤
⇤
hcos ✓p i =
cos
✓
d⌦
p
d⌦⇤
⇤ 2
= ↵H Pz h(cos ✓p ) i

y

)
x

⇤
hcos ✓p iPz =↵H h(cos ✓p⇤ )2 i⇤
3hcos ✓p i=

αH: hyperon decay parameterθp*: θ of daughter proton in Λ rest frame↵H(if perfect detector)

Stronger ﬂow in in-plane than in out-of-plane
could make local vorticity along beam axis, thus polarization
T. Niida, HI-Pub 202027

Polarization along the beam direction
5

Au+Au sNN = 200 GeV
20%-60%0.0005STAR
Some models
cannotdescribe
the sign but some can
Au+Au
s NN = 200
GeV
2〈cos(θp*)〉

STAR

Sine structure
as expected from the elliptic ﬂow
1〈Pz sin(2φ-2Ψ )〉 [%]

sub

0.001

STAR, PRL123.13201 (2019)

do. Note that they reasonably describe “global” PH.
Λ +Λ
AMPT (x 0.2)
- F. Becattini
Karpenko, PRL.120.012302 (2018)
0.5 and I.BW
(spectra+v 2 )- X. Xia et al., PRC98.024905 (2018)
BW (spectra+v 2 +HBT)

0- Y. Sun and C.-M. Ko, PRC99, 011903(R) (2019)- Y. Xie, D. Wang, and L. P. Csernai, Eur. Phys. J. C (2020) 80:39- W. Florkowski et al., Phys. Rev. C 100, 054907 (2019)−0.0005

fit: p +2p sin(2φ-2Ψ )−0.0010⇤
Pz / hcos ✓p i

01

- H.-Z. Wu et al., Phys. Rev. Research 1, 033058 (2019)02

Λ

p =0.016±0.003 [%]Λ

p =0.015±0.003 [%]1

0.5<p <6 GeV/ c

1

T

1

2

3

φ-Ψ [rad]

0

20

40

60

80

Centrality [%]2<latexit sha1_base64="om9ym3UaXtuXg/XESzfKofyBSJk=">AAACFHicbVDLahtBEJxVXory8Do55jJEBAwGsRsC8dHEFx8ViB6glZfeUUsaNDszzPQGFKGP8MW/4osPNibXHHLL32T0OCSSCxqKqm66uwqrpKck+RPVHj1+8vRZ/XnjxctXrw/iwzddbyonsCOMMq5fgEclNXZIksK+dQhlobBXzM5Wfu87Oi+N/kZzi8MSJlqOpQAKUh4ft/MfPLPOWDI8U6AnCjNhfEZTJMjtRQaeMrfW87iZtJI1+D5Jt6TJtmjn8e9sZERVoiahwPtBmlgaLsCRFAqXjazyaEHMYIKDQDWU6IeL9VNL/iEoIz42LpQmvlb/nVhA6f28LEJnCTT1u95KfMgbVDQ+GS6kthWhFptF40rxEMAqIT6SDgWpeSAgnAy3cjEFB4JCjo0QQrr78j7pfmylSSv9+ql5+mUbR529Y+/ZEUvZZ3bKzlmbdZhgl+ya3bK76Cq6ie6jn5vWWrSdecv+Q/TrL8ran0o=</latexit>

FIG. 2. (Color online) ⟨cos θp∗ ⟩ of Λ and Λ̄ hyperons as a funcazimuthal
angle φ relative to the second-order event
T. tionNiida, of
HI-Pub
2020

FIG. 3. (Color online) The second Fourier sine coeﬃcientof the polarization of Λ and Λ̄ along the beam direction as
a function of the collision centrality in Au+Au collisions at

28

Disagreement in Pz sign
4

Hydrodynamic model

Opposite sign
UrQMD IC + hydrodynamic model
F. Becattini and I. Karpenko, PRL.120.012302 (2018)

AMPT

­

X. Xia, H. Li, Z. Tang, Q. Wang, PRC98.024905 (2018)

Same sign-

px [GeV/c]

Chiral kinetic approach

FIG. 5. The average polarizations hPx · sign(Y )i, hPy · sign(

FIG. 2. Map of longitudinal component of polarization of midrapidity ⇤ from a hydrodynamic calculation corresponding topp GeV (left) and Pb+Pb colli
Au+Au
collisions
at at
200
20-50% central Au-Au collisions at sNN = 200 GeV (left) central
and 20-50%
central Pb-Pb
collisions
sNN = 2760 GeV (right).

Y. Sun and C.-M. Ko, PRC99, 011903(R) (2019)-+

Chiral kinetic approach4

4

Yilong Xie et al.: Fluid Dynamics Study of th

PICR model

where ' is the transverse momentum azimuthal angle,(p ,p )
0z x y
Fig.
5
shows
the
resultsofhP·sign(Y)i, hPy · sign(Y )i4x
set to be zero at the reaction plane. In the above equaand hPz i for the 3⇤ hyperons as functions of azimuthaltion the longitudinal spin component is a function of thespectrum alone at Y = 0. By expanding it in Fourier
angle p in 20-50% central Au+Au collisions at 200 GeV
series in ' and retaining only the elliptic flow term, one
2
and
Pb+Pb
collisions
at 2760 GeV, where the whole
obtains:

High resolution (3+1)D PICR hydrodynamic model
Y. Xie, D. Wang, and L. P. Csernai, EPJC80.39 (2020)- Blast-wave model

range of p is divided into 24-0.5%
bins. We
0.5%can see that thedT /d⌧ @S (pT , Y = 0) =2v2 (pT ) cos 2'
shapes of hPx · sign(Y)i, hPy · sign(Y )i and hPz i are in
4mT @'
0analogy to sin p , cos p and sin(2 p ) respectively,
dT 1=
v2 (pT ) sin 2'
(13)
-1
-0.5%
0.5%
d⌧ mT
as described by Eq. (12). The
features of three quanPy (GeV)

-

+ ­­

py [GeV/c]-

AMPT, Au+Au 200 GeV 20-50%z

S. Voloshin, EPJ Web Conf.171, 07002 (2018), STAR, PRL123.13201

Partly (one of component showing the same sign)1-2
meaning, comparing this result to eq. (7) that in thistities at two collisionalenergies are quite similar. We
case:have also checked that the harmonic behaviors also ex-3

- Glauber/AMPT IC + (3+1)D viscous hydrodynamics

dT 1
polarizationof quarks ist at energies 7.7-62.4
GeV. It is worthwhile to pointv2 (pT )-4f2 (pT ) = 2

d⌧ mT

G
-3
-2
-1
0
1 Px2 and
3
that although the -4global
polarization
P4zG areThis simple formula only applies under special assump(GeV)
zero due to the symmetry and PPyG
is almost vanishing at
H.-Z. Wu et al., Phys. Rev. Research 1, 033058 (2019)x
p FIG. 3. Second harmonic of the longitudinaltions with regard to the hydrodynamic temperature evocomponent of ⇤
s
=
200
GeV
[18]
and
2760
GeV
due to the reaNN
polarization f2 from hydrodynamic simulations[37]as a function
lution, but it clearly shows the salient features of theFig. above
3.
(Coloronline) The transverse
distrib
FIG. 4: polarization(Color online)
longitudinal
spin polarizationof pT forindi↵erent
energies.
son giventheparagraph,the localmomentum
polarization
longitudinal
at Average
mid-rapidity
as a functionof- Thermal modelof longitudinal polarization, ⇧0z , for Au-Au 200 GeV colof quarks
as a functionof itazimuthalangle
φp fordiﬀerent
transverse
momentumand how
can provide
directinquantities
hP· signYi, parameter
hPy · signY
i and
hPzat
i are
all nonx
with
impact
ratio
b
=
0.68
rapiditybin |yrapidity
ranges.
0formationonthetemperature
gradientat
hadronization.
W. Florkowski et al., Phys. Rev. C 100, 054907(2019)
FIG. 3: (Color online) Time evolution of average longitudinal
vanishing.
We also second
see themagnitudes
of fhPx · sign(Y )i
The corresponding
harmonic
coefficients
It also shows, as has been mentioned - that it is driven by
2 arespin polarization of midrapidity quarks with momenta satisand displayed
hPy · sign(Y(around10%)
are energies:
larger thanin fig.)i
3 for
4 di↵erent
collision
7.7, that ofphysical quantities related to transverse expansion andfying px py > 0.
of the spinofdegrees
of freedom.
Furthermore,
the GeV (calculated
withinitialfrom
the UrQMD
that rium
it is independent
longitudinal
expansion.
keeps
same
signstate
distribution,i.e. (-, + , with-, +)hPz i 19.6
(around1%). theOur
resultforhP
z i is consistent[17]),
200magnitude
and 2760 GeV(with fromthe initial
amplitudeofof⇤ theazimuthal
dependence,bePolarization
hyperons
along thebeam line which cancascadewithgrowing
aboutstate
2% to 29
8% at
T. Niida, HI-Pub 2020
theviscoushydrodynamic
simulations[33].
from Monte Carlo Glauber [16]). It is worth noting that,
The above conclusion is confirmed by more realistic 3D

Incomplete thermal equilibrium of spin degree of freedom?
expressed as sin(2φ ), is larger for the larger rapidity,

Centrality and pT dependence of Pz modulation
5

STAR, PRL123.13201 (2019)

0.5

Λ +Λ
AMPT (x 0.2)
BW (spectra+v 2 )BW (spectra+v 2 +HBT)

0.6

STAR Au+Au sNN = 200 GeV
20%-60%2

STAR
Au+Au s NN = 200 GeV〈Pz sin(2φ-2Ψ )〉 [%]1

2〈Pz sin(2φ-2Ψ )〉 [%]BW parameters obtained with HBT: STAR, PRC71.044906 (2005)

0.4

Λ +Λ
hydro (x 0.2) 20%-50%
BW (spectra+v ) 20%-60%
2
BW (spectra+v +HBT) 20%-80%20.2

ond fitthe pio
via Haometryaccord⟨ωz

wheresection0
cal flowpoint (
0.5<p <6 GeV/ cT−0.2
βt = m
0
20
40
60
80
0
1
2
3
4
functio
Centrality [%]p [GeV/c]longituT
as Pz ≈
Strong centrality dependence as in v2
model
FIG. 3. (Color online)
The second
Fourier sine coeﬃcient
No strongpT dependence
but a hint
at pTheGeV/c
T<1second
uncFIG.of4. drop-oﬀ(Color online)
Fourier sine coeﬃcient ofmodelof the polarization of Λ and Λ̄ along the beam direction as the longitudinal polarization of Λ and Λ̄ hyperons as a funcvent
The
Blast-Wave
model
as
a
simpleestimateforkinematic
vorticity
candescribethedataafunctionofthecollision
centrality
in
Au+Au
collisionsat
s attion of pT for 20%-60% centrality bin in Au+Au collisions at
√
Figs.
3
√
s
=
200
GeV.
Open
boxes
show
the
systematic
uncer30
T.
Niida,
HI-Pub
2020
N
N
cer0

sN N = 200 GeV. Open boxes show the systematic uncer-

v1

v1 and vorticity/EM-field

v1

∆v1

0.002
Figure 3 shows a compilationof published[3, 12] and presented at this conference [10, 11] results
10 × v1(h )
NN
0
v
(
D
)
1
3
−
on the average global polarizationoflambdaandanti-lambda
hyperonsat
mid-rapidityin
mid-central
10 × v1(h )0collisions as a function of collision energy. The blue solid and dashed lines are the results of hydro−0.002∆v1 and without accounting for the hyperon feed-down contribution,
dynamic calculation [7, 13], with
−0.004 for the feed-down correction is outlined in [6] with Eq. 1 used for an estirespectively. The procedure
0
0
1
2
30
1
2
30
1
2
30
1
20 week ending
30
1
2
3
PHYSICAL REVIEW LETTERS
6 JANUARY 2017
PRL 118, 012301 (2017)mate of the polarization of the higher
spin
resonances.
Note
that
the
e↵ect
of
the
feed-downcorrection
p [GeV/c]p [GeV/c]p [GeV/c]p [GeV/c]p [GeV/c]
T
T
T
T
T
have not yet been created during the lifetime of the strong electric field, which is of the order of, or ALICE, PRL125.022301(2020)
is rather modest – at the level of ⇠ 15%.
5−40%
less than, 1 fm=c.
10−40%
1
pﬃﬃﬃﬃﬃﬃﬃ
ﬃ > 0.2 GeV/
Gursoy,Kharzeev,
and Rajagopal, PRC89.054905 (2014)pc
FIG. 2. Directed flow of positive and negative
particles from minimum bias Cu þ Au collisions at sNNT ¼ 200 GeV, as a function of
DOI: 10.1103/PhysRevLett.118.012301
3 < p T < 6 (GeV/c )
Das
et
al.,
PLB768(2017)260
bars:
stat. uncert.
−0.5
pT ,3in five centrality bins. The difference between the positive and negative spectra is shown in the−0.5lowerpanels,
where
the
open
boxes
Not feed-down correctedboxes (filled/empty): syst. uncert. (corr./uncorr.)STAR,
Nature,548,
62 (2017)
two nuclei,direction
a strong electricfieldvis
Hot Seeand dense
nuclearfor
matterbeen
extensively
show the systematic uncertainties.
the text
thehasdefinitionof thethepositivefor
1.created at the initial

PH [%]

v : sensitive to the initial tilt and EM-field−0.5is
0
0.5
−0.5
0
0.5
stage of the collision and the direction of the fieldstudied in nucleus-nucleus
collisionsΛΛ at the Relativistic
0.5
ηη
indicated by the arrow in Fig. 1. The 0.5
lifetime of the field
Heavy Ion Collider (RHIC) [1–4] and the Large Hadron
STAR, PRC76.024915 (2007)
might be very short, of the order of a fraction of 1 fm=c
Collider (LHC) [5–7]. Numerous experimental results have0+0ΛΛ (QGP) consisting of(e.g., t ∼ 0.25 fm=c from Ref. [14,15]), but the electricsuggested that a quark-gluon
plasma103 × [v 1(h ) − v 1(h−)]
v 1(D ) − v 1(D )charges from quarks and antiquarks that are present in thedeconfined quarks andgluonsis createdin these collisions.
TSTAR
prelim.
(20-60%)early stage of the collision would experience the Coulomb
At present, the emphasis
the detailed
Λ is on characterizingΛ(a)be pushed along or opposite to the field 10-40% centrality
force and so would
properties of the QGP.
ALICE prelim.
(15-50%)experimental
direction depending on the particle charge. The azimuthal
One of the most importantand informative
1
distribution of produced particles (includingΛ the properties
Λ of the QGP is
observables used to study
0 the effect of0
the electric
0 field) can be written as [14,16]
the azimuthal anisotropic flow, which can be characterized
by the Fourier coefficients extracted from the azimuthaldN "10−40%
distribution of the final state particles [8]. The second-order∝ 1 þ 2v1 cosðϕ − Ψ1 Þ " 2dE cosðϕ − ψ E Þ % % % ; ð1Þ
5−40%
Fourier coefficient (so called elliptic flow) and higher-orderdϕFourier coefficients vn (n > 2) are found to be very
3 < p T < 6 (GeV/c )Karpenko, Becattini, EPJ C77(2017)213
p
>
0.2
GeV/
c
where
ϕ
is
the
azimuthal
angle
for
a
particle,
Ψ
is
the
angle
π entropy density ratio
sensitive to the shear viscosity over1
PHSD+EFT
primary Λ-0.7*dv1/d ηoforientationforthefirst-order
event
plane,
and
the
upper
η=s
[9,10].
The
first-order
Fouriercoefficient
v
,
also
1
−0.02
Cu+Au |η|<2
Λ including feed-downdΔ v 1 / dη = [4.9 ± 1.7 (stat) ± 0.6 (syst)] ⋅ 10-1
0.5 dΔ v 1charged(lower) sign of " is for the positively−(negatively)/ dη = [1.68 ± 0.49+ (stat) ± 0.41- (syst)] ⋅ 10−-40.5
known as directed flow, is sensitive to the equation ofππparticles. ψ E STARdenotes theazimuthal angle of the electric
state
of
the
mediumandtherefore
could
be
a
possible
probe
|
η
|<1
1
1
−0.5
0
0.5
−0.5
0
0.5
field; it is strongly correlated +with Ψ1- (see Fig. 1) but
can3
of2 a QGP phase transition [11–13].
h due toh the fluctuation of thediffer from Ψ1Cu+Au
event by event
Recent1 theoretical studies suggest that an asymmetricT+ coefficientηη
initial nucleonAu+Au
distribution. The
dE characterizes
colliding system can provide new insights regarding thehhNN conductivity [14] the strength of dipole deformation induced by the electricT1properties of a QGP, such as the electric
−0.04
field
and is proportional to the electric conductivity ofand the time evolution of the quark densities [15]. Figure 1
1
Cu+Au
syst.
uncert.
the plasma. Thenthe directed
v1 of positively
Figure2: flow(coloronline) andTop left: v1 of positively (red) and negatively (blue) charged hadrons for the 5–4
shows an example of the distribution of spectators and+negatively
chargedparticles
canbeexpressedaspparticipants
and neutrons)in the transverse
0 (red) and D0 (blue) for the 10–4
Figure 3. Average global polarization of lambda hyperons
as a(protons
functionof collisionenergy.plane
Boxes indicate thecentralityh (pT-uncorr.)intervalinPb–Pbcollisions
at
s
=
5.02
TeV.
Top
right:
vofDNN
1for a Cu þ Au collision assuming an impact parameter of"psystematic uncertainties.
h-uncorr.)
v
¼
v
"
d(p
ð2Þ
1
1
E hcosðΨ1 − ψ E Þi;
1 centrality
6 fm. Because of the difference in the number of protons in
T interval in Pb–Pb collisions at
sNN = 5.02 TeV. Bottom left and right: Dv1 (h) = v1 (h+ ) v1 (h )

∆ v1

v1

NN

Δ v1

Δ v1

2
p < 2 GeV=c in 10%–30% centrality and becomes consistent with zero by 50%–60% centrality within large
systematic
uncertainties. The small but finite Δv agrees
1with the expectation for the effects of the initial electricfield. The sign flipping of the electric field discussed inRef.
0 [14] seems not to be observed within the current
uncertainty, which is close to the expectation discussed
in Ref. [16].
Figure 3 shows v and Δv in the 10%–40% centrality
10 Δv seems to10
bin. For 10
p < 2 GeV=c, theincrease with
[GeV]
p . Web
The v Conf.171,
results from07002
Au þ Au
collisions (thesso-called
S. Voloshin, EPJ(2018)
even component of v ) show much smaller values (∼ by afactor of 10) compared to those in Cu þ Au. Note that the
Cu+Auv
1: EM-field lifetime, quark density evolution, conductivity
odd component of v in Au þ Au collisions is similarly+h(EP)small [34]. The Δv1 in Au þ Au is consistent with zero. STAR,
PRL118.012301(2017)
0 ) in0 ), respectively. Dashed lines represent fits with a linear function.
where
hi means an
overparticles−0.06
Dvaverage(D)= vallv1all(Devents.
1
1 (DEquation (2) illustrates how the presence of an electric fieldCalculations for charged pions from the parton-hadronresults in charge
separation for directed flow. The strength(b)string-dynamics (PHSD) model [15], which is a dynamiof the charge separation depends
number of (anti)
0 andonDthe
0 directedTheD
flow as a function of pseudorapidity for the 10–40% centrality interval in Pb–
0.005
quarksexisting atCu+Au
the earliest stages pof the collision whencal transport approach in the partonic and hadronic
the electric field isstrong. Therefore,
measurement
collisions
at thesNN= 5.02ofTeV is shown in the top right panel of Fig. 2. The data suggest a positive slo
Au+Au
Y. Hirono, M. Hongo,
andT.
Hirano,charge-dependent directed flow can be used to test thephases, are compared to the data. As indicated in00therapidityquark productionfor
mechanism,
such as thedependence
two-wave sce- of the v1 of D and a negative slope for D , with a significance of ab
PRC90.021903(R)(2014)
pEq.
(2), the measured Δv1 could be smeared by thenario of quark production [17,18]. Also, understanding the
2s
in
both
cases.
The
slopesaredifferentfromthemeasurementsin
Au–Au
collisionsat
sNN = 2time evolutionof the quark density in heavy-ion collisions
0
V. Voronyuk et al.,fluctuations
PRC90.064903(2014)in ψ E and Ψ1 orientations, but note that theis very important GeV
for a detailedof the value is observed for both the D0 and D0 . Additionally, the v for D0 and[42],theoretical
whereprediction
a negative1
chiralmagnetic
effect[19,20]andthechiralmagnetic
wave
PHSD model takes such event-by-event fluctuations intomesonswith πtohp
4.2anGeV/c in the 10–40% centrality interval is about three orders of magnitu[21,22]. These effects
are supposed
emergeT i ⇡under
PHSD+EF(x0.1)
initial strong magnetic field and are actively searched for byaccount. The PHSD model calculates two cases: chargePHSD
largerthanπ the result obtained for charged particles with hpT i ⇡ 0.7 GeV/c in the 5–40% centrality cla
variousexperiments[23–27].
−0.005dependent v1 with and without the initial electric field
In this Letter, Theof the used for the charged hadron and D meson v measurements are imposed
different
pT intervals
0 we present
1the first measurement2341charge-dependent
directed
flow
in
Cu
þ
Au
collisions
at(EF). For the case with theFIG.EF
switched
on, Cuthemodel
pﬃﬃﬃﬃﬃﬃﬃﬃ
theprecisionof the data, which simultaneously limits the yield of high-pT charged31
hadr
s ¼ 200 GeV.
Thestatisticalresults are presentedfor
1.
ExampleofanoncentralþAucollisionviewedinp different[GeV/c]T. Niida, HI-Pub 2020
T~ caused bycollision centralities as a function of the particle transverse
assumes that all electric charges
are planeaffectedbytheEFfieldand00
the transverse
showing an
initialelectricEpatterns as those simulated in Ref. [56]. The rapidity dependence is qualitatively consistent with the spacetime-rapidity
dependence of fluid vorticity [17]. Within error bars, consisNe
tence between the data [6] and our simulation is seen.
measured
W.-T. Deng and X.-G. Huang, PRC93.064907sible(2016)
vorticwithin 2023-20
In Fi
Au+Au
20-50%In Fig6⇤ an|Y| < 1
Λ&Λ
ities, whil
collisΞmeasurem4ΩElectromaspondHigh statistics data of BES-II 7.7-19.6 GeV and FXT 3-7.7 GeV
selectin anmoe
2023-2025
2
on thw
Isobaric collision data (Ru+Ru, Zr+Zr), ~10% difference in B-fieldof error,
OAM
allocated
What
is a
0
from
Global polarization of multi-strangeness (Ξ and Ω)
the projec
show
10
100
that, withtal daForward upgrade in Run-2023
established√sNN (GeV)
K 0ior
is at
of
This
¯
FIG. 6. (Color online)(Left)
The
averaged⇤and⇤spin polarization
STAR BUR2020
imen
along y direction in 20-50% centrality range of Au+Au collisions as
azimu
STAR Au+Au s NN = 200 GeV
Projection (run2023)¯
a function of collisionenergy.
Theforrapidity
20-60%(40-80%2.5<η<4) window forΛ +Λ⇤+ and ⇤ is
out-o
Ξ
+
Ξ
+
|Y
|
<
1.
Open
points:
STAR
data
[5,
6].
Red
solid
points:thiswork.
Global/local polarizations at 5.02 TeV in LHC Run3
1
Ω
+Ω
which
0
(Right) The spin polarization PΛy, geometricfor ⌅ modeland ⌦ . Other parameters
Data
We w
Λ
,
PICR
hydro
are the same as the left panel. 0

OutlookSTAR

0

Measurements at lowest energies (2-2.4 GeV)

Future facilities/experiments
T. Niida, HI-Pub 2020

PH [%]HADES

ρPH [%]ALICE/CMS/ATLAS

00

Py (%)-

Ξ - , AMPT
Ω , AMPT

Λ

Λ

0.5

In Fig. 6 (right) we draw the spin polarization ofFTS⌅0 and⌦ for Au+Au collisions in 20 - 50% centrality range and rapidity window 0|Y | < 1 . The results are similar with that of¯ and can be understoodiTPC⇤ and ⇤
by noticing the mass orderingand spin ordering among ⇤, ⌅00 , and ⌦ η: m⇤2 < m⌅0 < m⌦4
and spin(⌦ ) = 3/2, spin(⌅0 ) = spin(⇤) = 1/2. Accord-η32

Summary
Global polarization of Λ has been observed at sNN = 7.7-200 GeVMost vortical ﬂuid (ω~1021 s-1) created in heavy-ion collisions
Energy dependence, increasing in lower sNN, is captured well by theoretical models
Λ-antiΛ splitting is not signiﬁcantAzimuthal angle dependence is not understood yet

Global spin alignment shows larger deviation from 1/3
φ meson ﬁeld may explain this large deviation?
Diﬀerent trend between RHIC and LHC φ or between φ and K* at RHIC

Polarization along the beam direction has been observed at sNN = 200 GeV
Qualitatively consistent with a picture of the elliptic ﬂow but agreement/disagreement among
the data and theoretical calculations in the sign

There are still many open questions and more precise data are needed.
T. Niida, HI-Pub 202033