Vorticity and polarization in heavy-ion collisions(重イオン衝突における渦と偏極)

Takafumi Niida(高エネルギー原子核実験グループ)

宇宙史センター構成員会議・成果報告＆交流会
Nov. 30, 2020

Heavy-ion collisions experiments
Main goals of heavy-ion collision experiments
to understand and quantify the properties ofquark-gluon plasma (QGP)
to map out QCD phase diagram

T. Niida, TCHoU Research Member Meeting 2020 Fall-

Critical Point search-

Signatures of 1st-order phase transition

2

RHIC-STAR experiment
Time Projection Chamber(|η|<1)Time Of Flight detector(|η|<0.9)
Beam-Beam Counter

Vertex Position Detector

Relativistic Heavy Ion Collider (RHIC)- in Brookhaven National Lab. (NY, USA)- 3.8 km in circumference- √sNN = 7.7-200 GeV for A+A
species: p+p, p(d)+Au, He+Au, Cu+Cu, Cu+Au, A+Au…
T. Niida, TCHoU Research Member Meeting 2020 Fall

Zero Degree Calorimeterwith Shower Maximum

Solenoidal Tracker At RHIC (STAR)- Full azimuth and wide rapidity coverage- Excellent particle identification

3

Challenge here:
Extract the medium properties, determining unknown dynamics, by measuring finally produced particles

4

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typical magnet
magnetarB ⇠ 0.1
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T. Niida, TCHoU Research Member Meeting 2020 Fall
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2(eB ⇠ m⇡ (⌧ ⇠ 0.2 fm))
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Important features in non-central heavy-ion collisions
B L

T

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

Orbital angular momentum

L=r⇥p
p
6
⇠ bA sN N ⇠ 10 ~Z.-T. Liang and X.-N. Wang, PRL94, 102301 (2005)

wikipedia

reaction plane→Chiral magnetic/vortical effects→Particle polarization
5

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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
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picturein whichthe orbital angular momentum of thepostscript
figures,
an erratumofistheadded
the final
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⇥
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!
=
⇡
y via some spin-orbitalyintosecondaryparticleangularspin
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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?)

S.A. Voloshin

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

• Vortical or QCD spin-orbit: Lambda and Anti-Lambda spins
T. Niida,
TCHoU(What
Research
Member Meeting 2020 Fall
DisableMathJax
is
MathJax?)aligned with L

6/30/16, 11:20 AM

6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 ✓

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

p

PΛ

πdN
dcosθ

slope=αHPH

Note: αH for Λ recently updated (BESⅢ and CLAS)
P.A. Zyla et al. (PDG), PTEP2020.083C01
αΛ=0.732±0.014, αΛ=-0.758±0.012* Published results are based on αΛ=-αΛ=0.64±0.013, but they are
scaled by αold/αnew when comparing to new results.
T. Niida, TCHoU Research Member Meeting 2020 Fall

-1

0
cosθ

1
7

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)*: angle of daughter proton
6/30/16,AM
φin 11:20
Λ restframepWhich authors of this paper are endorsers? | Disable MathJax (What is MathJax?)

8 hsin( 1
PH =
⇡↵H
Res(

Link back to: arXiv, form interface, contact.
Link back to: arXiv, form interface, contact.

2 of 2

T. Niida, TCHoU Research Member Meeting 2020 Fall

⇤
p )i

1)

STAR, PRC76, 024915 (2007)
6/30/16, 11:26 AM

8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
!0.02 in magnitude.
that theglobal!17 andstatistics
!
are
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
11
45
38
39
49
43
¯ hyperon global polarization has been
,41 Z. Chajecki,
P.
Chaloupka,
S.
Chattopadhyay,
H.
F.
Chen,
J.
H.
Chen,
J.
Y.
Chen,
J.
Cheng,
To
suppressthecontribution
totheglobalpolarization
The
!
and
!
0.02
0.02
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
9
36
3
3
49 TCHoU 38
49
49
Niida,
Research
MemberMeeting2020 Fall3 W. J. Llope,36 R. S. Longacre,−3
F.T.Liu,
H.
Liu,
J.
Liu,
L.
Liu,
T.
Ljubicic,
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 lower energies (2017)
STAR, Nature 548, 62 (2017)

Positive polarization signal at lower energies!

Au+Au 20-50%-

Λ this study

8

PH looks to increase in lower energies

Λ this studyΛ PRC76 024915 (2007)

6Λ PRC76 024915 (2007)420*based on αΛ=-αΛ=0.64±0.013

10
T. Niida, TCHoU Research Member Meeting 2020 Fall

2

10
sNN (GeV)
10

First observation in lower energies (2017)
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

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

Λ PRC76 024915 (2007)

6Λ PRC76 024915 (2007)

4

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

22

1⇠ 0.6-2.7 ⇥ 10 s

2-

The most vortical fluid!

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

0*based on αΛ=-αΛ=0.64±0.013

10
T. Niida, TCHoU Research Member Meeting 2020 Fall

2

10
sNN (GeV)
10

First observation in lower energies (2017)
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

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

Λ PRC76 024915 (2007)

6Λ PRC76 024915 (2007)

4

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

22

1⇠ 0.6-2.7 ⇥ 10 s

2

-

0

T. Niida, TCHoU Research Member Meeting 2020 FallμΛ: Λ magnetic moment
T: temperature at thermal equilibrium(T=160 MeV)

Hint of the difference between Λ and anti-Λ PH*based on αΛ=-αΛ=0.64±0.013

10

The most vortical fluid!

1- Effect of the initial magnetic field? (discussed later)2

10sNN (GeV)
10

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 at lower √sNN
because of baryon stoppingPH (⇤) [%] = 0.277 ± 0.040(stat) ±0.039
0.049 (sys)¯ [%] = 0.240 ± 0.045(stat) ±0.061 (sys)PH (⇤)
0.045

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

10102* based on αΛ=-αΛ=0.64±0.013

T. Niida, TCHoU Research Member Meeting 2020 FallsNN [GeV]

11

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, JPS2020 fall

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,
12

Differential studies for better understanding• Effect of initial magnetic field‣

Any particle-antiparticle difference?

• Energy dependence in lower energy• Discrepancy between data and models (“sign issues”)‣

Azimuthal dependence of PH‣

Local polarization along the beam direction• Particle species dependence‣

Different mass and spin

T. Niida, TCHoU Research Member Meeting 2020 Fall13

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

A possible probe of B-field

primary

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

7-39GeV

B = (P⇤⇠ 2 ⇥ 1011 [T]eB ⇠ 10

Feb. 20172•

T. Niida, TCHoU Research Member Meeting 2020 Fall
188
L. McLerran, V. Skokov / Nuclear Physics A 929 (2014) 184–190

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

STAR, QM17
Au+Au 20-50%

STAR preliminaryμΛ: Λ magnetic moment

P⇤¯ )T /(2µ⇤ )upper limit from ΔPH

2
m⇡Fig. 1. Magnetic field for static medium with Ohmic conductivity, σOhm .

Conductivity increases lifetime.

ΔPΛ~0.5%, T=160MeV

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.
• Based on thermal model, B-field at kinetic freeze-out
could
beof probed
Λ-antiΛshow time
evolution
the magnetic byfield inthe origin x⃗splitting= 0 as a function of theductivity σOhm . The results show that the lifetime of the strong magnetic field (eB• Current results are consistent with zero (except 7.7 GeV)
affected by the conductivity, if one uses realistic values obtained in Ref. [5].

But the splitting could be also due to other effects…
4. Energy dependence

14
In the previous section, we established that for realistic values of the conductiv

Need caution for the interpretation•w

www.nature.com/scientificreports/

Initial magnetic field• Effect of chemical potential (expected to be small)
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)•

Spin interaction with the meson field generated by the baryon current
L. Csernai, J. Kapusta, and T. Welle, PRC99.021901(R) (2019)•

fluid with nonzero charge density (right).
Different space time distributions and freeze-out of Λ and antiΛ

e
e
−0.02
w
101
102
www.nature.com/scientificreports √nsN N (GeV )n
While this basic mechanism
issimpleandgeneric,
it
has
not
been
p
0.10
b
system — the hot subatomic fluid consisting of strongly interacting
c(b)0.08 highly relativistic fluid is at extreme amongoas well as hadrons. This
12tratories, with the highest
temperature(~10
K),
flowing
over
the
sm
0.06
t
−23
0.00

O. Vitiuk, L.Bravina, E. Zabrodin, PLB803(2020)135298

m/scientificreports/

p
b
(a)
0.08
c
i
0.06
n
3
0.04
t
i
0.02of the magnetic field generated by a single swid
Figure 1. Illustration
0.10

PΛ̄ − PΛ•

L. P. CSERNAI, J. I. KAPUSTA, AND T. WELLE

www.nature.com/scientificreports/
www.nature.com/scientificreports

1.0
0.5
0.0
10

X. FigureGuo,2. J.
Wang,
PRC99.021901(R)
TheLiao,vorticity andin unitof MeV corresponding
to 1.5 × 10 sec (2019)), charge density nQ (middle,ωy (left,E.
19−1in unit of fm−3 = 1045 m−3) and magnetic field eB (right, in unit of mπ2 corresponding to 3.3 × 1014 Tesla) as
functions of collisional beam energy sNN (in unit of GeV = 109 eV ), with solid/dashed curves in each panel
T. Niida,
TCHoU
Member2020
Fallrepresenting
an Research
upper/lower estimatesandMeetingwith the shadedband
between them giving an idea of the expected

time scale (~10 sec). The present study will take a novel step to exp
hitherto unexplored 0.04
extreme regime and establish its presence in thetion about the fluid vorticity and net electric charge density (particula
0.02w
stopping in heavy ion collisions, we will estimate the magnitude of thshow that a novel featureof such a magnetic field is its considerably3
0.00
t
ously known source of magnetic field in heavy ion collisions), due ti−0.02
of angular momentum
conservation).
This feature turns
out to be crt
1010√sN N (GeV)
the spin hydrodynamic generation in heavy
ion collisions
and provids
fidifference in particle/anti-particle
globalpolarization.
¯
L. Csernai
etal.,
PRC99.021901(R)(2019)
FIG. 1. Difference in polarization of ! and ! hyperons, withPΛ̄ − PΛ

100 × (P Λ_ - P Λ )

1.5

20

50
sNN (GeV)

100

200

1

2

Figure 3. The induced polarization difference between hyperons and anti-hyperons,positive∆P = valuePΛ − meaningPΛ as a that it is opposite to the total angular mo9
47of theproducedfunction of collisional beam energy sNN (in unit of GeV = 10 eV ), in comparisonmentum
with STAR
data. The matter. The top panel (a) shows case I and15
the bottom
panel(b) showsincase II, as described in the text. The datasolid/dashed curves are obtained from the upper/lower estimates for eB (see solid/dashedcurvesrespectively

Demonstration of the Mechanismew[

PH [%]

Complete the energy dependence

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

STAR Au+Au 20%-50%
Nature548.62 (2017)
ΛΛ

ALICE Pb+Pb 15-50%
Λ

PRC76.024915 (2007)
Λ
Λ

Λ

Λ

•

STAR prelim. 54.4 GeVΛSTAR preliminary at 27 and 54 GeV*result (54 GeV) from K. Okubo (M2) in our group

HADES prelim. Au+Au 10-40%

PRC98.014910 (2018)
Λ
Λ

5

•

Λ

ALICE at 2.76 and 5.02 TeV•

STAR prelim. 27 GeV (y2018)
Λ+Λ

Expected signal is of the order ofcurrent statistical uncertainty

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

primary+feed-down•

HADES at 2.4 GeV••

Large uncertainty but still preliminary
Hopefully reduce systematic uncertainty

0

1

10

* based on αΛ=-αΛ=0.64±0.013
T. Niida, TCHoU Research Member Meeting 2020 Fall

102

3

10

sNN [GeV]
16

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

PH [%]

Complete the energy dependenceSTAR Au+Au 20%-50%

0.12

Au+Au

Nature548.62 (2017)
ΛΛΛ

HADES prelim. Au+Au 10-40%

PRC98.014910 (2018)ΛΛΛSTAR prelim. 54.4 GeVΛΛ

b=8.0 fm〈-ω y〉 (fm-1)

Λ

PRC76.024915 (2007)
Λ
Λ

5

0.1

ALICE Pb+Pb 15-50%

0.08
b=10.0 fm
0.06
0.04
0.02

STAR prelim. 27 GeV (y2018)
Λ+Λ

0
1
UrQMD+vHLLE, Λ
primary
primary+feed-down
AMPT, Λprimaryb=5.0 fm

primary+feed-down

2

3 4 5 6 7 10
sNN (GeV)

20 30 40

Interesting energy dependence of kinematic
FIG.vorticity
3. Initial kinematic
vorticity
mid rapiditymodel
as a functionof thepredicted
by aattransport(UrQMD)
collision
foral.,
impactparameters b(2020)= 5, 8, and 10 fm.
X.-G. energy
Deng et
PRC101.064908

0

1

10

T. Niida, TCHoU Research Member Meeting 2020 Fall

102

enough (our computation suggests a turning point aroundp3
10
sNN ⇠ 3 5 GeV depending on centrality), the particles
sNN [GeV] near the mid-rapidity are not effective angular-momentum
carriers and most of the angular momenta are carried by the17particles with large rapidity (but at large rapidity the angu-

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

PH [%]

Complete the energy dependenceSTAR Au+Au 20%-50%

0.12

Au+Au

Nature548.62 (2017)
ΛΛΛ

HADES prelim. Au+Au 10-40%

PRC98.014910 (2018)ΛΛΛSTAR prelim. 54.4 GeVΛΛ

b=8.0 fm〈-ω y〉 (fm-1)

Λ

PRC76.024915 (2007)
Λ
Λ

5

0.1

ALICE Pb+Pb 15-50%

0.08
b=10.0 fm
0.06
0.04
0.02

STAR prelim. 27 GeV (y2018)
Λ+Λ

0
1
UrQMD+vHLLE, Λ
primary
primary+feed-down
AMPT, Λprimaryb=5.0 fm

primary+feed-down

2

3 4 5 6 7 10
sNN (GeV)

20 30 40

Interesting energy dependence of kinematic
FIG.vorticity
3. Initial kinematic
vorticity
mid rapiditymodel
as a functionof thepredicted
by aattransport(UrQMD)
collision
foral.,
impactparameters b(2020)= 5, 8, and 10 fm.
X.-G. energy
Deng et
PRC101.064908

0

1

10

102

covered by HADESand STAR FXT+BES-Ⅱ
T. Niida, TCHoU Research Member Meeting 2020 Fallenough (our computation suggests a turning point aroundp3
2-3 GeV on centrality), the particles
10
sNN ⇠ 3 HADES:
5 GeV dependingsNN [GeV] near the mid-rapidity
STAR FXT:GeV angular-momentum
are3-7.7
not effective
carriers and STAR
most ofBES-II:
the angularmomenta
7.7-19
GeV are carried by the17particles with large rapidity (but at large rapidity the angu-Differential measurements: centrality
PH [%]

STAR, PRC98, 014910 (2018)1

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, TCHoU Research Member Meeting 2020 Fall18

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sha1_base64="7Ycjn4poto6BSVsPnpZjpWph0Rc=">AAAB+XicbVBNS8NAEJ3Ur1q/oh69LBbBU0lE0GPRi6dSwdZCG8Jmu22XbjZxd1MoS/6JFw+KePWfePPfuG1z0NYHA4/3ZpiZF6WcKe15305pbX1jc6u8XdnZ3ds/cA+P2irJJKEtkvBEdiKsKGeCtjTTnHZSSXEccfoYjW9n/uOESsUS8aCnKQ1iPBRswAjWVgpdt6eepDYqNKFpNPI8D92qV/PmQKvEL0gVCjRD96vXT0gWU6EJx0p1fS/VgcFSM8JpXulliqaYjPGQdi0VOKYqMPPLc3RmlT4aJNKW0Giu/p4wOFZqGke2M8Z6pJa9mfif18304DowTKSZpoIsFg0yjnSCZjGgPpOUaD61BBPJ7K2IjLDERNuwKjYEf/nlVdK+qPlezb+/rNZvijjKcAKncA4+XEEd7qAJLSAwgWd4hTfHOC/Ou/OxaC05xcwx/IHz+QNqMZQm</latexit><latexit

sha1_base64="7Ycjn4poto6BSVsPnpZjpWph0Rc=">AAAB+XicbVBNS8NAEJ3Ur1q/oh69LBbBU0lE0GPRi6dSwdZCG8Jmu22XbjZxd1MoS/6JFw+KePWfePPfuG1z0NYHA4/3ZpiZF6WcKe15305pbX1jc6u8XdnZ3ds/cA+P2irJJKEtkvBEdiKsKGeCtjTTnHZSSXEccfoYjW9n/uOESsUS8aCnKQ1iPBRswAjWVgpdt6eepDYqNKFpNPI8D92qV/PmQKvEL0gVCjRD96vXT0gWU6EJx0p1fS/VgcFSM8JpXulliqaYjPGQdi0VOKYqMPPLc3RmlT4aJNKW0Giu/p4wOFZqGke2M8Z6pJa9mfif18304DowTKSZpoIsFg0yjnSCZjGgPpOUaD61BBPJ7K2IjLDERNuwKjYEf/nlVdK+qPlezb+/rNZvijjKcAKncA4+XEEd7qAJLSAwgWd4hTfHOC/Ou/OxaC05xcwx/IHz+QNqMZQm</latexit><latexit

sha1_base64="7Ycjn4poto6BSVsPnpZjpWph0Rc=">AAAB+XicbVBNS8NAEJ3Ur1q/oh69LBbBU0lE0GPRi6dSwdZCG8Jmu22XbjZxd1MoS/6JFw+KePWfePPfuG1z0NYHA4/3ZpiZF6WcKe15305pbX1jc6u8XdnZ3ds/cA+P2irJJKEtkvBEdiKsKGeCtjTTnHZSSXEccfoYjW9n/uOESsUS8aCnKQ1iPBRswAjWVgpdt6eepDYqNKFpNPI8D92qV/PmQKvEL0gVCjRD96vXT0gWU6EJx0p1fS/VgcFSM8JpXulliqaYjPGQdi0VOKYqMPPLc3RmlT4aJNKW0Giu/p4wOFZqGke2M8Z6pJa9mfif18304DowTKSZpoIsFg0yjnSCZjGgPpOUaD61BBPJ7K2IjLDERNuwKjYEf/nlVdK+qPlezb+/rNZvijjKcAKncA4+XEEd7qAJLSAwgWd4hTfHOC/Ou/OxaC05xcwx/IHz+QNqMZQm</latexit><latexit<latexit

PH [%]

𝑝𝑝T dependenceof PH of PH
Centrality
dependence
Differential measurements: centrality
Centrality dependence of PH

STAR, PRC98, 014910 (2018)

1

20

p

sN N
40

200 GeV60

STAR, QM19 (by K. Okubo)

STAR Au+Au s NN = 200 GeVT|η|<1, 0.5<p <6 GeV/c• We see no• Wedependence
observe PHon 𝑝𝑝T at
27
or
54.4
GeV
increasing with

Λ

Λ

0.5

0

80

Centrality [%]• Enough statistics tocentrality
say PH flat in range• 540.5
GeV
usesGeV< study
𝑝𝑝T < 1.75
BBC
ZDCatbased• If Pand
low 𝑝𝑝Ton
H drops1
due
to scattering or
𝑅𝑅EP(𝐵𝐵𝑐𝑐𝑆𝑆𝑐𝑐𝐵𝐵𝑆𝑆𝑆𝑆𝑆𝑆𝑐𝑐𝑦𝑦)
high 𝑝𝑝T due to jet
fragmentation,it• This trend
previouslymustbeoutsidethissuggested by study at
𝑝𝑝T range(1)
6 November 20196 November 2019 54 GeV

11STAR, QM19

‣ We used BBC and ZDC based on
event plane
Au+Auresolution.
at 𝑠𝑠NN = 27 GeV

0.4 < pT < 3 GeV/c, |η| < 1
STAR preliminary‣ Polarization
may increase in more

peripheral collision.

Λ+Λ

peripheral+JBOHFUBM 13$ Au+Au at 𝑠𝑠NN = 27 GeV
15-75% centrality, |η| < 1
STARpreliminary".15NPEFM

200 GeV
Joseph Adams ― Quark Matter 2019 ― Wuhan, China

In most central collision → no initial angular momentum
Kosuke Okubo, Workshop on the QCD Phase Structure, CCNU, Nov, 2019
The polarization decreases in more central collisions.
Similar trend was confirmed at lower energies.
18
T. Niida, TCHoU Research Member Meeting 2020 Fall
GeVChina
Joseph Adams ― Quark Matter 201927― Wuhan,centralDifferential measurements:
azimuthalangleHUANG
DE-XIAN WEI, WEI-TIAN
DENG, AND XU-GUANG

PH(%)

in-planeSTAR preliminary

0.6

Au+Au 200GeV
20-50%

0.4

00STAR 200 GeV scaled using α =0.75
19.6 GeV|Y| < 162.4 GeVSTAR Collaboration Preliminary Data
200 GeV

3

15

Λ

2

Au+Au b=9 fm

019.6 GeV
62.4 GeV
200 GeV

1

-15

0

-30
-1.6 -0.8 0.0 0.8 1

0.5 1.0 1.5 2.0 2.5

0.2

0.4

0.6

φ

0.8

1

1.2

1.4
φ -ΨEP,1
ΛY

Figure 5
I. Karpenko and F. Becattini,
EPJC(2017)77.213
FIG. 10. The directed anΛ and Λ combined¯ polarization
FIG. 9. TheLeft:azimuthalangle
dependence
of
!
and
!
Preliminary results(108)
the STAR
for the global polarizationof ⇤ andD. Wei,W.fromDeng,
and collaboration
X. Huang, PRC99.014905(2019)
f and f , versus rapidity for

1 mid-central
2
in rapidity region| < 1 forAu+Auemission
collisions
19.6,to62.4,
and plane, for⇤ as |Ya functionof hyperon
angle atrelative
the eventAu+Au√pparameter
9 fmthefor s fr
200is
GeV.
in figure 3, published data have been
rescaled bto=reflect
collisions at sN
N =[6]
200 GeV. The experimental
data
alsoAsshown.

<PH>
0.2

new accepted value of ↵⇤ . Right: Hydrodynamic calculations (12) of PJˆ in the transverse
momentum plane, for the same colliding system.

- The data shows larger polarization for in-plane, while
many
modelspredict
theopposite,i.e.
largerfor
out-of-plane
energy dependence.
We here propose another observable foroppositetrend vorticity
for the φtion structures, in the local equilibrium picture, are more sensitive
to the thermal
Not
fully
understoodyet
the smoke-loop-type
vorticalstructure,thatis thespin harregion whichshould resul
variations as a function of space and time,
convoluted
with flow-driven
space-momentum

0

−0.2

0.2

30arXiv:2003.03640
F. Becattini and M. Lisa,

Au+Au 20-50 %

f1

φ-Ψ1

0.4

Py (%)

out-of-plane

PH,J (%)

4

PHYS

in-plane0

0.5

T. Niida, TCHoU Research Member Meeting 2020 Fall1

out-of-plane
monic coefficients
at finite
rapidity.
crepancyof will
be examinedcorrelations.
First
measurements (81) report PJ,⇤/⇤
to be independenttransversemoˆ
for pT . particle
2“T-vorticity”
GeV/c, distribution
in agreementwithhydrodynamic
predictions (12, 111) when
Recall 1.5
thatmentum
the charged
canthebedata?
demay explain
initialharmonicconditions
are
used.
It wasseen (1)(81) to(2019)be independent of pseudoφ-intoΨrealistic
1 [rad]composeddifferent
as alsoin Eq.
H. Wucomponents
et al.,
PR.Research1.033058
rapidity, though only a limited range, |⌘| < 1 could be explored. As we discuss in section 5,
in which the harmonic coefficients reflect the response of
V.19DI
several theories suggest there is much to be learned at forward rapidity.

“Local” polarization due to collective expansionzyx- Vorticity (thus polarization) along the beam direction

is expected from the “elliptic ﬂow”

T. Niida, TCHoU Research Member Meeting 2020 Fall

20

“Local” polarization due to collective expansion
Au+Au sNN = 200 GeV
20%-60%0.0005x

0−0.0005

STAR
Au+Au s NN = 200 GeV

0.5

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

fit: p +2p sin(2φ-2Ψ )0
1- Vorticity (thus polarization)
along
the2 beam direction

Λ p =0.016±0.003 [%]1
is expected from the “elliptic
ﬂow”=0.015
±
0.003
[%]
p
−0.001Λ- Data indeed show such1 a longitudinal polarization Pz-

STAR, PRL123.13201 (2019)1

2〈cos(θp*)〉STAR〈Pz sin(2φ-2Ψ )〉 [%]

sub

0.001

z

y

5

0

0
2
3
0
Sign problem amongdata1 and theoreticalmodels(hydro, kinetic theory, transport models)under the discussion
φ-Ψ is[rad]2
Becattini and Karpenko, PRL.120.012302 (2018)
Xia et al, PRC98.024905 (2018)
Voloshin, EPJ Web Conf.171, 07002 (2018)
∗
Sun
and
Ko,
PRC99,(2019)
FIG. 2. (Color online) ⟨cos θp011903(R)⟩ of Λ andΛ̄ hyperons as a func…moretion of azimuthal angle φ relative to the second-order event

T. Niida, TCHoU Research Member Meeting 2020 Fall

0.5<p <6 GeV/ c
T

20

40

60

80

Centrality [%]FIG. 3. (Color online) The second Fourier sine coeﬃcientof the polarization
Λ and Λ̄ along thebeam direction
head-onofcollision
peripheral
collision as20
a function of the collision centrality in Au+Au collisions atpatterns as those simulated in Ref. [56]. The rapidity depenOther particles to measurepolarization?
dence is qualitatively
consistent with the spacetime-rapidity
dependence of fluid vorticity [17]. Within error bars, consistence between the data [6] and our simulation is seen.

W.-T. Deng and X.-G. Huang, PRC93.064907 (2016)

P. A. Zyla et al. (Particle Data Group), Prog. Theor. Exp. Phys. 2020, 083C01 (2020)

cτ
(cm)

decay
mode

decay
parameter

magnetic
moment(μN)

spin

Λ (uds)1.115683 7.89

Λ->πp(63.9%)

0.7320.014−0.6131/2

Ξ- (dss)

1.32171

4.91

Ξ-->Λπ−0.4010.010(99.887%)−0.65071/2

Ω- (sss)

1.67245

2.46

Ω-->ΛK(67.8%)

-2.02

3/2

0.01570.002

Au+Au 20-50%

6Py (%)

Mass(GeV/c2)|Y| < 1

4

2

0
10

Natural candidates would be Ξ and Ω hyperons.

Λ&Λ
Ξ0
Ω-

100

√sNN (GeV)- Different spin and magnetic moments¯- Less feed-down in Ξ and Ω comparedΛ online) (Left) The
FIG. 6. to(Coloraveraged⇤and⇤spin polarization
Based on thermal model:- Could be different freeze-out- Different valence s-quarks
T. Niida, TCHoU Research Member Meeting 2020 Fallalong y direction in 20-50% centralityof Au+Au
ω/(2T),
P(s=3/2)collisions~ 4 ω/(5T)asP(s=1/2) ~range¯ isa function of collision energy. The F.Becattini
rapidity window
for
⇤
and
⇤
et al., PRC95.054902 (2017)|Y | < 1. Open points: STAR data [5, 6]. Red solid points: this work.
0(Right) The spin polarization P for ⌅ and ⌦ . Other parameters

da

vo
In
⇤
co
sp
in
on
OA
fro
sh
tal
io
Th
im
az
ou
21wh

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The time-reversal violation parameter βΩ is expected to
FIG. 1.
HereγΩ is unknown.
66 ized, its polarizationtransferred∗∗∗is partially∗∗∗∗∗ to daughter
2+
e75 magnetic(αΞ + PΞover· p̂Λ )p̂
+
β
P
×
p̂
+
γ
×
(P
×
p̂
)
p̂
Ξ rest frame.∗ Averaging
theangulardistribution
of
Ξ
Ξ
93
be
small.
This
combinedwiththeconstraint
that
α
+
Λ
Ξ
Λ
Λ
Ξ
Λ
(
Ξ̄
) and
PΛ =
,
parameter
be small,
2
s 67
areΛ.
proαΞbyP∗ΞEq.
· p̂∗Λ2 decay
76
the
Λ in
the rest
frameinof suchthe Ξ given
yields are parity
Both
steps
a1 +cascadesions at94 β violat+ Time-reversal
γ 2 = 1, limits violation
unmeasured
parameterβ γwould≈±1,Ω
em freezes 73
thenthepolarizationtransfer
C
leads
to
(3)
ΩΛ
: ≈
lines indi−−Λ95
resultinginapolarizationtransfer
C
≈
1
or
C
Ω
Λ
Ω
∗
∗
∗
1
ing, and
be
used
for
an
independentmeasure∗ − can77PΛ thus
=p̂C
P
=
(1
+
2γ
)
P
.
(4)
9].68 ThereΞΞΛ
74 where
is
the
unit
vectoroftheΛ
momentuminthepositionsΞΞ3Λ
96 −0.6.
−
+
C
⇡
+1
or
0.6
rization,it⌦⇤
75 Ξ rest frame. Averaging over the angular distribution of
69 ment of the polarization).
2 γ −of2 Ξ 2 (Ξ̄[13,97
Our analysis is based on the data of Au+Au collisions
78 Using the measured
value
for
the
parameter
14],C=+0.927,↵++=1
Ξﬀerent par- 76 the⌅ Λ⇤in the rest frame of the Ξ given by Eq. 2 yields
√
−
98 at
s
=
200
GeV
collected
in
2010,
2011,
2014,
and
N
N
79
the
polarizationtransfercoeﬃcient
for
Ξ
to
Λ
decay
is:
70
The
polarizationofthedaughterbaryoninaweak
depins. Thus
∗
∗
∗
1
−
77
P
=
C
P
=
(1
+
2γ
)
P
(4)
99 2016 by the STAR detector. Charged-particle tracks were
Ξ
Ξ Λ Ξ
Λ
Ξ.
137 Λ → pπ3sured, and
1
a
spin
1/2
hyperonisdescribed
bythe
Lee-Yang−
80 71 cay of C
=
(2
×
0.89
+
1)
=
+0.927.
(5)
100 measured in the time projection chamber (TPC) [18],ΞΛ81
138 indicate
s at most, 78 Using the3measured value for the γΞ− parameter [13, 14],
Parentparticlepolarizationcanbestudiedbymeasuringdaughterparticlepolarization!
101
which
coversthefullazimuthandapseudorapidity
range 139 cays [26−
72 formula
intransfer
terms
of theforthreeα (parity
79 the[11–13]
polarizationcoeﬃcientΞ to Λparameters
decay is:102 of |η| < 1. The collision vertices were reconstructed usingents of the
140 daughter
1
22
73Niida,violatingpart),
the time reversal
symme80 ResearchCΞ−β=(violation
× 0.89= +0.927.
(5)
T.
TCHoU
MemberMeeting
Fall + 1)ofΛ
103 the measured charged-particle tracks and were required
3 (22020
81
hyperons,
sha1_base64="AL7wa3OoMc3SpqicK7MKJ5pBoHM=">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</latexit>

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asfirst ob-rest
55 directly
depends onpolarization:
60 parent
frame denotedbythe
anhyperonasterisk.
56 particles [10]. In parity-violating weak decays the daugh−am energy61
Ξ− (Ξ̄+ ) hyperon decay
happensintwo
steps:
Ξ→1dN∗∗(1 +inαHthe
56=
PH · p̂rest) , frame(2)of the hyperon,62 to57 betterter
distribution− particle−−
B∗Λ+π with subsequent dΩdecay 4π
Λ → p+π . If Ξ is polare 200 GeV
∗
63 58
ized,
its
polarizationispartiallytransferredtodaughterdirectlydependsonthehyperonpolarization:
57 whereαisthehyperondecay
parameter,P
H
H is them, the po∗
64 Λ. Both steps
in
such
a
cascadedecay
violat58 hyperon
polarization,andp̂
theparity
unit vector
in theB isarened by the
59 directionof thedaughterbaryonmomentum,both in the65
and thus
can beusedforanindependentmeasureheing,
nonreldN
1∗∗−+
60 parent rest frame denotedbyanasterisk.
66
mentof the polarization
of
Ξ
(
Ξ̄
).
e 59
T is theThe (2)polarization of the daughter baryon in a two par82
(1
+
α
=
P
·
p̂
)
,
H
−
+
−
H
B
∗
61
Ξ
(
Ξ̄
)
hyperondecay
happensintwo
steps:
Ξ
→
dΩ
4π
es
is
given
67
The polarizationof the daughter baryon in −a weak− de83 ticle decay of spin 3/2 hyperon, Ω → Λ + K, is also−
62 Λ+πwith subsequent decay Λ → p+π . If Ξ is polar84 described by three parameters αΩ , βΩ , and γΩ [15]. The
68 cay of a spin 1/2 hyperon is described by the Lee-Yang
63 ized,its polarization
is partiallytransferredto daughter
Gettingdifficult due
to smaller
decayparameter for85∗Ξdecay
and parameter
Ω…
α,determines
theangulardistribution
where
α
is
the
hyperondecay
parameter,
P
is
the
69 60
formula[11–13]
in
terms
of
the
three
parametersα(parityΩH
64 Λ. Both steps in such a cascade decay are parity violatH(1) part), β↵⇤= 0.732,↵the= anreversal
0.401,↵symme= 0.0157
86 of Λ in the Ω rest frame and is measured to be small [14]:∗⌅ for⌦ measure70 violating 65(violation
of
time
ing,
and
thus
can
be
used
independent
61 hyperon polarization, and p̂
is
the
unit
vector
in
the
B
2
2
−
+
87 αΩ = 0.0157±0.0021; this makes the Ω polarization mea71 try), and 66γ(satisfying
α
+
β
+
γ
=
1).
For
a
particular
ment
of
the
polarization
of
Ξ
(
Ξ̄
).
mean
spin
62 directionofthedaughterbaryonmomentum,
both
in
the
88 surement
via analysis of the daughter Λ angular distribuThepolarizationofthedaughterbaryoninaweak
de72 case of Ξ 67
→
Λ
+
π
decay
it
reads:of the fluid
spin68 1/2
spin
3/2
89
tion
practically
impossible.
The
polarizationtransfer
in
cay
of
a
spin
1/2
hyperonisdescribed
bythe
Lee-Yangparentrest
frame
denoted∗∗∗∗∗ by an∗ asterisk.
∗∗
m63volume
(α
+
P
·
p̂
)
p̂
+
β
P
×
p̂
+
γ
×
(P
×
p̂
p̂
Ξ69 formulaΞ Ξof theΛthree Ξ∗Ξ [11–13]
Λ Λ in termsΛΞα (parity
Λ)parameters
90 this caseis determinedby theγΩ parameterfrom
via [15–17]:
Similarly,
daughterΛ polarization
Ω:PΛ =Polarizatione direction−+ of daughter Λ ∗in a ∗weak decay of Ξ: ,−64
Ξ 70 (violatingΞ̄ ) hyperon
happens in two steps: Ξ → ∗part), β1(violation+ αdecay· p̂theΞ PΞ ofΛ time reversal symme∗∗
12
2(basedon
Lee-Yangformula)
−
91
P
=
C
P
=
(1
+
4γ
)
P
(6)
Ω
Ω Λ Ω
Λ
Ω.
71 try), and γ (satisfying α + β + γ = 1). For a particular
−
−
−
5
73
(3)
as 65
antiparΛ+π∗ 72T.D.
withsubsequent
decay
Λ
→
p+π
.
If
Ξ
is
polarLee
and
C.N.
Yang,
Phys.
Rev.108.1645(1957)
case
of
Ξ
→
Λ
+
π
decay
it
reads:
74
where
p̂
is
the
unit
vectoroftheΛ
momentumin thee polariza-

Ξ and Ω polarization measurements

Λ

92

×10

3

2000

1500

STAR

20%

year2

1000

3

500

Ξ global polarizations at √sNN = 200 GeV and 27 GeV
PH [%]TN (STAR), RHIC&AGS AUM2020
3PΛ (7.7)=7.34± 3.02 [%]STAR Preliminary STAR Au+Au 20%-50%
Nature548.62 (2017)
ΛΛ
PRC76.024915 (2007)
ΛΛ
PRC98.014910 (2018)
ΛΛ

2

ALICE Pb+Pb 15-50%
PRC101.044611 (2020)ΛΛ

1STAR Au+Au
20%-80%+Ξ + Ξ (via daughter Λ )+Ξ +Ξ

- less sensitive due to smaller αΞ=-0.4 than αΛ=0.732

Ξ PH via daughter Λ PH (by granddaughter proton)with the polarization transfer CΞΛ=+0.927- positive polarization with 2.2σ level- slightly larger than inclusive Λ PH
- close to AMPT prediction
W.-T. Deng and X.-G. Huang, PRC93.064907 (2016)(20-50% for 27 GeV)

0
AMPT PRC99, 014905 (2019)
Λ +Λ

−1

Ξ PH by analyzing daughter Λ distributions0ΞαΛ = 0.732 ± 0.014
α = -0.758 ± 0.012ΛαΞ- = -αΞ+ = -0.401 ± 0.010
γ =1
Ω

10

2

10

3

10

sNN [GeV]* published results are rescaled by αold/αnew~0.87
T. Niida, TCHoU Research Member Meeting 2020 Fall23Ξ global polarizations at √sNN = 200 GeV and 27 GeV
PH [%]TN (STAR), RHIC&AGS AUM2020
3PΛ (7.7)=7.34± 3.02 [%]STAR Preliminary STAR Au+Au 20%-50%
Nature548.62 (2017)
ΛΛ
PRC76.024915 (2007)
ΛΛ
PRC98.014910 (2018)
ΛΛ

2

ALICE Pb+Pb 15-50%
PRC101.044611 (2020)ΛΛ

1STAR Au+Au
20%-80%+Ξ + Ξ (via daughter Λ )+Ξ +Ξ

- less sensitive due to smaller αΞ=-0.4 than αΛ=0.732

Ξ PH via daughter Λ PH (by granddaughter proton)with the polarization transfer CΞΛ=+0.927- positive polarization with 2.2σ level- slightly larger than inclusive Λ PH
- close to AMPT prediction
W.-T. Deng and X.-G. Huang, PRC93.064907 (2016)(20-50% for 27 GeV)

0
AMPT PRC99, 014905 (2019)
Λ +Λ

−1

Ξ PH by analyzing daughter Λ distributions0ΞαΛ = 0.732 ± 0.014
α = -0.758 ± 0.012ΛαΞ- = -αΞ+ = -0.401 ± 0.010
γ =1
Ω

10

2

10

3

10

Lighter particles could be more polarized (Ξ<Λ)- Earlier freeze-out (of multi-strangeness)leads to larger PH (Ξ>Λ)-

sNN [GeV]* published results are rescaled by αold/αnew~0.87
T. Niida, TCHoU Research Member Meeting 2020 Fall

Naive expectations in Ξ vs. Λ PH

O.Vitiuk, L.V.Bravina, and E.E.Zabrodin, PLB803(2020)135298-

Feed-down: ~15-20% reduction for primary Λ PH
23Ω global polarizations at √sNN = 200 GeV
PH [%]TN (STAR), RHIC&AGS AUM2020
3PΛ (7.7)=7.34± 3.02 [%]STAR Preliminary STAR Au+Au 20%-50%
Nature548.62 (2017)ΛΛΩ PH via daughter Λ PH assuming the polarizationtransfer CΩΛ=+1

PRC76.024915 (2007)
ΛΛ
PRC98.014910 (2018)
ΛΛ

2

ALICE Pb+Pb 15-50%
PRC101.044611 (2020)ΛΛ

1STAR Au+Au
20%-80%+Ξ + Ξ (via daughter Λ )+Ξ +Ξ+Ω + Ω (via daughter Λ )- Based on the vorticity picture, the data seems tofavor CΩΛ=+1 (γΩ=+1) rather than CΩΛ=-0.6 (γΩ=-1)* In other words, γΩ can be measured in HIC
assuming the global polarization(20-50% for 27 GeV)

0
AMPT PRC99, 014905 (2019)
0
Λ +Λ
Ξ
Ω

−1

- Large uncertainty, to be improved in future analysisαΛ = 0.732 ± 0.014
α = -0.758 ± 0.012ΛαΞ- = -αΞ+ = -0.401 ± 0.010
γ =1- Also close to AMPT expectation

Ω

10

2

10

3

10

sNN [GeV]* published results are rescaled by αold/αnew~0.87
T. Niida, TCHoU Research Member Meeting 2020 Fall

24

OutlookMore precise/differential measurements will be done in the following years
High statistics data of BES-II 7.7-19.6 GeV and FXT 3-7.7 GeV
Isobaric collision data (Ru+Ru, Zr+Zr), ~10% difference in B-field
Quantifying CME
IsoBaric CollisionsAu+Au
at RHIC
Forward detectors
ininRun-2023
200 GeV

BUR2020, STAR Note SN0755

44 Ruthenium

Ru

Same Baryon #Different Proton #2

Zirconium

96
40

Zirconium

SimilarW.-T.
Bulk BackgroundDeng, X.-G. Huang,
Different
CME!Ma, & G. Wang,
G.-L.

1

0

96
40

Zr

PRC2016
10

20

30

40

50

Centrality (%)

Similar Bulk BackgroundT. Niida,Different
TCHoUCME!
Research Member Meeting 2020 Fall

60

70

Λ , geometric model
Λ0, PICR hydroΞ - , AMPT
Ω , AMPT

Ru

15
10

Projection (run2023)
Λ +Λ +
Ξ -+Ξ +
Ω +Ω

1

20

PH [%]

eB/mπ296
sobaric Collisions
96
40 Zirconium
44 Ruthenium

325

104 ×(HSS-HOS )4STAR Au+Au s NN = 200 GeV
20-60% (40-80% for 2.5<η<4)

Zr

Data
Λ
Λ

0.5

FTS

5
0

ρ

Test
of
CME
—
Isobaric
Collisions@
RHIC
Crucial96 Test of CME — Isobaric Collisions

Shuzhe Shi

Shuzhe Shi

Shuzhe Shi

PH [%]

Quantifying CME in IsoBaric Collisions at RHIC

lisions at RHIC#

Electrom
select an
2023-20of errorallocate
What isthe prothat, wiestablish
K 0 is a

10

20

30

40

0

50

60

70

Centrality (%)
iTPC
0

η

2

4

η

25

Summary
Global and local polarization of hyperons has been observed in heavy-ion
collisions
Most vortical ﬂuid (ω~1021 s-1) created in heavy-ion collisions
Energy dependence of global polarization, increasing in lower sNN, is captured well bytheoretical models, but there are sign problems to be understood
Toward more diﬀerential/precise measurements, e.g. ﬁrst measurements of Ξ and Ω

There are still many open questions and more precise measurements are needed
for better understanding the nature of vorticity and polarization in HIC.

T. Niida, TCHoU Research Member Meeting 2020 Fall26

ご興味があれば…
高速回転する流体――クォーク・グルーオン・プラズマの渦度
新井田貴文〈Department of Physics and Astronomy, Wayne State University

江角晋一〈筑波大学数理物質系，宇宙史研究センター

niida＠bnl.gov〉

esumi.shinichi.gn＠u.tsukuba.ac.jp〉

ビ ッ グ バ ン 数 マ イ ク ロ 秒 後，宇 宙 はによる効果とは別に，衝突する原子核内にクォーク・グルーオン・プラズマ（QGP）

含まれる陽子の電荷の移動により，反応平と呼ばれる物質で満たされていたと考えら

面に垂直な方向に強磁場が発生する可能性れる．物質の基本構成要素であるクォークが指摘されている．磁場によるスピン偏極は通常核子などのハドロンに閉じ込められの場合，磁気モーメントの符号の違いによているが，量子色力学（QCD）によると，り，単純な軌道角運動量の効果とは違い，

高温または高密度下ではその閉じ込めから

粒子と反粒子間では偏極方向は反対になる．

解放され，クォークとグルーオンのプラズ

強磁場が存在すると，QCD の非自明な真マ状態になる．QGP の性質やハドロンか空構造から，強い相互作用の持つ基本的ならの相転移機構は十分には理解されておら対称性の一つであるカイラル対称性に関すず，これらを解明するためのアプローチがる様々な新しい現象が誘起されると予測さ高エネルギー原子核衝突実験である．

れており，興味深い研究対象である．

現在，米国 BNL 国立研究所やスイスと粒 子 の ス ピ ン 測 定 は，ハ イ ペ ロ ン（sフランス国境にある欧州原子核研究機構にクォークを含むバリオン）の崩壊を利用す

おいて，巨大加速器を用いて光速近くまでることで可能である．ハイペロンはバリオ

加速した原子核同士を衝突させる実験が行

ンと中間子等へ崩壊するが，弱い相互作用

われている．衝突により作り出される物質による崩壊ではパリティが保存せず，崩壊の温度は数兆度（太陽中心温度の数十万倍

バリオンの運動量ベクトルとハイペロンの高い）に達し，エネルギー密度は QGP 生

スピンに相関があることが知られている．

成に必要な密度の 5 倍以上であることが測

BNL-STAR 実験では，金原子核衝突デー

定からわかっている．これまでの実験結果

タを用いて，ラムダ粒子のスピン偏極測定と理論計算との比較により，QGP の粘性（正確にはエントロピー密度で割った粘性を行った．核子対あたりの衝突エネルギーsNN ＝7.7‒200 GeV においてラムダ粒子の比）は非常に小さく，気体というより完全

スピン偏極が初めて測定された．この結果流体に近いことが判明している．

は衝突で作られた物質が回転していること

原子核衝突により生成される QGP は回を実験的に示す証拠である．局所的熱平衡

転していると理論的に予測されてきたが，の仮定のもとで，スピン偏極から渦度を計

実験的証拠はこれまでにない．QGP が回算すると ω〜1022 s−1 となった．この値は転している場合，これまでの実験結果の解

大きさのスケールは違うものの，これまで釈に影響を及ぼす可能性もあり，また原子に観測されたどの渦度よりも速いことが判

核衝突のモデル，特に初期条件を決める上明した．また，ラムダ粒子と反ラムダ粒子でも重要な要素となる．QGP が回転しては，実験誤差の範囲で有意な差は無いが，いるという描像は，衝突する 2 つの原子核

系統的に反ラムダ粒子のシグナルが大きい

が反対方向へ移動するために，衝突関与部

ように見える．これは初期の磁場による偏が角運動量保存のために回転を続けようと極の可能性を示している．STAR 実験は，することからくる．この軌道角運動量は，

今年からビーム走査実験 II を開始しており，反応平面に垂直な方向を指す．衝突で作りアップグレードされた検出器で高統計デー

出される物質が軌道角運動量を持つと，ス
ピン ‒ 軌道相互作用によって生成粒子のスタを収集し，スピン偏極の詳細測定および―Keywords―
中心衝突度：
原子核衝突を特徴づける量．
2 つの原子核が正面衝突する
場合を中心衝突，2 つの原子核中心がずれて衝突する場合
を非中心衝突と呼ぶ．
反応平面：
原子核進行方向と 2 つの原子核中心を結ぶベクトルで成す
平面．下図における破線で表される面．

2 つの原子核が非中心衝突したときに作られる磁場 B と軌
道角運動量 L の向きを示す図．

日本物理学会誌 2019 10月号
高速回転する流体- クォーク・グルーオン・プラズマの渦度 -磁場効果の検証を行う予定である．

ピンが偏極すると予測される．また，回転最近の研究から

T. Niida, TCHoU Research Member Meeting 2020 Fall

高速回転する流体727©2019 日本物理学会

27

Back upT. Niida, TCHoU Research Member Meeting 2020 Fall

28

C a simple rational number in all cases where the conser(38)f⇤R C⇤R 13 f⌃0 R C⌃0 R SR PR
P⇤meas = 2
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
mayfrom measurement
as: of Λ originating from parent R
to a ⇤. In ⇤the eq.( 37),⇤f⇤R (f⌃0 R ) is the fractionµ
S(S +of1) be extractedfΛR : 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
1
2
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
Primary Λ polarization
will bedilutedby 15%-20%
into1/2measured
imental measurementsof theglobal polarizationof hy−→ 1/2+ 0− ⇤s. The polarization1 transfer is the same
Parity conserving:
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:= µR ).
netic
moment has opposite sign (µ−1/5
19.6 GeV THERMUS feed-down probabilities. Let us asR+0.900(0 → " + π 0
This
also
that
thevorticity
polarizationof daughter
particles
sume that thethermalis $ = 0.1 andthe magAccording
tothe
THERMUSmodel [42],tuned
to suggests−−p+0.927( →"+πnetictofield
is B = 0. In thethis case,according to eq.of(15),
theparent! e.g. Ξ, Ω
atcansNN
be=usedmeasurepolarizationits−1/3& 0 → " + γ reproduce semi-central Au+Au collisions
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 feed29
T. Niida, TCHoU
Research
MemberMeeting
2020
Fall
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.

¯ (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 ¯thebackground
distribution obtained
P30
different
assumptions.
H =T. Niida, 2014
TCHoU
Research
MemberMeeting
2020
Fall
peak
inbackgroundthe normalized
dE/dx
distribution.
and ! with 0.5 < pT < 6 GeV/c and |η| < two
1 wereanalyzed
Bg

⇤!p+⇡

↵

=

↵