Global polarization in heavy ion
collisions
Sergei A. Voloshin

T H E I N T E R N AT I O N A L W E E K LY J O U R N A L O F S C I E N C EFirst observationof fluid vortices
formed by heavyion collisions
PAGES 34 & 62

SUBATOMIC SWIRLS
CLIMATE CHANGEBOOKSSTEM CELLSPARISAGREEMENT

SUMMER
SELECTIONYOUTHFULSECRETSTime for nations to matchwords with deeds

page 1

PAGE 25

Recommended reading forthe holiday season
PAGE 28

NATURE.COM/NATURE
3 August 2017Vol. 548, No. 7665

How the hypothalamus helps
to control the ageing process
PAGE 52

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

S.A. VoloshinGlobal polarization in heavy ion
collisions
Sergei A. Voloshin

T H E I N T E R N AT I O N A L W E E K LY J O U R N A L O F S C I E N C EFirst observationof fluid vortices
formed by heavyion collisions
PAGES 34 & 62

SUBATOMIC SWIRLS
CLIMATE CHANGEBOOKSSTEM CELLSPARISAGREEMENT

SUMMER
SELECTIONYOUTHFULSECRETSTime for nations to matchwords with deeds

page 1

PAGE 25

Recommended reading forthe holiday season
PAGE 28

Outline (“Towards the systematic
study of vorticity in HIC”):✦ Vorticity and global polarization✦ Global polarization / spinalignment — how to measure✦ Experimental results. Older andnewer.
✦ “Local” vorticity field:• phi, pT dependence…
• (vorticity)Z and anisotropic flow
✦ Global polarization and chiralanomalous effects

NATURE.COM/NATURE
3 August 2017Vol. 548, No. 7665

How the hypothalamus helps
to control the ageing process
PAGE 52

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

S.A. VoloshinTitle: Globally Polarized
Quark-gluon
Plasma in Non-central A+A
Globalpolarization
Nuclear Theory
Collisions[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 of(Submitted on 18 Oct 2004 (v1), last revised 7 Dec 2005 (this version, v5))

Title: Polarized secondary particles in unpolarized high energy hadrona few tens of percent!
hadroncollisions?
Abstract:
Produced partons
have large local relative orbital angular momentum along the direction opposite to the reaction plane in the early stage
Nuclear
Theory[nucl-th/0410089]
Polarizedcollisions.
secondaryParton
particles
in unpolarizedenergyhadron-hadro...
of non-central heavy-ion
scattering
is shown tohighpolarize
quarksalong the same direction due to spin-orbital coupling. Such glob

Authors:
A. VoloshinquarkSergei
polarization
will lead to many observable consequences, such as left-right asymmetry of hadron spectra, global transverse polarization of(Submitted
21 Oct dileptons
2004) and hadrons. Hadrons from the decay of polarized resonances will have azimuthal
thermalon
photons,
asymmetry similar to the elliptic flo
xGlobal hyperon polarization is predicted within different hadronization scenarios and can be easily tested.
0+ In this shortnote
I1speculateon=
someconsequences of the high energy collision picture in which the orbital angular momentum of the
s
=
!
l
1
⇢ !Abstract:⇡⇡yycolliding 4hadrons
canbe converted
into secondary
particleangularmomentumsome spin-orbital
Comments:
pages in
RevTexwith 2 postscript
figures,
an erratumis spin
added
to the finalvia
publishedversion interaction. In particular I discuss apossibility to observe a non-zero polarization of secondary particles (e.g. hyperons) at midrapidity (xF = 0) and at low transverse momentum.
Subjects: also speculate
Nuclear(nucl-th);
EnergytoPhysics- Phenomenology(hep-ph)thatTheory
such effects
couldHigh
contributethe produced
particle directed
and elliptic flow observed in relativistic nuclear collisions.
Journal reference:
Erratum-ibid.Lett.96:039901,2006
Authors:Phys.Rev.Lett.94:102301,2005;
Zuo-Tang Liang (Shandong U),
Xin-Nian Wang (LBNL)(Submittedon
18 Oct 2004 (v1), last revised 7 Dec 2005 (this version, v5))
Comments:
2 pages,
Latex
DOI:
10.1103/PhysRevLett.94.102301
z+ number:Nuclear(nucl-th) ! s = 1
Report
LBNL-56383
lProduced⇡Subjects:⇡!Abstract:⇢0 Theoryy = 1 partonsyhave large local relative orbital angular momentum along the direction opposite to the reaction pl
Cite
arXiv:nucl-th/0410089
Cite
as:as:
arXiv:nucl-th/0410079
ofnon-central heavy-ionfor
collisions.
Parton scattering is shown to polarize quarks along the same direction due to spin-orbital(or arXiv:nucl-th/0410089v1
thisversion)(or arXiv:nucl-th/0410079v5
for thisversion)⇠ 10 fm

Title: Globally Polarized Quark-gluon Plasma in Non-central
Nuclear Theory
Collisions

Title: Polarized secondary particles in unpolarized high en
hadron collisions?

quarkSergei
polarization
will lead to many observable consequences, such as left-right asymmetry of hadron spectra, global transve
Authors:
A. Voloshin
thermal on
photons,(Submitted
21 Octdileptons
2004) and hadrons. Hadrons from the decay of polarized resonances will have azimuthal asymmetry sim

Submission
history
Globalhyperon polarization is predicted within different hadronization scenarios and can be easily tested.
Submission
history

Abstract: In this short note I speculate on some consequences of the high energy collision picture in which the orbit

From:
SergeiA.
Voloshinemail]From:
Xin-Nian
Wang[view [viewemail]
Comments:
4hadrons
pages
incan
RevTexwith 2 postscript
figures, anerratum
is added
to momentum
the final publishedversioncollidingbe converted
into secondary
particleangularspin
via some
spin-orbital interaction
[v1]
Thu,
21
Oct
2004
19:43:03
GMT(3kb)[v1] Mon, 18Oct2004
18:54:46
GMT(34kb)
Subjects:
Nuclear
Theory non-zero(nucl-th);High(What
EnergyPhysics- Phenomenology(hep-ph)possibility
toobservepolarization
secondaryparticles (e.g.
hyperons) at midrapidity (xF = 0) and atWhichauthorsof thispaper areendorsers?
MathJax
is of
MathJax?)[v2]
Fri, 22
Oct 2004
02:25:19
GMT(34kb) | aDisable
Journalreference:Phys.Rev.Lett.94:102301,2005;
Erratum-ibid.Lett.96:039901,2006
also
speculatesuch effects could contributeto the produced particle directed and elliptic flow observed in relati[v3] Mon, 25
Oct 2004
18:35:22
GMTthat(34kb)
Link
to: arXiv,form interface,contact.
[v4]
Tue,back
26DOI:
Apr
2005 18:42:39
GMT (37kb)
10.1103/PhysRevLett.94.102301[v5] Wed, 7 Dec
2005 02:02:09
GMT Latex(37kb)
Comments:
2
pages,
Reportnumber:
LBNL-56383
Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)

Subjects:
Cite
as:

Nuclear
Theory (nucl-th)
arXiv:nucl-th/0410079
Link back to: arXiv, form interface, contact.
Cite as:arXiv:nucl-th/0410089(or arXiv:nucl-th/0410079v5 for this version)(or arXiv:nucl-th/0410089v1 for this version)

Submission history

Submission
history
From: Xin-Nian Wang [view email]TsukubaGlobalScience Week, Tsukuba, Japan, September 28, 2017
page [v1]2 Mon, 18 Oct 2004 18:54:46
GMT(34kb)

S.A. VoloshinTitle: Globally Polarized
Quark-gluon
Plasma in Non-central A+A
Globalpolarization
Nuclear Theory
Collisions[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 of(Submitted on 18 Oct 2004 (v1), last revised 7 Dec 2005 (this version, v5))

Title: Polarized secondary particles in unpolarized high energy hadrona few tens of percent!
hadroncollisions?
Abstract:
Produced partons
have large local relative orbital angular momentum along the direction opposite to the reaction plane in the early stage
Nuclear
Theory[nucl-th/0410089]
Polarizedcollisions.
secondaryParton
particles
in unpolarizedenergyhadron-hadro...
of non-central heavy-ion
scattering
is shown tohighpolarize
quarksalong the same direction due to spin-orbital coupling. Such glob

Authors:
A. VoloshinquarkSergei
polarization
will lead to many observable consequences, such as left-right asymmetry of hadron spectra, global transverse polarization of(Submitted
21 Oct dileptons
2004) and hadrons. Hadrons from the decay of polarized resonances will have azimuthal
thermalon
photons,
asymmetry similar to the elliptic flo
xGlobal hyperon polarization is predicted within different hadronization scenarios and can be easily tested.
0+ In this shortnote
I1speculateon=
someconsequences of the high energy collision picture in which the orbital angular momentum of the
s
=
!
l
1
⇢ !Abstract:⇡⇡yycolliding 4hadrons
canbe converted
into secondary
particleangularmomentumsome spin-orbital
Comments:
pages in
RevTexwith 2 postscript
figures,
an erratumis spin
added
to the finalvia
publishedversion interaction. In particular I discuss apossibility to observe a non-zero polarization of secondary particles (e.g. hyperons) at midrapidity (xF = 0) and at low transverse momentum.
Subjects: also speculate
Nuclear(nucl-th);
EnergytoPhysics- Phenomenology(hep-ph)thatTheory
such effects
couldHigh
contributethe produced
particle directed
and elliptic flow observed in relativistic nuclear collisions.
Journal reference:
Erratum-ibid.Lett.96:039901,2006
Authors:Phys.Rev.Lett.94:102301,2005;
Zuo-Tang Liang (Shandong U),
Xin-Nian Wang (LBNL)(Submittedon
18 Oct 2004 (v1), last revised 7 Dec 2005 (this version, v5))
Comments:
2 pages,
Latex
DOI:
10.1103/PhysRevLett.94.102301
z+ number:Nuclear(nucl-th) ! s = 1
Report
LBNL-56383
lProduced⇡Subjects:⇡!Abstract:⇢0 Theoryy = 1 partonsyhave large local relative orbital angular momentum along the direction opposite to the reaction pl
Cite
arXiv:nucl-th/0410089
Cite
as:as:
arXiv:nucl-th/0410079
ofnon-central heavy-ionfor
collisions.
Parton scattering is shown to polarize quarks along the same direction due to spin-orbital(or arXiv:nucl-th/0410089v1
thisversion)(or arXiv:nucl-th/0410079v5
for thisversion)⇠ 10 fm

Title: Globally Polarized Quark-gluon Plasma in Non-central
Nuclear Theory
Collisions

Title: Polarized secondary particles in unpolarized high en
hadron collisions?

quarkSergei
polarization
will lead to many observable consequences, such as left-right asymmetry of hadron spectra, global transve
A. Voloshin
1 @vzand hadrons. Hadrons from the decay of polarized resonances will have azimuthal asymmetry sim
1Authors:
thermalphotons,
dileptons⇡! = 2(Submittedr ⇥history
v on 21 Oct 2004)
2 @x is predicted within different hadronization scenarios and can be easily tested.
Submission
hyperon polarization
Submission Global
history
Abstract: In this short note I speculate on some consequences of the high energy collision picture in which the orbit
From:
SergeiA.
Voloshinemail]
From: Xin-Nian
Wangcolliding[view [viewemail]
Comments:
4hadrons
pages
incan
RevTexwith 2 postscript
figures, anerratum
is added
to momentum
the final publishedversionbe converted
into secondary
particleangularspin
via some
spin-orbital interaction
[v1]
Thu,
21
Oct
2004
19:43:03
GMT(3kb)[v1] Mon, 18Oct2004
18:54:46
GMT(34kb)
!/T
⇠
up
to
a
few percent
Guess:v (What⇠
0.2,
x -⇠Phenomenology
5particles
fm ) (e.g.(hep-ph)Subjects:
Nuclear
Theory(nucl-th);High
EnergyPhysics
possibility
toobserveanon-zeropolarizationofsecondaryhyperons)at
midrapidity(xF = 0) and atWhichauthors
of
this
paper
are
endorsers?
|
DisableMathJax
is
MathJax?)[v2] Fri, 22 Oct 2004 02:25:19 GMT (34kb)
Journalreference:Phys.Rev.Lett.94:102301,2005;
Erratum-ibid.Lett.96:039901,2006
also
speculatesuch effects could contributeto the produced particle directed and elliptic flow observed in relati[v3] Mon, 25
Oct 2004
18:35:22
GMTthat(34kb)
Link
to: arXiv,form interface,contact.
[v4]
Tue,back
26DOI:
Apr
2005 18:42:39
GMT (37kb)
10.1103/PhysRevLett.94.102301[v5] Wed, 7 Dec
2005 02:02:09
GMT Latex(37kb)
Comments:
2
pages,
Reportnumber:
LBNL-56383
Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)
Subjects:
Nuclear
Theory (nucl-th)
Cite
as:arXiv:nucl-th/0410079
Link back to: arXiv, form interface, contact.
Cite as:arXiv:nucl-th/0410089(or arXiv:nucl-th/0410079v5 for this version)(or arXiv:nucl-th/0410089v1 for this version)

Submission history

Submission
history
From: Xin-Nian Wang [view email]TsukubaGlobalScience Week, Tsukuba, Japan, September 28, 2017
page [v1]2 Mon, 18 Oct 2004 18:54:46
GMT(34kb)

S.A. VoloshinTitle: Globally Polarized
Quark-gluon
Plasma in Non-central A+A
Globalpolarization
Nuclear Theory
Collisions[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 of(Submitted on 18 Oct 2004 (v1), last revised 7 Dec 2005 (this version, v5))

Title: Polarized secondary particles in unpolarized high energy hadrona few tens of percent!
hadroncollisions?
Abstract:
Produced partons
have large local relative orbital angular momentum along the direction opposite to the reaction plane in the early stage
Nuclear
Theory[nucl-th/0410089]
Polarizedcollisions.
secondaryParton
particles
in unpolarizedenergyhadron-hadro...
of non-central heavy-ion
scattering
is shown tohighpolarize
quarksalong the same direction due to spin-orbital coupling. Such glob

Authors:
A. VoloshinquarkSergei
polarization
will lead to many observable consequences, such as left-right asymmetry of hadron spectra, global transverse polarization of(Submitted
21 Oct dileptons
2004) and hadrons. Hadrons from the decay of polarized resonances will have azimuthal
thermalon
photons,
asymmetry similar to the elliptic flo
xGlobal hyperon polarization is predicted within different hadronization scenarios and can be easily tested.
0+ In this shortnote
I1speculateon=
someconsequences of the high energy collision picture in which the orbital angular momentum of the
s
=
!
l
1
⇢ !Abstract:⇡⇡yycolliding 4hadrons
canbe converted
into secondary
particleangularmomentumsome spin-orbital
Comments:
pages in
RevTexwith 2 postscript
figures,
an erratumis spin
added
to the finalvia
publishedversion interaction. In particular I discuss apossibility to observe a non-zero polarization of secondary particles (e.g. hyperons) at midrapidity (xF = 0) and at low transverse momentum.
Subjects: also speculate
Nuclear(nucl-th);
EnergytoPhysics- Phenomenology(hep-ph)thatTheory
such effects
couldHigh
contributethe produced
particle directed
and elliptic flow observed in relativistic nuclear collisions.
Journal reference:
Erratum-ibid.Lett.96:039901,2006
Authors:Phys.Rev.Lett.94:102301,2005;
Zuo-Tang Liang (Shandong U),
Xin-Nian Wang (LBNL)(Submittedon
18 Oct 2004 (v1), last revised 7 Dec 2005 (this version, v5))
Comments:
2 pages,
Latex
DOI:
10.1103/PhysRevLett.94.102301
z+ number:Nuclear(nucl-th) ! s = 1
Report
LBNL-56383
lProduced⇡Subjects:⇡!Abstract:⇢0 Theoryy = 1 partonsyhave large local relative orbital angular momentum along the direction opposite to the reaction pl
Cite
arXiv:nucl-th/0410089
Cite
as:as:
arXiv:nucl-th/0410079
ofnon-central heavy-ionfor
collisions.
Parton scattering is shown to polarize quarks along the same direction due to spin-orbital(or arXiv:nucl-th/0410089v1
thisversion)(or arXiv:nucl-th/0410079v5
for thisversion)⇠ 10 fm

Title: Globally Polarized Quark-gluon Plasma in Non-central
Nuclear Theory
Collisions

Title: Polarized secondary particles in unpolarized high en
hadron collisions?

quarkSergei
polarization
will lead to many observable consequences, such as left-right asymmetry of hadron spectra, global transve
A. Voloshin
1 @vzand hadrons. Hadrons from the decay of polarized resonances will have azimuthal asymmetry sim
1Authors:
thermalphotons,
dileptons⇡! = 2(Submittedr ⇥history
v on 21 Oct 2004)
2 @x is predicted within different hadronization scenarios and can be easily tested.
Submission
hyperon polarization
Submission Global
history
Abstract: In this short note I speculate on some consequences of the high energy collision picture in which the orbit
From:
SergeiA.
Voloshinemail]
From: Xin-Nian
Wangcolliding[view [viewemail]
Comments:
4hadrons
pages
incan
RevTexwith 2 postscript
figures, anerratum
is added
to momentum
the final publishedversionbe converted
into secondary
particleangularspin
via some
spin-orbital interaction
[v1]
Thu,
21
Oct
2004
19:43:03
GMT(3kb)[v1] Mon, 18Oct2004
18:54:46
GMT(34kb)
!/T
⇠
up
to
a
few percent
Guess:v (What⇠
0.2,
x -⇠Phenomenology
5particles
fm ) (e.g.(hep-ph)Subjects:
Nuclear
Theory(nucl-th);High
EnergyPhysics
possibility
toobserveanon-zeropolarizationofsecondaryhyperons)at
midrapidity(xF = 0) and atWhichauthors
of
this
paper
are
endorsers?
|
DisableMathJax
is
MathJax?)[v2] Fri, 22 Oct 2004 02:25:19 GMT (34kb)
Journalreference:Phys.Rev.Lett.94:102301,2005;
Erratum-ibid.Lett.96:039901,2006
also
speculatesuch effects could contributeto the produced particle directed and elliptic flow observed in relati[v3] Mon, 25
Oct 2004
18:35:22
GMTthat(34kb)
Linkback
to: arXiv,form interface,contact.
[v4]
Tue,
26DOI:
Apr
2005 18:42:39
GMT (37kb)
10.1103/PhysRevLett.94.102301
Nonrelativistic
statisticalmechanics (NSM)[v5] Wed, 7 Dec
2005
02:02:09
GMT(37kb)
13
Comments:
2
pages,
Latex
Reportnumber:
LBNL-56383
Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)
S(S+1) !
Subjects:
Nuclear
Theory(nucl-th)p(T, µ
,
B,
!)
/
exp[(
E
+
µ
Q
+
µ
·
B
+
!
·
(S
+
L))/T
]
Cite
as:
arXiv:nucl-th/0410079
S ⇡ Particles,i[9] Z. T. Liangi andiX. N. Wang, “Globally polarized quarktional School on Elementary
Hercegnovi(Gor3
T
Link back to: arXiv, form interface, contact.
gluon plasma in non-central
don and Breach, New York, London, 1968).
Cite
as:arXiv:nucl-th/0410089(or arXiv:nucl-th/0410079v5
forA+A
this collisions,”
version) Phys. Rev.
Global hyperon polarization at local
thermodynamic
withRev.
vorticity,
Lett.
94, 102301 (2005)equilibrium
Erratum: [Phys.
Lett.
[28] L. D. Landau and E. M. Lifshits, Statistical Physics, 2nd96,039901
doi:10.1103/PhysRevLett.94.102301
Ed., Pergamon Press, 1969.
(ormagnetic
arXiv:nucl-th/0410089v1
for this version)field
and (2006)]
feed-down[nucl-th/0410079].
Submission
history[10]
S.
A.AnnanVoloshin,secondaryparticles
in unFrancesco Becattini, Iurii Karpenko, Michael
Lisa, “PolarizedIsaac Upsal,and Sergei
A. Voloshin[29] A. Vilenkin, “Quantum Field Theory At Finite Temperature In A Rotating System,” Phys. Rev. D 21, 2260
highenergyhadron-hadroncollisions?,”
nucl(1980). doi:10.1103/PhysRevD.21.2260
1Dipartimento di Fisica, Universita‘ di polarizedFirenze, and
INFN,
SezionediREVIEW
Firenze, C
Florence,
Italy(2017)
PHYSICAL
95,
0549022
th/0410089.
[30] F. Becattini and L. Tinti, Annals Phys. 325, 1566 (2010)
INFN, Sezione
di Firenze, Florence, Italy
From:email]
3 Xin-Nian Wang [viewI. Abelev
et al.Columbus,[STAR Collaboration],“Global polardoi:10.1016/j.aop.2010.03.007 [arXiv:0911.0864 [gr-qc]].
Physics Department, The [11]OhioB.
State
University,
Ohio 43210, USA
4
TsukubaGlobalScience
Week,
Tsukuba,
Japan,
September
28,
2017
izationmeasurement
in
Au+Au
collisions,”
Phys.
Rev.
[31]
R.
h.
Fang,
L. g. Pang,
Wang and X. n. Wang,
Wayne
State
University,
Detroit,
Michigan
48201,
USA
page [v1]2 Mon, 18 Oct
S.A.Q.Voloshin
2004hyperon
18:54:46polarization
GMT (34kb)at local thermodynamic equilibrium with
Globalvorticity,
12

Submission history

3

3

4

The most direct analogy to the HI case.
page 3

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

S.A. VoloshinGlobal polarization: how it is measured

How to quantify the e%ect (I)PRL 118, 012301 (2017)

PHYSICAL REVIEx[33] J. Adams et al. (STAR Collaboration), Directed flow inpﬃﬃﬃﬃﬃﬃﬃﬃ
Know
the direction
theAuþ Au collisions
at sNN ¼ 62.4of
GeV,
Phys. Rev. C 73,
034903(2006). momentum.
angular●[34] B. I. Abelev et al. (STAR Collaboration), System-Size
Independenceof Directed
Flow Measured
at the BNL
On average,
spectators
deflect
Relativistic Heavy Ion Collider, Phys. Rev. Lett. 101,
BBCs
“outwards”!
BBCs252301(2008).
●
Reveal polarization by[35] S. A. Voloshin and T. Niida, Ultrarelativistic nuclear collisions: Direction of spectator flow Phys. Rev. C 94, 021901
zpreferentially emitting(R) (2016).
Spinning[36] A. M. Poskanzer and S. A. Voloshin, Methods for analyzing
daughter proton in spin
anisotropic flow in relativistic nuclear collisions, Phys. Rev.
Lambdasdirection
C 58, 1671 (1998).
spectators[37] D. Teaney and L. Yan, Triangularity and dipole asymmetry
in relativistic heavy ion collisions, Phys. Rev. C 83, 064904(2011).
[38] M. Luzum and J. Y. Ollitrault, Directed Flow at Midrapidity*
in Heavy-Ion Collisions, Phys. Rev. Lett. 106, 102301
Weak,parityviolatingdecay“goldenchannel”**y(2011).
Λ*p*[39] B. Abelev et al. (ALICE Collaboration), Directed Flow of*Charged Particles at Midrapidity Relative to the Spectator ⇤ppﬃﬃﬃﬃﬃﬃﬃﬃ
Plane in Pb þ Pb Collisions
at sNN ¼H
2.76 H
TeV, Phys.
⇤
Rev. Lett. 111, 232302 (2013).
*[40] C. A. Whitten (STAR Collaboration), The beam-beampcounter: A local polarimeter⇤at STAR, AIP*¯ Conf. Proc.
⇤
980, 390 (2008).
π[41] C. E. Allgower et al. (STAR Collaboration), The STAR*
endcap electromagnetic calorimeter, Nucl. Instrum.
p
Methods Phys. Res., Sect. A 499, 740 (2003).
parity-violating decay[42] P. Bożek, Event-by-event viscous hydrodynamics forpﬃﬃﬃﬃﬃﬃﬃﬃ
Isaac Upsal – Feb. 2017
Cu-Au collisions at6 sNN ¼ 200 GeV, Phys. Lett. B 717,
daughter proton preferentially
287 (2012).

Lambdas are “selfanalyzing”

⃗S

θ

[4

[4

[4

[4

[4

⃗ follow the distribution:
Λ s with Polarization P
1 < P = hs i/s < 1dN
11⃗( 1+α P cos θ )=1+α P⋅p^ )=
(
[4
4π
dΩ 4π
dN / 1 + ↵ P cos ✓ [5
⇤
!
p
+
⇡
α=0.642±0.013 [measured]d cos ✓p^ is the daughter proton momentum direction in↵ = ↵ ⇡ 0.624 [5the Λ frame (note that this is opposite for Λ )
3
[5
⃗
⃗
|
|
0< P <1 : P= α p^⃗p⃗pdecays into the direction ofΛʼs spin (opposite for anti-Λ)y of fluid createdof daughter proton in Λ rest frame

angular event
momen-orderplane
page 4[4

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

S.A. Voloshin[5Global polarization: how it is measured

How to quantify the e%ect (I)PRL 118, 012301 (2017)

PHYSICAL REVIEx[33] J. Adams et al. (STAR Collaboration), Directed flow inpﬃﬃﬃﬃﬃﬃﬃﬃ
Know
the direction
theAuþ Au collisions
at sNN ¼ 62.4of
GeV,
Phys. Rev. C 73,
034903(2006). momentum.
angular●[34] B. I. Abelev et al. (STAR Collaboration), System-Size
Independenceof Directed
Flow Measured
at the BNL
On average,
spectators
deflect
Relativistic Heavy Ion Collider, Phys. Rev. Lett. 101,
BBCs
“outwards”!
BBCs252301(2008).
●
Reveal polarization by[35] S. A. Voloshin and T. Niida, Ultrarelativistic nuclear collisions: Direction of spectator flow Phys. Rev. C 94, 021901
zpreferentially emitting(R) (2016).
Spinning[36] A. M. Poskanzer and S. A. Voloshin, Methods for analyzing
daughter proton in spin
anisotropic flow in relativistic nuclear collisions, Phys. Rev.
Lambdasdirection
C 58, 1671 (1998).
spectators[37] D. Teaney and L. Yan, Triangularity and dipole asymmetry
in relativistic heavy ion collisions, Phys. Rev. C 83, 064904(2011).
[38] M. Luzum and J. Y. Ollitrault, Directed Flow at Midrapidity*
in Heavy-Ion Collisions, Phys. Rev. Lett. 106, 102301
Weak,parityviolatingdecay“goldenchannel”**y(2011).
Λ*p*[39] B. Abelev et al. (ALICE Collaboration), Directed Flow of*Charged Particles at Midrapidity Relative to the Spectator ⇤ppﬃﬃﬃﬃﬃﬃﬃﬃ
Plane in Pb þ Pb Collisions
at sNN ¼H
2.76 H
TeV, Phys.
H⇤
Rev. Lett. 111, 232302 (2013).
*[40] C. A. Whitten (STAR Collaboration), The beam-beampcounter: A local polarimeter⇤at STAR, AIP*¯ Conf. Proc.
⇤
980, 390 (2008).
π[41] C. E. Allgower et al. (STAR Collaboration), The STAR*
endcap electromagnetic calorimeter, Nucl. Instrum.
p
Methods Phys. Res., Sect. A 499, 740 (2003).
parity-violating decay[42] P. Bożek, Event-by-event viscous hydrodynamics forpﬃﬃﬃﬃﬃﬃﬃﬃ
Isaac Upsal – Feb. 2017
Cu-Au collisions at6 sNN ¼ 200 GeV, Phys. Lett. B 717,
daughter proton preferentially
287 (2012).

Lambdas are “selfanalyzing”

⃗S

θ

[4

[4

[4

[4

[4

⃗ follow the distribution:
Λ s with Polarization P
1 < P = hs i/s < 1dN
11⃗( 1+α P cos θ )=1+α P⋅p^ )=
(
[4
4π
dΩ 4π
!
dN / 1 + ↵ P cos ✓ [5
NSM:
P
⇡
⇤
!
p
+
⇡
α=0.642±0.013 [measured]2T
d cos ✓p^ is the daughter proton momentum direction in↵ = ↵ ⇡ 0.624 [5the Λ frame (note that this is opposite for Λ )
3
[5
⃗
⃗
|
|
0< P <1 : P= α p^⃗p⃗pdecays into the direction ofΛʼs spin (opposite for anti-Λ)y of fluid createdof daughter proton in Λ rest frame

angular event
momen-orderplane
page 4[4

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

S.A. Voloshin[5Global polarization: how it is measured

How to quantify the e%ect (I)PRL 118, 012301 (2017)

PHYSICAL REVIEx[33] J. Adams et al. (STAR Collaboration), Directed flow inpﬃﬃﬃﬃﬃﬃﬃﬃ
Know
the direction
theAuþ Au collisions
at sNN ¼ 62.4of
GeV,
Phys. Rev. C 73,
034903(2006). momentum.
angular●[34] B. I. Abelev et al. (STAR Collaboration), System-Size
Independenceof Directed
Flow Measured
at the BNL
On average,
spectators
deflect
Relativistic Heavy Ion Collider, Phys. Rev. Lett. 101,
BBCs
“outwards”!
BBCs252301(2008).
●
Reveal polarization by[35] S. A. Voloshin and T. Niida, Ultrarelativistic nuclear collisions: Direction of spectator flow Phys. Rev. C 94, 021901
zpreferentially emitting(R) (2016).
Spinning[36] A. M. Poskanzer and S. A. Voloshin, Methods for analyzing
daughter proton in spin
anisotropic flow in relativistic nuclear collisions, Phys. Rev.
Lambdasdirection
C 58, 1671 (1998).
spectators[37] D. Teaney and L. Yan, Triangularity and dipole asymmetry
in relativistic heavy ion collisions, Phys. Rev. C 83, 064904(2011).
[38] M. Luzum and J. Y. Ollitrault, Directed Flow at Midrapidity*
in Heavy-Ion Collisions, Phys. Rev. Lett. 106, 102301
Weak,parityviolatingdecay“goldenchannel”**y(2011).
Λ*p*[39] B. Abelev et al. (ALICE Collaboration), Directed Flow of*Charged Particles at Midrapidity Relative to the Spectator ⇤ppﬃﬃﬃﬃﬃﬃﬃﬃ
Plane in Pb þ Pb Collisions
at sNN ¼H
2.76 H
TeV, Phys.
H⇤
Rev. Lett. 111, 232302 (2013).
*[40] C. A. Whitten (STAR Collaboration), The beam-beampcounter: A local polarimeter⇤at STAR, AIP*¯ Conf. Proc.
⇤
980, 390 (2008).
π[41] C. E. Allgower et al. (STAR Collaboration), The STAR*
endcap electromagnetic calorimeter, Nucl. Instrum.
p
Methods Phys. Res., Sect. A 499, 740 (2003).
parity-violating decay[42]vector
P. Bożek,mesons
Event-by-event viscous hydrodynamics forStrong decays of s>1/2 particles, e.g.
pﬃﬃﬃﬃﬃﬃﬃﬃ
Isaac Upsal – Feb. 2017
Cu-Au collisions at6 sNN ¼ 200 GeV, Phys. Lett. B 717,
daughter proton preferentially
287 (2012).

Lambdas are “selfanalyzing”

⃗S

θ

⃗p

⇤0 direction of
decays into
Kthe
!⇡+K

Λʼs spin (opposite for anti-Λ)+y of fluid created

dN / (1d cos ✓⇤⇢00 ) + (3⇢00

1) cos2 ✓⇤2 ⇤dN / w |Y |2 + w |Y |2 + w |Y
2
2 ⇤
|
/
w
cos
✓
+
(w
+
w
)
sin
✓ /2
⇤
0
1,0
+1
1,1
1
1,
1
0
+1
1
of daughter
proton
in
Λ
rest
frame
d cos ✓
angular momen--order event plane
page 4

[4

[4

[4

[4

[4

⃗ follow the distribution:
Λ s with Polarization P
1 < P = hs i/s < 1dN
11⃗( 1+α P cos θ )=1+α P⋅p^ )=
(
[4
4π
dΩ 4π
!
dN / 1 + ↵ P cos ✓ [5
NSM:
P
⇡
⇤
!
p
+
⇡
α=0.642±0.013 [measured]2T
d cos ✓p^ is the daughter proton momentum direction in↵ = ↵ ⇡ 0.624 [5the Λ frame (note that this is opposite for Λ )
3
[5
⃗
⃗
|
|
0< P <1 : P= α p^

⃗p

!K +K

[4

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

S.A. Voloshin[5Global polarization: how it is measured

How to quantify the e%ect (I)PRL 118, 012301 (2017)

PHYSICAL REVIEx[33] J. Adams et al. (STAR Collaboration), Directed flow inpﬃﬃﬃﬃﬃﬃﬃﬃ
Know
the direction
theAuþ Au collisions
at sNN ¼ 62.4of
GeV,
Phys. Rev. C 73,
034903(2006). momentum.
angular●[34] B. I. Abelev et al. (STAR Collaboration), System-Size
Independenceof Directed
Flow Measured
at the BNL
On average,
spectators
deflect
Relativistic Heavy Ion Collider, Phys. Rev. Lett. 101,
BBCs
“outwards”!
BBCs252301(2008).
●
Reveal polarization by[35] S. A. Voloshin and T. Niida, Ultrarelativistic nuclear collisions: Direction of spectator flow Phys. Rev. C 94, 021901
zpreferentially emitting(R) (2016).
Spinning[36] A. M. Poskanzer and S. A. Voloshin, Methods for analyzing
daughter proton in spin
anisotropic flow in relativistic nuclear collisions, Phys. Rev.
Lambdasdirection
C 58, 1671 (1998).
spectators[37] D. Teaney and L. Yan, Triangularity and dipole asymmetry
in relativistic heavy ion collisions, Phys. Rev. C 83, 064904(2011).
[38] M. Luzum and J. Y. Ollitrault, Directed Flow at Midrapidity*
in Heavy-Ion Collisions, Phys. Rev. Lett. 106, 102301
Weak,parityviolatingdecay“goldenchannel”**y(2011).
Λ*p*[39] B. Abelev et al. (ALICE Collaboration), Directed Flow of*Charged Particles at Midrapidity Relative to the Spectator ⇤ppﬃﬃﬃﬃﬃﬃﬃﬃ
Plane in Pb þ Pb Collisions
at sNN ¼H
2.76 H
TeV, Phys.
H⇤
Rev. Lett. 111, 232302 (2013).
*[40] C. A. Whitten (STAR Collaboration), The beam-beampcounter: A local polarimeter⇤at STAR, AIP*¯ Conf. Proc.
⇤
980, 390 (2008).
π[41] C. E. Allgower et al. (STAR Collaboration), The STAR*
endcap electromagnetic calorimeter, Nucl. Instrum.
p
Methods Phys. Res., Sect. A 499, 740 (2003).
parity-violating decay[42]vector
P. Bożek,mesons
Event-by-event viscous hydrodynamics forStrong decays of s>1/2 particles, e.g.
pﬃﬃﬃﬃﬃﬃﬃﬃ
Isaac Upsal – Feb. 2017
Cu-Au collisions at6 sNN ¼ 200 GeV, Phys. Lett. B 717,
daughter proton preferentially
287 (2012).

Lambdas are “selfanalyzing”

⃗S

θ

⃗p

⇤0 direction of
decays into
Kthe
!⇡+K

Λʼs spin (opposite for anti-Λ)+y of fluid created

dN / (1d cos ✓⇤⇢00 ) + (3⇢00

1) cos2 ✓⇤NSM: ⇢00 ⇡1
3 + (!/T )22 ⇤dN / w |Y |2 + w |Y |2 + w |Y
2
2 ⇤
|
/
w
cos
✓
+
(w
+
w
)
sin
✓ /2
⇤
0
1,0
+1
1,1
1
1,
1
0
+1
1
of daughter
proton
in
Λ
rest
frame
d cos ✓
angular momen--order event plane
page 4

[4

[4

[4

[4

[4

⃗ follow the distribution:
Λ s with Polarization P
1 < P = hs i/s < 1dN
11⃗( 1+α P cos θ )=1+α P⋅p^ )=
(
[4
4π
dΩ 4π
!
dN / 1 + ↵ P cos ✓ [5
NSM:
P
⇡
⇤
!
p
+
⇡
α=0.642±0.013 [measured]2T
d cos ✓p^ is the daughter proton momentum direction in↵ = ↵ ⇡ 0.624 [5the Λ frame (note that this is opposite for Λ )
3
[5
⃗
⃗
|
|
0< P <1 : P= α p^

⃗p

!K +K

[4

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

S.A. Voloshin

[5

e
n
t
n

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ization measurement in Au+Au collisions,” Phys. Rev.
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φ (20-60%)nReaction plane
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-0.3
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20
30
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50
60
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-0.5
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0.5
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spin C
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FIG.
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FIG. 4. (Color
online)Global polarizationof !inhyperons
as aPrevious
ΛSaitoh,polarization
resultAu+Au
52 (2016) doi:10.1038/nphys3526.
doi:10.1103/PhysRevC.89.054905[arXiv:1401.3805[hep-colwith
respect
to thereactionplane
in mid-central
Au+Au!
functionofcentrality
given
as
a
fraction
of
the
total
inelastic
hadronic¯.
Symbol
keys
are
the
same
as
in
functionof!
pseudorapidityη√nThe ! [18]andS. !P. hyperon
globalpolarization
has been
Heims andE. zero-consistent.
T.
Jaynes. “Theory
of Gy- lisions atph]]. s
GeVasversusof thevector meson.
200
GeV(year2004)
wasNN
cross section. Symbol
keys=
are200the samein Fig. p3.TOnly
statistical
=
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±
Fig.
3.
A
constant
line
fit
to
these
data
pointsyieldsP!
mromagnetic
E↵ects atand
Some Related
Magnetic[38]
L.
McLerranandV.
Skokov,“Comments
About
the Elecmeasuredin
Au+Au
collisions
center-of-massenergies
√
−3
2
The
sizes
of
the
statisticaluncertainties
areindicatedby er√
uncertainties
areshown.
/ndf = 6.5/10 for
Au+Au
collisions
at 34,sNN 143= (1962)9.6) × 10 with χPhenomena”,
Rev.
Mod.
Phys.
tromagnetic
Field
in
Heavy-Ion
Collisions,”
Nucl.
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sNN = 62.4 and 200 GeV with the STAR detector at RHIC.
ror bars,A andthesystematic
uncertainties by caps . The K ∗0
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doi:http://dx.doi.org/10.1103/RevModPhys.34.143
929,
184(2014)
doi:10.1016/j.nuclphysa.2014.05.008√
mpolarizationofAn upper limit
of |Pfor¯ | ! 0.02 for the global!,!
have been [hep-ph]].
shifted slightly in pT for clarity. The
with χ 2 /ndf [19]= 14.3/10
Au+Au
collisionsand
at D.
sNNJ.=Wang,
62.4 GeV
F. Becattini,
L. Csernai“⇤ polariza- data points[arXiv:1305.0774¯
s! and !region
hyperons
the STAR
detector
acceptanceis FIG.
C.9:
Acceptanceeffects
anduncertainties
horizontal
line
indicatestheunpolarized
expectation
Same
as
Fig.
4,systematic
dottedcurve
corresponds
tion inwithin
peripheral
heavy
ion
collisions,”
Phys. Rev.
C dashed[39]
Z.
T. Liang
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X.
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“Spin
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is far below
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88, no.limit
3, 034905(2013) theErratum:[Phys.
Rev. C ization
93,
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A+A
Phys. linesLett.
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The
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horizontal
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(3)correctedassumesa perfect
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no.in6, Ref.
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629,discussed
20 (2005) doi:10.1016/j.physletb.2005.09.060[nuclnvalues discussed[1],(2016)]
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falls within the predicted acceptancepredictions
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the
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for
hyperons.
For
the
case
of
an
imperfect
detector,
only.
Dashedcurve
corresponds
tofeed-downcorrecte
th/0411101].
∗gregion from the10.1103/PhysRevC.88.034905
more realistic calculations [arXiv:1304.4427[4] based on the[nucl0 consider the average of ⟨sin(φp − %RP )⟩ but
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∗0
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as
a
take
into
account
the
fact
that
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integral
over
the
solid
0
The including
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C 77, 061902(2008)
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⌃
!
!
∗
∗
∗
∗
d
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anglement
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ion
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!
!
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s

PΛ

PΛ

ρ

00

STAR results circa 2007

p (GeV/c)- 3+1D viscous hydro+cascade model predicts P*~0.2%
for Au+Au 200 GeV.

Tsukuba
Week,
Tsukuba,
September 28, 2017 A(pH , p )S.A. Voloshin⟨sin(φJapan,
and pagethe 5NERSC Center at LBNL
for Global
their Science
support.
This
p − %RP )⟩ =p

Energy dependence (𝜌vector00) meson V by making the direct productquarks (or anti-quarks).
Spin alignment,
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it to(𝜌theba𝑝𝑇transforming
dependence)
cture STARenvisaged
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In a00coupled
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normalized
spin density matrix ρ V f
al A + A collision, a QGP is formed and STARobtain
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tor mesons ass and anti-quarks in the QGP are polarized.
STAR preliminary⎛⎞(1+Pq )(1+Pq̄ )hem, there are also quarks and anti-quarks¾ First measurement of 𝜙-3+P P
00¾ Non-significant𝑝q q̄
dependence withalignmentatn the accompanying processes such as the meson spin
⎜
⎟
1−P
P
q
large
systematical
q̄
V
⎜
⎟
𝑠𝑁𝑁 ρ
= 19-62GeV.
00=uncertainties dom⎠
ering of the partons and the subsequent par3+Pq Pq̄
⎝Z.-T. Liang, X.-N. Wang / Physics Letters B 629 (2005) 20–26
the residual backg(1−P
de, etc. These quarks and anti-quarks are¾ 𝜌00 shows weak beam 0
q )(1−Pq̄ )estimation(under0
3+Pq Pq̄
investigation).
zed by higher transverse momenta and are energy dependence.
f
Hence,
we
obtain
µL
,
where
1/µ
is
the
interaction
range
and
L
in
Eq.
(7)
by
P
ence
is
that
we
shouldreplacePq̄q̄
ed.0 Hence, there are different possibilities0
typicalrelativeorbitalFirst,
angularmomentumbewhich is thepolarizationof the anti-quark created
1
−
P
P
ns
to be
produced.
they
can be proq q̄
V (rec)=,ρ
two-colliding partons. When the initial pT of athefragmentation process.
This result has been co00
the recombination of the quarks and anti3 + Pq Pq̄ data [13,16–18]. It has b
is much larger than p0 , the quark will not be popared with the available
QGP, this corresponds to the hadronizaand allout
thethat,non-diagonal
elementszero.
Ass. But such a quark can still recombine with a
found
the available
data canare
only
be fitte
ariolow(1).p Second,they
can aalso
be formed
zed
anti-quark
toform
hadron,accordthe
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polarized
in
Pd = Pūis=taken
Pd̄ ≡asPeffectively
Ps̄ , we obt
Pu =T
q , and Ps =ecombinationof scenario
the quarks/anti-quarks
inthe hadronization(2). The spin alignopposite direction
as ∗theleadingquark, and the pomesonsasandK
2017/7/14 results for ρ Biao
Tu@SQM2017,10-15
July, Utrecht
University
2017/7/14
Biao Tu@SQM2017,10-15 July, Utrecht University
14
fraghorthosefrom theaccompanying
processes.
such formed
vectormesons can beobtainedization is Pq̄ =2−βPq , where β ≈ 0.5 was obtai
1 − Pq
1 ofWepolarase,ρ(rec)= 0 orthePq̄ recombination= 0⇢00into⇡ Eq. (7).
haveertingwe
Pq have
NSM:
[19]
by
fitting
the data[13,16–18]. Hence, for the fi
2=,ρ
3 + (!/T)quarks
V (anti-quarks)
00
2
ks
with
unpolarizedanti-quarks
=
1/3,
even
if
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of
the
constituent
3
+
P
rank
V
’s,
q
00
rized
beforerecombination.
and thiscorresponds
to the hadronization∗ (rec) 1 1−βP
Pqq2 PsK+
V (frag) =ally, Finally,
we consider
hadronization
scenario (3),ρ(2).
theythecan
also be produced
via= 3 + P2 P
. .
ρ00
(
00
↑
q
s
3 − βPq
V +theX.
agmentationa polarized
quark q →entation of ofa fastquark/anti-quarkfrom∗ρ B 629 (2005)K20–26
Z.-T. Liang, X.-N. Wang / Physics Letterskely
happensforquarkswithlarge
rapidities
We Vseethat both
smallers corresponds to the scenario (3). Clearly,=1For’s otherthan ρthefirst ρrank
hadrons,ρ V than00 are00 andQGP
and may
play an importantfor hadrons
they areproducedvia
recombination
similadifferent
hadronization
scenarios
shouldThese
resultsbeconsideredasreplacea parametrizat
p0 = µL0 , where
1/µ is the interaction
range
and Lcanenceis that
we should
Pof0q̄ in Eq. (7) b
region. The
situationinthis
TsukubaScience
Week,
Tsukuba,
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2017
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Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

S.A. Voloshin

00Globalpolarization, 2017
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Tsukuba Global Science Week, Tsukuba, Japan, September
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S.A. Voloshin

9Vorticity, magnetic fieldobal polarization measure
Extracted Physical Parameters

da and Antiation

fromnull result• Significant vorticity signal– Hints at falling with energy,
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Isaac Upsal – August 2017

15

8

Polarization of anti-Lambdas is higher
than that of Lambdas - indication of themagnetic field effect?
page 8

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

S.A. Voloshin

Vorticity, magnetic fieldobal polarization measure
Extracted Physical Parameters

da and Antiation

fromnull result• Significant vorticity signal– Hints at falling with energy,
despite increasing Jsys
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Isaac Upsal – August 2017

15

8

Polarization of anti-Lambdas is higher
than that of Lambdas - indication of themagnetic field effect?
page 8➜ Omega/T of the order of a few percent
eB ⇠ 10 2 m2⇡➜ Magnetic fields

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

S.A. Voloshin

D. Tlusty, T. Todoroki, M. Tokarev, S. Trentalange, R.
E. Tribble,
Tribedy,
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O. D.
known
as directedP. flow,
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11
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a QGP phasetransitionF.[11–13].
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Xu,
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Xu,
Z.
Xu,
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Xu,
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Xu,
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Yang,
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as the electric
conductivity [14]
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Zhang, J. B. Zhang,shows
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andZhonL. McLerran, V. Skokov / Nuclear Physics A 929 (2014) 184–190 J. Zhang, X. P. Zhang, S. Zhang, Y. 38
n
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18
12
participants (protons
neutrons) in the transverse plane
L. Zhou, X. Zhu, Y. Zoulkarneeva,
and M.andZyzak
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for þ
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Au collisionatassuming
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sNN =an200
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field lifetime.
ncertainties. The small but finite Δv agrees
pectation for the effects of the initial electric
gn flipping of the electric field discussed in
6 fm. Because of the difference in the number of protons ineems not to be observed within the current L. Adamczyk, J. K. Adkins, G. Agakishiev,(STARM. M.Collaboration)
Aggarwal, Z. Ahammed, I. Alekseev,
D. M. Anderson,
A. Aparin, D. Arkhipkin, E. C. Aschenauer, M. U. Ashraf, A. Attri, G. S. Averichev, X. Bai,
which is close to the expectation discussed R.V.Aoyama,
PHSD+EF
Bairathi,AGH
R. Bellwied,
K.Technology,
Bhati, P. Bhattarai,
Bielcik,30-059,
J. Bielcikova,
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Science A.
andFPACS, J.Cracow
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nent of v1 ) show much smaller values (∼ by acompared to those in Cu þ Au. Note that thenent of v1 in Au þ Au collisions is similarly
The Δv1 in Au þ Au is consistent with zero.
vLuo,(y,p G.)L. =hcos()i1. Magdy,
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Ma,
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for charged pions from the parton-hadron~cplaneshowing
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field
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K. Meehan,
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Mei, anZ.initial
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Minaev,mthechargedifference
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Ψ
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micsFig.(PHSD)
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which
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aof Au spectators.
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T. K. Nayak, G. Nigmatkulov, T. Niida, direction
L. V. Nogach,
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Cu+Au
rt approach in the partonic and hadronic
G. Odyniec, A. Ogawa, K. Oh, V. A. Okorokov, D. Olvitt Jr, B. S. Page, R. Pak, Y. X. Pan, Y. Pandit,
Y. Panebratsev, B. Pawlik,
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Au+Au
compared
to
the
data.
As
indicatedinA.
M.
Poskanzer,
N.
K.
Pruthi,M.
Przybycien, J. Putschke, H. Qiu, A. Quintero, S. Ramachandran, R. L. Ray,of the conductivity owing to expansion of the medium can only decrease the lifeR. done
Reed, forM. J. Rehbein, H. G. Ritter, J. B. Roberts, O. V. Rogachevskiy, J. L. Romero, J. D. Roth, L. Ruan,
field andnot be consideredhere. Our bysimulationsareeagnetic
measuredΔvwillcould
besmearedthe√ thusJ. Rusnak, O. Rusnakova, N. R. Sahoo, P. K. Sahu, I. Sakrejda, S. Salur, J. Sandweiss, A. Sarkar,
1
1 we R. 0
ions at energy s = 200 GeV and fixed impact parameter b = 6 fm. InJ. Fig.
Schambach,P. Scharenberg, A. M. Schmah, W. B. Schmidke, N. Schmitz, J. Seger, P. Seyboth, N. Shah,
in
ψ
and
Ψ
orientations,
but
note
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the
E
1
E. Shahaliev,
olution of the magnetic field in the origin x⃗ = 0 as a function of the electriccon- P. V. Shanmuganathan, M. Shao, A. Sharma, M. K. Sharma, B. Sharma, W. Q. Shen, S. S. Shi,
2
Z.
Shi,
Q.
Y. Shou, E. P. Sichtermann, R. Sikora, M. Simko, S. Singha, M. J. Skoby, D. Smirnov, N. Smirnov,
results
show event-by-eventthat the lifetime of the fluctuations
strong magnetic field(eB > mπ ) is not
el
takes
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into
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H. M. Spinka, πB.(x0.1)
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M.
Strikhanov,B.
Stringfellow,
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Sumbera,B. Summa, Z. Sun, Y. Sun, X. M. Sun, B. Surrow,e PHSD model calculates two cases: charge- D. N. Svirida, A. H. Tang, Z. Tang,
PHSD
πT. Tarnowsky,
A. Tawfik, J. Thäder, J. H. Thomas, A. R. Timmins,−0.005D.
Tlusty,T.
Todoroki,
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Tokarev,S.
Trentalange,
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vpendence
1 with and without the initial electric field0
3 R. Varma, A.4N. Vasiliev,
T. Ullrich, D. G. Underwood,
I. Upsal,1 G. Van Buren, 2
G. van Nieuwenhuizen,
R.
Vertesi,F.
Videbæk,S.
Vokal,S.
A.
Voloshin,A.
Vossen,G.
Wang,F. Wang, J. S. Wang, Y. Wang,
he case with the EF switched on, the modelp [GeV/c]
H. Wang,
Y. Wang, J. C. Webb, G. Webb, L. Wen, G. D. Westfall,
H. Wieman, S. W. Wissink, R. Witt, Y. Wu,
section, we established that for realistic values of the conductivities
the elecT Xu, Z. Xu, N. Xu, J. Xu, C. Yang, Y. Yang,
tious
all
electric
chargesareaffected
by
the
EF
and
Z. G. Xiao, W. Xie, G. Xie, K. Xin, Q. H. Xu, Y. F. Xu, H.
elds in heavy-ion collisions are almost unmodified by the presence of themedium.
S. Yang,
Y. Yang, Q. Yang, Y. Yang, Z. Ye, Z. Ye, L. Yi, K. Yip, I. -K. Yoo, N. Yu, H. Zbroszczyk, W. Zha,
nsafelya largeseparationofv
betweenpositive
andAtP. Zhang,
the time
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only
X.
S. Zhang, ofY. Zhang,
J. B. Zhang, Z.EM
Zhang,fields
S. Zhang, (~0.25
J. Zhang, J. fm)
Zhao, C.
Zhong,
use the magnetic field generated
magnetic
1 by the original protons only. ThisJ. Zhang,
FIG.
3.
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and
L. Zhou,flow
X. Zhu,Y.positive
Zoulkarneeva, andand M.negative
Zyzak
pproximatedfollows in Fig. 3(a). In Fig. 3(b), theabout 10% of all charges are produced
ticles as asshown
the difference between the
spectra as a function of pT in(STARtwo
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page1 cZ
9
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23

3

1

14

6

51

17

3

34

23 Au-SP
1

3

18

38

19

8

42

23

23

40

15

51

35

13

35

19

23

3

52

23

26

3

37

10

18

38

4

23

3

42

1

9

11

34

34

27

32

54

39

43

52

36

23

41

5

28

27

3

24,24

40

23

28

50

23

3

40

45

43

6

∆ v1

3

23

35

7

48

19

38

7

51

38
40

Energy dependence. Comparison to hydro

…
and
AMPT
L-G. Pang et al. / Nuclear Physics A 00 (2017) 1–4
4

L-G. Pang et al. / Nuclear Physics A 00 (2017) 1–4

While both calculations are
consistent with data, details
differ.
Fig. 4. (Left) The global polarization of ⇤ from AMPT model for 2 di↵erent impact paramete
20

50% collisions). (Right) The model data comparison for with and without feed-down cont4. Acknowledgements
page 10

HL, QW and XLX are supported by the MSBRD
in China under the G
S.A. Voloshin

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

ment cannot be properly called a precision fit because, as
we have mentioned in the Introduction, several effects in theter (SQM 2013), J. Phys. Conf. Ser. 509, 012054 (2014)[15] F. Becattini, G. Inghirami, V. Rolando, A. Beraudo,
319
L. Del Zanna, A. De Pace, M. Nardi, G. Pagliara, and V. Chan320
dra, Eur. Phys. J. C75, 406 (2015), arXiv:1501.04468 [nucl-th]
321 [16] U. Heinz and R. Snellings, Ann. Rev. Nucl. Part. Sci. 63, 123322(2013), arXiv:1301.2826 [nucl-th]
323 [17] L. P. Csernai, D. D. Strottman,
and C. Anderlik, Phys. Rev.
324
C85, 054901 (2012), arXiv:1112.4287 [nucl-th]
325 [18] Y. Jiang, Z.-W. Lin,and J. Liao, (2016), arXiv:1602.06580
326[hep-ph]327 [19] D. E. Kharzeev, J. Liao, S. A. Voloshin, and G. Wang, Prog.
328
Part. Nucl. Phys. 88, 1 (2016), arXiv:1511.04050 [hep-ph]329 [20] L. Adamczyk et al. (STAR), Phys. Rev. C88, 014902 (2013),
330
arXiv:1301.2348 [nucl-ex]
1
331 [21] M. Anderson et al., Nucl. Instrum. Meth. A499, 659 (2003),
332
arXiv:nucl-ex/0301015 [nucl-ex]
333 [22] C. A. Whitten (STAR), Proceedings, 12th International Work334
shop on Polarized ion sources, targets and polarimetry (PSTP
2007), AIP Conf. Proc.RP
980, 390 (2008)
1 335
336 [23] F. S. Bieser et al., Nucl. Instrum. Meth. A499, 766 (2003)
337 [24] G. Agakishiev et al. (STAR), Phys. Rev. C85, 014901 (2012),
338
arXiv:1109.5446 [nucl-ex]
339 [25] L. Adamczyk et al. (STAR), Phys. Rev. Lett. 112, 162301
340(2014), arXiv:1401.3043 [nucl-ex]
341 [26] S. A. Voloshin and T. Niida, (2016), arXiv:1604.04597 [nucl342
th]Vorticity and directed flow

317

3

318

3

Good description of directed flow
requires accounting for vorticity!

Slope, dv /dη proportional to vorticity?

v ⌘ cos(

)

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

Fig. 6 Directed flow of pions for different values of ηm parameter with
η/s = 0.1 compared with STAR data [22]page 11

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

S.A. Voloshinment cannot be properly called a precision fit because, as
we have mentioned in the Introduction, several effects in theter (SQM 2013), J. Phys. Conf. Ser. 509, 012054 (2014)[15] F. Becattini, G. Inghirami, V. Rolando, A. Beraudo,
319
L. Del Zanna, A. De Pace, M. Nardi, G. Pagliara, and V. Chan320
dra, Eur. Phys. J. C75, 406 (2015), arXiv:1501.04468 [nucl-th]
321 [16] U. Heinz and R. Snellings, Ann. Rev. Nucl. Part. Sci. 63, 123322(2013), arXiv:1301.2826 [nucl-th]
323 [17] L. P. Csernai, D. D. Strottman,
and C. Anderlik, Phys. Rev.
324
C85, 054901 (2012), arXiv:1112.4287 [nucl-th]
325 [18] Y. Jiang, Z.-W. Lin,and J. Liao, (2016), arXiv:1602.06580
326[hep-ph]327 [19] D. E. Kharzeev, J. Liao, S. A. Voloshin, and G. Wang, Prog.
328
Part. Nucl. Phys. 88, 1 (2016), arXiv:1511.04050 [hep-ph]329 [20] L. Adamczyk et al. (STAR), Phys. Rev. C88, 014902 (2013),
330
arXiv:1301.2348 [nucl-ex]
1
331 [21] M. Anderson et al., Nucl. Instrum. Meth. A499, 659 (2003),
332
arXiv:nucl-ex/0301015 [nucl-ex]
333 [22] C. A. Whitten (STAR), Proceedings, 12th International Work334
shop on Polarized ion sources, targets and polarimetry (PSTP
2007), AIP Conf. Proc.RP
980, 390 (2008)
1 335
336 [23] F. S. Bieser et al., Nucl. Instrum. Meth. A499, 766 (2003)
337 [24] G. Agakishiev et al. (STAR), Phys. Rev. C85, 014901 (2012),
338
arXiv:1109.5446 [nucl-ex]
339 [25] L. Adamczyk et al. (STAR), Phys. Rev. Lett. 112, 162301
340(2014), arXiv:1401.3043 [nucl-ex]
341 [26] S. A. Voloshin and T. Niida, (2016), arXiv:1604.04597 [nucl342
th]Vorticity and directed flow

317

3

318

3

Good description of directed flow
requires accounting for vorticity!

Slope, dv /dη proportional to vorticity?

v ⌘ cos()

10-40% Au+Au Collisions

STAR Preliminary

0.02

p

π+

π-

K+

Λ

Λ

K0s

y=0

K

dv1 / dy |Fig. 6 Directed flow of pions for different values of ηm parameter with
η/s = 0.1 compared with STAR data [22]

p
-

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

0

− 0.02− 0.047 8 9 10

20

30

40

50 60 70100

200sNN (GeV)¯ K ± , KS0 , and ⇡ ± in 10-40%
FIG. 11. (Color online) Beam energy dependence of v1 (y) slope for p, ⇤, p̄, ⇤,Au+Au collisions [46, 90].

Slope at 2.76 TeV is approximately 3 times
smaller than at 200 GeV

page 11

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 201710 - 40%

S.A. Voloshin

Energy dependence. Following v1 slope

page 12

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

S.A. Voloshin

Energy dependence. Following v1 slope

For a meaningful results at LHC energy we need about 100 larger statistics

page 12

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

S.A. VoloshinSTAR++ dependenceCentrality
PH

T. Niida, QCD Chirality Workshop 2017

0.015

Au+Au 200 GeV|η|<1, 0.4<p <6 GeV/cSTAR Preliminary

T

0.01

Λ

Λ

0.005
0
box: syst. uncert.

20

40

60
Centrality [%]Weak centrality dependence for Λ
Not enough statistics for a real conclusion.
Looks to slightly
increasein peripheral events for anti-Λ
(might be slightly
improved)
16

T. Niida, QCD Chirality Workshop 2017
page 13

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

S.A. Voloshin

the second term on the right-hand-side of eq. (3) does contribute to the polarization vector. This additional term
shes in the non-relativistic limit of the flow k k ⌧ 0 and of the particle as well (kpk ⌧ ").
edequationafter eq.
(4), weof the initially
proton momentumnder
the conditions
explored
in reported
the paper theand angularaccordingdistribution
to our calculations,the relative contribution ofneglected term
to ⇧0y⇧insmall and positive.
later
it increases
and at 4.75 fm/c olarization
vectorIn (3)
ouris convention,
whichHowever,follows forthatof times,ref. [10],this vector
0 . eq.
timei.e.
chosenthe stoppingof theregimeit overcomesthe first
at high |px | and small/2,
the for⇤ spin,whereasthehydrodynamical
usual convention
in -particle
physics
has term
as maximal
As a consequence, the overall pattern of the pT -dependence of ⇧0y (px , py ) changes considerably with respect totion.
Therefore, the correct formula for the angular distribution with ↵ = 0.647 reads:
previous calculation, with a maximal positive (i.e. opposite to the angular momentum, see fig. 1 in the paper)rization of 8% 1at dNhigh |px | 1and small |py | and ⇤a minimum at -6% (negative, i.e. along the angular momentum) at=(1while+ 2↵⇧momentum
0 · p̂ )h |py | and small |px | momenta,
theaverage of the ⇧0y remains negative, see figure below.
⇤

Vorticity vs hyperon momentum

N d⌦

4⇡

2Π0y(px,py)

4
we erroneously
stated that, because of parity symmetry, the integral term on theving the time derivative of and the gradient of 0 vanishes. In fact, because of thector under reflection ( 0 , ) ! ( 0 ,), the Fermi-Dirac distribution gets changed:

Py(GeV/c)

2

nF =

1

e

0"

-6%

·p+µ/T + 1-4%!

1e 0 "+ ·p+µ/T + 1
4%

8%

0%
0 8% 4% 0%
t-hand-sideof eq. (3) does contributeto the polarization vector. This additional term
limit of the flow k k ⌧ 0-4%
and of the particle as well (kpk ⌧ ").
d in the paper and according to our calculations, initially the relative contribution of-2-6%
q. (3) is small and positive. However, for later times, it increases and at 4.75 fm/c g of the hydrodynamical regime - it overcomes the first term at high |px | and small
rall patternof the pT -dependence of ⇧0y (px , py ) changes considerably with respect to-4
a maximal
to2 the angularmomentum, see fig. 1 in the paper)-4 positive-2 (i.e. opposite
04
and small |py | and a minimum at -6% (negative, i.e. along the angular momentum) at
Px(GeV/c)ta, while the momentum
average of the ⇧0y remains negative, see figure below.
Erratum: ⇤ Polarization in Peripheral Heavy Ion Collisions. 1: (Color online)
ReplacementofWang,figure3. Rev.
TheC y88,component
F. Becattini,
L.P. Csernai, D.J.
Phys.
034905 (2013) (left panel) and the modulus of the polarization (right panel)
he rest frame of the⇤s as a function of momentum in the transverse plane (i.e., at pz = 0).
F. Becattini, L.P. Csernai, D.J. Wang, and Y.L. Xie

PACS innumbers: 25.75.-q,
24.70.+s, 47.32.Ef
ote thatcorrected
figure 3 above,
we have plotted the polarization normalized to 1, that isS.A.
2⇧Voloshinwith ⇧ as
Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017
page the14

the second term on the right-hand-side of eq. (3) does contribute to the polarization vector. This additional term
shes in the non-relativistic limit of the flow k k ⌧ 0 and of the particle as well (kpk ⌧ ").
edequationafter eq.
(4), weof the initially
proton momentumnder
the conditions
explored
in reported
the paper theand angularaccordingdistribution
to our calculations,the relative contribution ofneglected term
to ⇧0y⇧insmall and positive.
later
it increases
and at 4.75 fm/c olarization
vectorIn (3)
ouris convention,
whichHowever,follows forthatof times,ref. [10],thisvector0 . eq.
T. Niida, QCD Chirality Workshop 2017
timei.e.
chosenthe stoppingof theregimeit overcomesthe first
at high |px | and small/2,
the for⇤ spin,whereasthehydrodynamical
usual convention
in -particle
physics
has term
as maximal
As a consequence, the overall pattern of the STARpT -dependence of ⇧0y (px , py ) changes considerably with respect totion.
Therefore,
thecorrect
formulafortheangular distribution with ↵ = 0.647 reads:
previous calculation, with a maximal positive (i.e. opposite to the angular momentum, see fig. 1 in the paper)rization of 8% 1at dNhigh |px | 1and small |py | and ⇤a minimum at -6% (negative, i.e. along the angular momentum) at=(1while+ 2↵⇧momentum
0 · p̂ )h |py | and small |px | momenta,
theaverage of the ⇧0y remains negative, see figure below.
⇤

Vorticity vs hyperon momentum$$""#

4⇡

PH

N d⌦

2Π0y(px,py)

0.02STAR Preliminary
Au+Au 200 GeV
4
we erroneously
stated that, because of parity symmetry, the20%-60%,
integral|ηtermon the|<1ving the time derivative of and the gradient of 0 vanishes. In fact, because of theΛΛ
ctor under reflection ( 0 , ) ! ( 0 ,), the Fermi-Diracgetschanged:0.01distribution

Py(GeV/c)

2

nF =

1

e

0"

-6%

·p+µ/T + 1-4%!

1e 0 "+ ·p+µ/T + 1
4%

8%

0%
0 8% 4% 0%0t-hand-sideof eq. (3) does contributeto the polarization vector.
This additional term
limit of the flow k k ⌧ 0-4%
and of the particle as well (kpk ⌧ ").
d in the paper and according to our calculations, initially thebox:
relative
contribution ofsyst. uncert.
-2-6%
q. (3) is small and positive. However, for later times,−itincreases and at 4.75 fm/c 0.01
01 |px | and2 small 3
4g of the hydrodynamical regime - it overcomes the first term
at highp [GeV/c]rall patternofthep-dependence
of
⇧
(p
,
p
)
changesconsiderablywithrespect
to
T
T
0y
x
y
-4
a maximal
to2 the angularmomentum, see fig. 1 in the paper)-4 positive-2 (i.e. opposite
04Nosigniﬁcant
pmomentum)
T dependence was observ
and small |py | and a minimum at -6% (negative, i.e. alongtheangularat polarization
No obvious increase of thePx(GeV/c)ta, while the momentum average of the ⇧0y remains
negative,
figurebelow.
withincurrent
uncertainties
with seetransverse
momentum.
Erratum: ⇤ Polarization in Peripheral Heavy Ion Collisions. 1: (Color online)
ReplacementofWang,figure3. Rev.
TheC y88,component
F. Becattini,
L.P. Csernai, D.J.
Phys.
034905 (2013) (left panel) and the modulus of the polarization (right panel)
he rest frame of the⇤s as a function of momentum
in Chirality
the transverse
plane (i.e., at pz = 0).
T. Niida, QCD
Workshop 2017
F. Becattini, L.P. Csernai, D.J. Wang, and Y.L. Xie

PACS innumbers: 25.75.-q,
24.70.+s, 47.32.Ef
ote thatcorrected
figure 3 above,
we have plotted the polarization normalized to 1, that isS.A.
2⇧Voloshinwith ⇧ as
Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017
page the14Azimuthal
anglephidependence
Going
into details:
dependence

Note : Smearing of the observed EP (Ψ𝑜𝑏𝑠 ) is not corrected yet in 𝜙 − Ψ𝑜𝑏𝑠

¾ No significant signal for off-peak Λ candidates (red points).
¾ 𝑃𝐻 shows a similar azimuthal dependence for Λ and Λ.
𝜋3𝜋 𝜋¾ The significance of Δ𝑃𝐻 , for Λ and Λ conbined, between [0,8 ] and [ 8 ,2 ] is
4.7𝜎.
¾ Consistent with the picture of maximum vorticity in the equator.
2017/7/14

page 15

Biao Tu@SQM2017,10-15 July, Utrecht University

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

9

S.A. Voloshin

Azimuthal
anglephidependence
Going
into
details:
dependence
Fig. 2. The rapidity and azimuthal
angle distribution of ⇤ spin projected t

In section II, in the unnumbered equation after eq. (4), we reported the angular distribution of the proton momentum
dN/d⌦⇤ as a function of the polarization vector ⇧0 . In our convention, which follows that of ref. [10], this vector
has a maximal magnitude of 1/2, i.e. the ⇤ spin, whereas the usual convention in particle physics has as maximal
magnitude 1, i.e. 100% polarization. Therefore, the correct formula for the angular distribution with ↵ = 0.647 reads:psNN = 200 GeV (middle) and Au+Au

1 dN
1
=
(1 + 2↵ ⇧0 · p̂⇤ )
⇤
N d⌦
4⇡

p

sNN = 62.4 GeV (right) collision

In section II, below eq. (3), we erroneously stated that, because of parity symmetry, the integral term on theright hand side of eq. (3) involving the time derivative of and the gradient of 0 vanishes. In fact, because of the
non-invariance of the four-vector under reflection ( 0 , ) ! ( 0 ,), the Fermi-Dirac distribution gets changed:

1generated during
1
and
the
fluid
evolution.
As
shown
in
Fig.
2
!
e
+1
e
+1
and the second term on the right-hand-sideof eq. (3) does
contributeto the polarization ofvector.
This additional
termangular momentum. Loc
which
is
the
direction
theglobalvanishes in the non-relativistic limit of the flow k k ⌧and of the particle as well (kpk ⌧ ").
Under the conditions explored in the paper and according to our calculations, initially the relative contribution ofa cosinewhich
indicates
the neglected term to ⇧ in eq. (3) is small
and positive. structure
However, for later times,
it increases
and at 4.75 fm/ca- vortex ring [10]. The he
the time chosen for the stopping of the hydrodynamical regime - it overcomes the first term at high |p | and small
andbackward
rapidity.
The polarization
at mid-rapidity sho|p |. As a consequence, the overall patternof the p-dependence of ⇧ (p, p ) changes considerablywith respect toour previous calculation, with a maximal positive (i.e. opposite to the angular momentum, see fig. 1 in the paper)
polarization of 8% at high |p | and small maximal|p | and a minimummagnitude
at -6% (negative, i.e. alongtheangularmomentum) atofthepolarization
at 62.4 GeV is abouthigh |p | and small |p | momenta, while the momentum average of the ⇧ remains negative, see figure below.
nF =

0"

0 "+

·p+µ/T·p+µ/T

0

0y

x

y

T

x

0y

x

y

y

x
0y
Note
: Smearing of the observed EP (Ψ𝑜𝑏𝑠) is not corrected yet in 𝜙 − Ψ𝑜𝑏𝑠y

2Π0y(px,py)¾ No significant signal for off-peak Λ candidates (red points).
¾ 𝑃𝐻 shows a similar azimuthal dependence for Λ and Λ.
2
𝜋
3𝜋 𝜋
-6%
¾ The significance of Δ𝑃𝐻 , for Λ and Λ conbined, between [0,8 ] and [ 8 ,2 ] is
-4%
4.7𝜎.
0% 4% 8%
0 8% 4% 0%
Nuclear-4%¾ Consistent with the picture of maximum vorticity in the equator.
Physics A

Py(GeV/c)

4

Nuclear Physics A 00 (2017) 1–4

-6%

-2

www.elsevier.com/locate/procedia

2017/7/14

XXVIthInternational Conference on Ultrarelativistic Nucleus-Nucleus9Collisions
Biao Tu@SQM2017,10-15 July, Utrecht
University(Quark Matter 2017)

-4
-4

-2

0

2

4

Px(GeV/c)pr 2017

Erratum: ⇤ Polarization in Peripheral Heavy Ion Collisions

Local and global ⇤ polarization in a vortical fluid QM2017

Hui Lia , Hannah Petersenb,c,d , Long-Gang Pang*b,e,f , Qun Wanga , Xiao-Liang
Xiaa , Xin-Nian Wangg,fFIG. 1: (Color online)
Replacementoffigure3.
Theycomponent(leftpanel)
andthemodulusofthepolarization(rightpanel)
F. Becattini, L.P. Csernai, D.J. Wang, and Y.L. Xie
a Department of Modern Physics, University of Science and Technology of China, HeFei, 230026, China
TsukubaGlobalScience
Week,
Tsukuba,
Japan,
September
28,
2017
page
15of the ⇤s as a function of momentum in the transverse plane (i.e., at pz = 0).
S.A. Voloshin
in the restframebF. Becattini, L.P. Csernai, D.J. Wang, Phys. Rev. C 88, 034905 (2013)

Fig. 3. The rapidity and azimuthal angle distribution of ⇤ spin projected to y
Frankfurt Institute for Advanced Studies, Frankfurt am Main, 60438, Germany

[34] D. Kharzeev and A. Zhitnitsky, Charge separation induced by P-odd bubbles in QCD matter,
Nucl. Phys. A797 (2007) 67–79, [arXiv:0706.1026].

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[36] D. E. Kharzeev, J. Liao, S. A. Voloshin, and G. Wang, Chiral magnetic and vortical eﬀects inhigh-energy nuclear collisionsâĂŤA status report, Prog. Part. Nucl. Phys. 88 (2016) 1–28,[arXiv:1511.04050].

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Chiral Vortical effect (CVE) - separationof the baryon charge along vorticity

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page 16

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

S.A. Voloshin

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

6

B*ﬁeld p

spin

S. Schlichting and SV, in preparation

Chiral Separation Effect (CSE) - separationof88theaxial
Physics(2016)
1–28 charge along the magnetic field

J5 = 2⇡1 2 µ(Qe)B

RH#
#
LH

Can be:net baryon number,
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)electric
charge,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 LHE
quarks’ current is generated in the opposite direction but their contribution
to the axial< 0 the5v current J would be the same as that of RH quarks. For µnet
strangenesscurrent will flip direction.

B*ﬁeld p spin
J /µ B
RH#
Idea (S. Shlichting# and S. Voloshin, in preparation)
LH be related to the axial current J5
Λ polarization may
5

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 BE and examine the energy changing rate of the system. The straightforward electrodynamic
small auxiliary electric field E
RR
E = [(Qe) 5 ]EE · B.
E
way of computation ‘‘counts’’ the work per unit time (i.e. power) done by such an electric field P = xE EJ · E
Ex
Alternatively for this systemof chiral fermions, the (electromagnetic) chiral anomaly suggests the generation of axial charges
R
E · BE with CA = (Qe)2 /(2⇡ 2 ) the universal anomaly coefficient. Now a nonzero axial chemical
at the rate dQ5 /dt = xE CA E
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 ]Eidentification:

Use (kaon) charge asymmetry instead(8)of μv

Z
Z (with Q > 0)
on is for just one kind of right-handed(RH) quarks
E LH[(Qe) 5(and]EE · BEanti-quarks)= [CA µ5 ]EE ·theB
quarks). For left-handed (LH) quarks
ExEx
rrent EJ5 would be the same as that of RH quarks. For µ < 0 theE field. Thus the 5 must take the universal value CA µ5 =for any auxiliary E

B

Qe

Qe
2⇡ 2

µ5 that is completely fixed by the chiralanomaly.
The transportphenomenonin Eq. (4) bears a distinctive feature that is intrinsically different from Eq. (7). The chiral
xistence of such a current
we turn
on an arbitrarily++ coefficient while the usual conductivity is T -odd
K[26].
K CME
magnetic conductivity 5 is a T -even transportThat is, theof the system. The straightforward
electrodynamicv
v while the usual conducting current iscurrent can be generated
as an equilibrium current without producing entropy,
necessarily dissipative.
+K+
Ksuch an electric field
P
J
E
Qe
E
B.
5
E
E
x
x

hN
N i
hN
µ R/T /or µ /T /R
d S. Voloshin,in preparation)hN
E·E + N i
= E · E = [( ) ]hN

N
+N

i
i

al anomaly suggests2.2.
theofeffectaxial charges
Thegenerationchiral separation
nomaly coefficient. Now a nonzero axial chemical
By reminding ourselves of the axial counterpart in Eq. (5) of the vector current, which we have discussed so far, it may becharge, thus the energychanging
rate
viaWorkshop
anomaly
T. Niida,
QCD
2017 under certain circumstances in response
naturalto ask:couldChirality
axial current
also be generated
5 to external probe fields? The
answer is positive.
complementarytransport phenomenon to the CME has been found and named the Chiral Separation
These reasonings therefore
leadAtothe following

y be related to the axial current J
Effect (CSE) [61,62]:

asymmetry instead(8)of μv

5

EJ5 =

=

E.

sB

(9)

E field, with its magnitude in proportion to the system’s
It states that an axial current is generated along an external B(nonzero) vector chemical potential µ as well as the field magnitude. The coefficient (which may be called the CSE
conductivity) is given by s = 2Qeµ.
⇡2
Qe page 17
TsukubaGlobalin
Week,way,
Tsukuba,
Japan,
28, 2017
S.A. Voloshin
Intuitively the fixed
CSE mayby
be theunderstood
the following
as illustrated
in September
Fig. 2. The magnetic
field leads to a spinthat is completely
chiralScience

µ

PH

PH

STAR

Z

E
x

Use
(kaon)
charge asymmetry instead0.01
of μv
E[C µ ]EE · B
(8)

Z

P

identification:

PΛ vs net charge, net strangeness++    ++
0.005

E=[(Qe) 5 ]EE · B

E
x

A

5

E field. Thus the 5 must take the universal value A 5 = Qe2 µ5 that is completely fixed by the chiralfor any auxiliary E
Qe
2⇡anomaly.
The transport phenomenon in Eq. (4) bears a distinctive feature that is intrinsically different from Eq. (7). The chiral++ coefficient while the usual conductivity is T -odd
K[26].
K CME
magnetic conductivity 5 is a T -even transportThat is, thev as an equilibrium current without producing entropy,v while the usual conducting current iscurrent can be generated
necessarily dissipative.
+
K+
K 0
C µ

hN
N i
µ /T /
hN + N ior

2.2. The chiral separation effecthNµ /T /hN

N+N− 0.005

PH

PH

Λ

E
s B.

0.005

0.005

0

0

Λ

slope (x100)
Λ = 0.919± 1.147
Λ = -0.979± 1.273

(9)

−0.2

E field, with its magnitude in proportion to the system’s
It states that an axial current is generated along an external B(nonzero) vector chemical potential µ as well as the field magnitude. The coefficient (which may be called the CSE
conductivity) is given by s = 2Qeµ.
⇡2Intuitively the CSE may be understood in the following way, as illustrated in Fig. 2. The magnetic field leads to a spin
E This effect implies that the positively charged quarks have theirpolarization (i.e. ‘‘magnetization’’) effect, with hEsi / (Qe)B.
E field direction, while the negatively charged anti-quarks have their spins oppositely
spins preferably aligned along the B
−RH
0.005
− 0.005
E i.e. with more
E k Es) will have oppositealigned. Now
quarks and antiquarks(with paverage momentum
hEpi (x100)/ hEsi / (Qe)B,
slope (x100)
slope
E Furthermore with nonzero µ 6= 0 (e.g. considering
RH quarks/antiquarks moving in the direction parallel/antiparallel to B.
Λ
=
0.919
±
1.147
Λ = 0.169
0.295
E The±LHµ > 0) there would then be a net current of RH quarks/antiquarks EJR / hEpi(nQ nQ̄ ) / (Qe)µB.
quarks/antiquarks

0.01 current
0.01
E 1.273
Λ EJ=L /-0.979
Λ = 0.503± 0.327
would form an−opposite(Qe)µ±
B
but contribute the −sameas the RH quarks/antiquarks
to form together anEaxial current along the magnetic field: EJ5 / (Qe)µB.
It is instructive to recast (4) and (9) in terms of the RH and LH currents EJR/L , as follows:

−0.2

E E
EJR/L = J ± J5 = ± R/L B
E
2

0

0.2

measured Ach

−0.5

0

PH

i
i

By reminding ourselves of the axial counterpart in Eq. (5) of the vector current, which we have discussed so far, it may be
GeV,
20-60%
T. Niida,
QCD
Workshop2017
STAR
Preliminary
naturalto ask:couldChirality
axial current
also be generated
undercertain circumstances Au+Au
in response200
to externalprobe
fields? The
0.01
0.01
answer is positive. A complementary transport phenomenon to the CME has been found and named the Chiral Separation− 0.01
Effect (CSE) [61,62]:

EJ5 =STAR Pr0meas

No clear trendNe

0.5

measured Ak(10)

T. Niida, QCD Chirality Workshop 2017with R/L = 4Qeµ . The above has the simple interoperation as the CME separately for the purely right-handed and purely⇡ 2 R/ Lleft-handed Weyl fermions: note the sign difference in the RH/LH cases. It reveals that the CME and the CSE are two sides of

No clear trend within current uncertainties.
Need more events…

T. Niida,page
QCD
18Chirality Workshop 2017 Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

S.A. Voloshin

20Vorticity and/from elliptic flowyzvorticityyxpage 19x

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

S.A. Voloshin

Vorticity and/from elliptic flowyzvorticityyxpage 19x

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

S.A. Voloshin

(a)

z

1.5 10-3

vorticity3

1.0 1032

5.0 10-42-3

1

0.0 100

0

x

-1
-2

-5.0 10-4-1.0 10

-3

y
x

-1

-5.0 10-3-2-4-2.0 10-3

-4

-1

0

1

2

3

5.0 10-3
0.0 100

-3

-2

-2

1.0 100-1.5 10-3-3

1.5 10-2

1-3-4

f=f0; Π0z

4

py [GeV]py [GeV]

Π0y

y

4

Vorticity and/from elliptic flow(b)4

-1.0 10-2-1.5 10-2
-4

-3

-2

-1

0

1

2

3

4

A study of vorticity formationin high energy nuclear collisions
px [GeV]px [GeV]F. Becattini,1, 2 G. Inghirami,3, 1 V. Rolando,4, 5 A. Beraudo,6
L. Del Zanna,1, 2, 7 A. De Pace,6 M. Nardi,6 G. Pagliara,4, 5 and V. Chandra8

(c)

(d)

1

Dipartimento di Fisica e Astronomia, Università di Firenze, Via G. Sansone 1, I-50019 Sesto F.no (Firenze), Italy
2
INFN - Sezione di Firenze, Via G. Sansone 1, I-50019 Sesto F.no (Firenze), Italy
3Frankfurt Institute for Advanced Studies (FIAS), Johann Wolfgang Goethe University, Frankfurt am Main, Germany
4
Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, Via Saragat 1, I-44100 Ferrara, Italy
5
INFN - Sezione di Ferrara, Via Saragat 1, I-44100 Ferrara, Italy
6
INFN - Sezione di Torino, Via P. Giuria 1, I-10125 Torino, Italy
7
INAF - Osservatorio Astrofisico di Arcetri, L.go E. Fermi 5, I-50125 Firenze, Italy8
Indian Institute of Technology Gandhinagar, Ahmedabad-382424, Gujrat, India(Dated: August 18, 2015)

arXiv:1501.04468v3 [nucl-th].04468v3 [nucl-th] 17 Aug 2015

pose, we have run ECHO-QGP with an initial profile:

INTRODUCTION

p We present a quantitative study of vorticity formation in peripheral ultrarelativistic heavy ion collisions at
sNN = 200 GeV by using the ECHO-QGP numerical code, implementing relativistic dissipative hydrodynamics in the causal Israel-Stewart framework in 3+1 dimensions with an initial Bjorken flow profile. We consider
and discuss di↵erent definitions of vorticity which are relevant in relativistic hydrodynamics. After demonstrating the excellent capabilities of our code, which proves to be able to reproduce Gubser flow up to 8 fm/c, weshow that, with the initial conditions needed to reproduce the measured directed flow in peripheral collisions
corresponding to an average impact parameter b = 11.6 fm and with the Bjorken flow profile for a viscous Quark
Gluon Plasma with ⌘/s = 0.1 fixed, a vorticity of the order of some 10 2 c/fm can develop at freezeout. The
ensuing polarization of ⇤ baryons does not exceed 1.4% at midrapidity. We show that the amount of developed
directed flow is sensitive to both the initial angular momentum of the plasma and its viscosity.

I.

The hydrodynamical model has by now become a paradigm
for the study of the QCD plasma formed in nuclear collisions at ultrarelativistic energies. There has been a considerable advance in hydrodynamics modeling and calculations ofthese collisions over the last decade. Numerical simulationsin 2+1D [1] and in 3+1 D [2–7] including viscous corrections
are becoming the new standard in this field and existing codes
are also able to handle initial state fluctuations.
An interesting issue is the possible formation of vorticity inperipheral collisions [8–10]. Indeed, the presence of vorticity may provide information about the (mean) initial state of
the hydrodynamical evolution which cannot be achieved otherwise, and it is related to the onset of peculiar physics in theplasma at high temperature, such as the chiral vortical e↵ect[11]. Furthermore, it has been shown that vorticity gives rise
to polarization of particles in the final state, so that e.g. ⇤baryon polarization - if measurable - can be used to detect
it [12, 13]. Finally, as we will show, numerical calculationof vorticity can be used to make stringent tests of numericalcodes, as the T-vorticity (see sect. II for the definition) is expected to vanish throughout under special initial conditions in
the ideal case.
Lately, vorticity has been the subject of investigations in
refs. [9, 10] with peculiar initial conditions in cartesian coordinates, ideal fluid approximation and isochronous freezeout.
Instead, in this work, we calculate di↵erent kinds of vorticity with our 3+1D ECHO-QGP 1 code [3], including dissipative relativistic hydrodynamics in the Israel-Stewart formulation with Bjorken initial conditions for the flow (i.e. withngent test of numerical implementations of Israel-Stewart
ory in Bjorken coordinates.

1 The code is publicly available at the web site http://theory.fi.infn.it/echoqgp

gure 14: (color online) Magnitude (panel a) and components (panels b,c,d) of the polarization vector of the ⇤ hyperon in its
rest frame.

1tanh Ax sinh(ybeam |⌘|)
(36)⌧
I. INTRODUCTIONu = u = u = 0), henceforth denoted as BIC. It shou
u⌘ =

x

y

⌘

u x = uy = u⌘ = 0
pointed out fromwork is to make aenergy and not todata. Therefore, ofects such as visco
freezeout and init
initial conditions

VORTICITIE

In this paper we
The Minkowskian
Levi-Civita symbo
We will use the resumed to be sum
will be sometimes
The covariant der
the exterior deriva
tive.

II.

Unlike in classcurl of the veloci
in relativistic hydapplications (see a

We have found that the magnitude of the 1/⌧ x ⌘ compointed out from the very beginning that the purpose onent of the thermal vorticity at freezeout can be as large aswork is to make a general assessment of vorticity at top R
The hydrodynamical model has by now become a paradigm
2energy and not to provide a precision fit to all the ava
for the meets
study of the the
QCD plasma
formed in nuclear
colli10 and yet its mean value is not large enough to produce
whichcausality
constraint(see Appendix B). It isdata. Therefore, our calculations do not take into accou
sions at ultrarelativistic energies. There has been a consider⌘fects such as viscous corrections to particle distribution
able advancein hydrodynamics
modeling flow
and calculationsofolarization of ⇤ hyperons much larger than 1%, which is a
found
that
the
directedisvery
sensitive
toaninitialu. smfreezeoutandinitialstate
fluctuations,
that
is
we
use
these collisions over the last decade. Numerical simulations
4 many events.
1
initial conditions obtained averaging over[1] and inpositive
3+1 D [2–7] including
viscouscorrections
nsistently lower estimate in comparison with other recent
Forinarea2+1D
small
value
of
the
parameter
A
=
5
⇥
10
fm
becoming the new standard in this field and existing codes3
are also able to handle initial state fluctuations.
culations based on di↵erent initial conditions. We havecorresponding
to
a
J
=
3.32
⇥
10
, keeping all other paramey
An interesting issue is the possible formation of vorticity incollisions [8–10]. Indeed, the presence of vorticund that theof directed flow,
at Global
this energy,
has Tsukuba,tersperipheral
fixed,
thedirectedflow
exhibits
two
wigglesaroundTsukubaScience Week,
2017initial
page magnitude
19
S.A. slight
Voloshin
A. Notations
ity Japan,
may provideSeptember
information about28,
the (mean)state of(a)z

1.5 10-3

vorticity3

1.0 1032

5.0 10-42-3

1

0.0 100

0

x

-1
-2

-5.0 10-4-1.0 10

-3

y
x

-1

-5.0 10-3-2-4-2.0 10-3

-4

-1

0

1

2

3

5.0 10-3
0.0 100

-3

-2

-2

1.0 100-1.5 10-3-3

1.5 10-2

1-3-4

f=f0; Π0z

4

py [GeV]py [GeV]

Π0y

y

4

Vorticity and/from elliptic flow(b)4

-1.0 10-2-1.5 10-2
-4

-3

-2

-1

0

1

2

3

4

A study of vorticity formationin high energy nuclear collisions
px [GeV]px [GeV]F. Becattini,1, 2 G. Inghirami,3, 1 V. Rolando,4, 5 A. Beraudo,6
L. Del Zanna,1, 2, 7 A. De Pace,6 M. Nardi,6 G. Pagliara,4, 5 and V. Chandra8

(c)

(d)

1

Dipartimento di Fisica e Astronomia, Università di Firenze, Via G. Sansone 1, I-50019 Sesto F.no (Firenze), Italy
2
INFN - Sezione di Firenze, Via G. Sansone 1, I-50019 Sesto F.no (Firenze), Italy
3Frankfurt Institute for Advanced Studies (FIAS), Johann Wolfgang Goethe University, Frankfurt am Main, Germany
4
Dipartimento di Fisica e Scienze della Terra, Università di Ferrara, Via Saragat 1, I-44100 Ferrara, Italy
5
INFN - Sezione di Ferrara, Via Saragat 1, I-44100 Ferrara, Italy
6
INFN - Sezione di Torino, Via P. Giuria 1, I-10125 Torino, Italy
7
INAF - Osservatorio Astrofisico di Arcetri, L.go E. Fermi 5, I-50125 Firenze, Italy8
Indian Institute of Technology Gandhinagar, Ahmedabad-382424, Gujrat, India(Dated: August 18, 2015)

arXiv:1501.04468v3 [nucl-th].04468v3 [nucl-th] 17 Aug 2015

pose, we have run ECHO-QGP with an initial profile:

INTRODUCTION

p We present a quantitative study of vorticity formation in peripheral ultrarelativistic heavy ion collisions at
sNN = 200 GeV by using the ECHO-QGP numerical code, implementing relativistic dissipative hydrodynamics in the causal Israel-Stewart framework in 3+1 dimensions with an initial Bjorken flow profile. We consider
and discuss di↵erent definitions of vorticity which are relevant in relativistic hydrodynamics. After demonstrating the excellent capabilities of our code, which proves to be able to reproduce Gubser flow up to 8 fm/c, weshow that, with the initial conditions needed to reproduce the measured directed flow in peripheral collisions
corresponding to an average impact parameter b = 11.6 fm and with the Bjorken flow profile for a viscous Quark
Gluon Plasma with ⌘/s = 0.1 fixed, a vorticity of the order of some 10 2 c/fm can develop at freezeout. The
ensuing polarization of ⇤ baryons does not exceed 1.4% at midrapidity. We show that the amount of developed
directed flow is sensitive to both the initial angular momentum of the plasma and its viscosity.

I.

The hydrodynamical model has by now become a paradigm
for the study of the QCD plasma formed in nuclear collisions at ultrarelativistic energies. There has been a considerable advance in hydrodynamics modeling and calculations ofthese collisions over the last decade. Numerical simulationsin 2+1D [1] and in 3+1 D [2–7] including viscous corrections
are becoming the new standard in this field and existing codes
are also able to handle initial state fluctuations.
An interesting issue is the possible formation of vorticity inperipheral collisions [8–10]. Indeed, the presence of vorticity may provide information about the (mean) initial state of
the hydrodynamical evolution which cannot be achieved otherwise, and it is related to the onset of peculiar physics in theplasma at high temperature, such as the chiral vortical e↵ect[11]. Furthermore, it has been shown that vorticity gives rise
to polarization of particles in the final state, so that e.g. ⇤baryon polarization - if measurable - can be used to detect
it [12, 13]. Finally, as we will show, numerical calculationof vorticity can be used to make stringent tests of numericalcodes, as the T-vorticity (see sect. II for the definition) is expected to vanish throughout under special initial conditions in
the ideal case.
Lately, vorticity has been the subject of investigations in
refs. [9, 10] with peculiar initial conditions in cartesian coordinates, ideal fluid approximation and isochronous freezeout.
Instead, in this work, we calculate di↵erent kinds of vorticity with our 3+1D ECHO-QGP 1 code [3], including dissipative relativistic hydrodynamics in the Israel-Stewart formulation with Bjorken initial conditions for the flow (i.e. withngent test of numerical implementations of Israel-Stewart
ory in Bjorken coordinates.

1 The code is publicly available at the web site http://theory.fi.infn.it/echoqgp

gure 14: (color online) Magnitude (panel a) and components (panels b,c,d) of the polarization vector of the ⇤ hyperon in its
rest frame.

1tanh Ax sinh(ybeam |⌘|)
(36)⌧
I. INTRODUCTIONu = u = u = 0), henceforth denoted as BIC. It shou
u⌘ =

x

y

⌘

u x = uy = u⌘ = 0
pointed out fromwork is to make aenergy and not todata. Therefore, ofects such as visco
freezeout and init
initial conditions

VORTICITIE

In this paper we
The Minkowskian
Levi-Civita symbo
We will use the resumed to be sum
will be sometimes
The covariant der
the exterior deriva
tive.

II.

Unlike in classcurl of the veloci
in relativistic hydapplications (see a

We have found that the magnitude of the 1/⌧ x ⌘ com- Should
be strongly“correlated”
with elliptic flow
pointed out from the very beginning that the purpose onent of the thermal vorticity
at freezeout
can be aslarge aswork is to make a general assessment of vorticity at top R
The hydrodynamical model has by now become a paradigm
2energy and not to provide a precision fit to all the ava
for the meets
studyincreaseof the the
QCD plasma
formed inenergy)
nuclearcolli10 and yet its mean value
is notenergy
large enoughto produce(might- Weakwhichcausality
constraint(see Appendix B). It is
dependence
even
with
data. Therefore, our calculations do not take into accou
sions at ultrarelativistic energies. There has been a consider⌘fects such as viscous corrections to particle distribution
able advancein hydrodynamics
modeling flow
and calculationsofolarization of ⇤ hyperons much larger than 1%, which is a
found
that
the
directedisvery
sensitive
toaninitialu. smfreezeoutandinitialstate
fluctuations,
that
is
we
use
these collisions over the last decade. Numerical simulations- Measurements wrt 𝚿2 - good RP resolution
4 many events.
1
initial conditions obtained averaging over[1] and inpositive
3+1 D [2–7] including
viscouscorrections
nsistently lower estimate in comparison with other recent
Forinarea2+1D
small
value
of
the
parameter
A
=
5
⇥
10
fm
becoming the new standard in this field and existing codes3
are also able to handle initial state fluctuations.
- Might
culations based on di↵erent
initialconditions.
We
have
corresponding
to
a
J
=
3.32
⇥
10
, keeping all other parameprovide detailed informationonvelocity
fieldsy
An interesting issue is the possible formation of vorticity incollisions [8–10]. Indeed, the presence of vorticund that theof directed flow,
at Global
this energy,
has Tsukuba,tersperipheral
fixed,
thedirectedflow
exhibits
two
wigglesaroundTsukubaScience Week,
2017initial
page magnitude
19
S.A. slight
Voloshin
A. Notations
ity Japan,
may provideSeptember
information about28,
the (mean)state of

Blast wave parameterizationyrmax = R(1
s

b
s

x

a cos(2 s )]b ⇡ 2a sin(2 s )Number of emitting “sources”:/ [1 + 2s2 cos(2 b )]Transverse rapidity (boost):s2 ⇡ a⇢⇡ ⇢t,max [r/rmax ( s )][1 + b cos(2 s ]⇢⇡ ⇢t,max (r/R)[1 + (a + b) cos(2 s ]1(r ⇥ v)z =r✓@(rv )
@r

@vr
@

◆

v ⇡

v r ⇡ ⇢t!z ⇡ (⇢t,max /R) sin(n s )[bnR≈10 fm, T≈100 MeV

page 20⇢max (r/R)2a sin(2 s )an ]Pz = !z /(2T ) ⇡ 0.1 sin(n s )[bnTsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

an ]S.A. Voloshin

Blast wave parameterizationyrmax = R(1
s

b
s

x

a cos(2 s )]b ⇡ 2a sin(2 s )Number of emitting “sources”:/ [1 + 2s2 cos(2 b )]Transverse rapidity (boost):s2 ⇡ a⇢⇡ ⇢t,max [r/rmax ( s )][1 + b cos(2 s ]⇢⇡ ⇢t,max (r/R)[1 + (a + b) cos(2 s ]1(r ⇥ v)z =r✓@(rv )
@r

@vr
@

◆

v ⇡

v r ⇡ ⇢t!z ⇡ (⇢t,max /R) sin(n s )[bnR≈10 fm, T≈100 MeV⇢max (r/R)2a sin(2 s )an ]Pz = !z /(2T ) ⇡ 0.1 sin(n s )[bnan ]The effects should be present also at higher harmonics,
e.g. for triangular flow.
Provides connection to vn(pt) and azFemto measurements
page 20

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

S.A. Voloshin

Downloaded from http://science.sciencema

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alternately
rotated
by
an
air
motor
neglectoftheother.
with strength JI equal to the intrinsic magnetic intensity of rotation.
<}uantity seems to decrease "e1'y rapidly. lL must be remarked llOWmeritlies
theageiieies
the
of
and
two
sets
peculiarbrought
to
rest,
the
changeof flux forT"
The complete expression foris known (and can readily be shown
ever
book.
of first
different speeds and different directionstlmt
this excellentof ro-the small ordmates cannot be measul'ed with sufficientfromprinciples) to be
W. E. CASTLE
precision.
tation being determined by thefluxmeter.We shal1 therefore use tbe first foul' ordinntes on1.1. The
JULY 30, 1915]—~Q sin 0 —jgQ sin
163
T" = —T' = SCIENCE
cos 0,
The0 fluxmeter
was compensated for extraneous

Barnett and Einstein-de Haas effects

¹.

—.

~

t,

Downloaded from http://science.sciencemag.org/ on March 21, 2017mean of the nllmbel's deduced 696
from them is
698
ARTICLES
SPECIALwasandelectromotive
readmirrorforces,byin much of
the inertia
but thewith anatsame way, ofrior be8encouraged.
new excess
methods are
wheredenotes Nothe
ofsugthe mademomentabout
system2
apparatus,
but tempt at improvement inandthese desirable enids,
gested for securing
scalefailed
to to0.1
mm. at the scaledistance 8- "Evpel'imental prooj
BY ROTATIONMAGNETIZATION
the an axis
its orbital
overwiththe
momentPhysics.
of 0,124.
tlie e.1Jistence oj Ampèl'e's confirm thiscoresult
any certainty;
and of inertia
reasons why velocity
excellentofstatement
is made ofangular11
1 b2m, =meters.
Afterallsuspected
sourcesofsystefurther
investigationwas
postponed
until
they
shouldbesought.
—in thisb
ABOUT
six years ago
I publishedjourthat diameterof theorbit
about
AB theVol.
making
If
angle
SecondSeries.
October,
VI.90(4)rgzgwith,were 0.yeliminated,were available.
molecula1'
CU7'7'ents."
By
Prof. eA. EINSTl!.IN and Dl'. W. J. DE HAAS.
Chapter VI. was originally written as a pro- better facilities
matic
aneffectwaserror
the made, again with Mirs.
that onI havein which
it wasa noteRecently
iseugenics
circularthe nalorbitof the more
rabid shown
sort,
test
againstleft corresponding
precisely withFnrther
that (Comlllunicatedpre-it follows fromthe curve
Barnett's
experiments
which haveassistance,by Prof.
H. A. thatsomewhat
modified
its
and
in
even
presentof magnetism
moderntheoryanymagnetic
3''
yieldeddefiniteandresults.
In
theconclusive
the ——mr' =tomr'form presents a rather strong contrast
dicted by the above(6)theory and inexplic8 =magnetized
2 by a sort
1,85
substance
shouldbecometwo nearly similar rods ofissue withthe final experiments
2Q)
It takes
preceding chapter.
§ 2. Consequencem0/ theexistence 0/ a magnetic
moment
2
on
able
other
any
hitherto
proposed.
theorysteel
shafting
were
mounted
with
their
axes
of
view
mechanistic,
development,
fatalistic,
•
/a/
=
145,4
0,320.10seton(Communicatedinthemeeting
of
April
23,
1915).
of moleculargyroscopic
processbeing
8
Eliminating
and
from
3f
we
get
magnetic magnetic intensity of rotathat horizontal and perpendicularwhich would assign to heredity all the ills(5),of momentum.
Theto theintrinsic
Rotation
intomeridian,f inand any
two similar coils of insulated
the indi- produce
heir to, and would
flesh isrotation.
deprive slhould
Q tion per unit speed, and the change of fluxm were mounted—'aboutTHE
their0 centers.
—
—
and
'rhe
momentof thebyvibrating
was determined
his career
tointrinsic
altervidual of all ability
an7"
substance= —intensitysinmagnetic
0x + ,0 2 wirecos. TheseW"henit had ofbeeninertia
discovered
OBRSTED systemthat magnetic
actionsy(7)(werei connected coin series
with oneatanothercharacter or to deviate from the course which coilsrod
d*ensitythecenter
of
the
iron
per
unit
e
to
axis
paralleltotheof
proportionalrotation,AnychangetIle bymomentof momentum.2ID?
of tbea bymagnetizedbymeaburing
theofchangeoffrequenC'y
pl'oduced
additionfate had marked out for him in the constitu- and with a Grassot fluxmeter, and were oppoaregauss/r.p.s.
exertednot
onIypermanent
lllagnets,
but byalso
electric of
X
3.1
were
found
to
be
10-7
speed,—
sitely
wound
so
that
any
variations
in
the
inat
his
had
of
This
tion
germ-plasm.
protestthemagnetizaand
theangularvelocity,(like
Dividing this expression byp, sin 0, as in the case of an ordinary magto ofa inertia,
coupledeterminedbytIle vector
body
gives
rise seemedsmall
momentis aC'curately
lmown.
noX
effecton maxwells/cm.2 aperproduced
the time and still has occasion and utility. tensity of the earth's fieldand
currents,
there
to be0whichtwoentirely
different
ways equationin which
10-5
1.9
rer.p.s.,
of
tion
to
the
directedtheearth)
oppositely
intrinsic
of Oneneticrotation:
intensity
getis antheattempt
the fluxmeter.
of the rods remained at rest;to evaluate
The field,
book as wea wholedm?
dI
foundfield
1) fol'a We
lllagnetic
canit be produred.
This conception,
however, conldand environment,show whileother, mountedspectively.
in a region in whichbiologically heredity
which towould
magnetic
intensity
be theproduced
7 dt
&
=
.2
di
1,13.10. . . (5)QmearthYsthemagnetic
intensitywascompensatedthat anboth are indispensable, and accordinglyFromexperiments
madefor a hardly
different be
pur- considered as satisfactory—' — the'electricaroundbyandphysicists
soon
tried toQ=
0,0126
2 to—
MAGNETIZATIONROTATION.
BY
H =circulating
II i byt an
cos
8
.
the
be
+
(8)
should current
electric
current
flowing
in
a
very
large
that nieither
emphasized,iLebedew
in 1912 it can be
shown
that
poseby bybalanced viewcoil, was alternately
an airmotor
If the rotatedneglect of the other.
ofe ofrotation.
substancein theIn thisdirectionrefer
the thetwoactions
tocoefficientone
thesame deduced
cause. (calculatedAMPÈRE
succeededwhnumerical
beenfrom theknowntheIf erenow
wetake 1300
fol'andthebasmagnetization
fl'om
merit
lies
the peculiar magnetization,
ageiieies
the two sets ofbrought torest, theinchangeof flux for
BARNETT.
BY S. andJ.
non-magnetic
suLbstances
not
more
than
a
rotatingbodyismagnetic,
pro0 experimentally attainablearedifferent
Theof values
so smalldifferent speeds andthis excellentofbook.
directionsinof comparisonroso
by hiscelebrated0] rurrents
in doing
ecurvehystel'esisof thematerialhypothesis
nnd the constantsof circulating
the cad) weminuteof ofthe magnetization
we of
have
the
intensity,
shouldrestult;
otherW. E.term
CASTLE
tationbeing
determinedbyorbitthe fraction
fluxmeter.
If
cu
the
second
is
the
is
not
circular"alue
fornegative
electrons.
withportional
negligible.
In toitoccurredtheftI.thatwhile
tothinking
about
originme,The fluxmeter was compensated for extraneous
I909
aroundtbe
any resistance.
in ironthereobserved
is produced at thesametoexpression
wise
not SPECIAL
a veryminute(except
extent).
m molecules
findforspeed.
themaguetic without
momentencounteringof the cy linde!'terrestrialforthat a substancewhichmagnetism,
II
an
whose
6rst
termisandismagnetic
identical
we obtain
with that of
ARTICLES
waselectromotive
read by (andmirrorforces,Preliminary
mentionedintheis distancenot, ofof8atomic
course, possible to obtain
ironbeenassulllption
experimentsThe
same
made thein tbetheoryexpl'essedof electronsin tbeand scaleandto 0.1mm. at constituted
theItscale
It ,hasour aim tois verifYI
relationby (5).
We
BYthe
ROTATION
MAGNETIZATIONto
ideashasfore, whose
accordingof Langevinothers,termsecondthe meters.
same order
of
and
as
that
of (8).
magnitude(8) note
470.
Is
After
all
suspected
sourcesofsysterods
fromtoentirelyfreemagnetization,andobreferredappeared,thoughdoubtfully,
ABOUT six years ago I published in this jourLORENTZ,
form
in in.which
it hasplace
been thatdevelopedby H. A.
or amolecularorbital6xed
withindividual
systems
I'lhall e.g.
show
the first
the calcnlated
effectis not the
too
matic
eliminated,
anmoments
effectwas negative
error were magnetic
Ifto
assumehas
value
for werethat
ordinarily
theaccepted
shown
that theon theinthe
which
it was e/m
nalwe
note
711
in
in leftshow
effecttheofaservations
on
of
mlade
changescasequestionalwaysWith
thesenumbel'sequation
(17)
leads
to
the
value
corresponding
preciselywiththat
prein magnitude268
in —thisx. from zero)and differingmust become
magnetizedof magnetism
moderntheoryanyviz.
only
difference
being Let
that, thelike
electric
in general,
the
to of
be observed.
body
be an currents
iron cylinder
with radiussmail
electroninshould
andslow
motion,e with the
2~v, where
Xby Io',put Qand =inexplicabove
the 90theory
rod
flux.
iron
rotatedresiduallarge
atmagnetic
aa, speedof about
Togetherchange7p
sort dicted
substance
becomemagnetizedbyana sort gyroscopic
of molecularactionangularvelocity.
gyroscopic
bymolecularon onother theory
any receiving
hitherto
proposed.
are aboutnow
J'egarded
elementary
set ableon beingofprocess
in- an-gularlllolecularrevolutions
flux
revolutions
seconid.
Later
observations
is theinweobtaintorotavelocity
second,for thethethecurrents
proportional
angular per
R,rotateitst, 1,1.
verticalshallofdeduce
fromvelocity,=
i as
0-7aaxis.
per1)
h whichmay
becan
roentioned
here 1thaas.,uroinga, cil'culation
pure'Ve
cylindl'ical
form, wecalcu·
The
intrinsic
magnetic
intensityofrotathe experiments
deflectionsof intotorsionThus
moment on
in itsconsiderwith zeroinmagnetic
any ofinof
a thecylinderrotation.on
Rotationslhould
produceanyiron, observed
and
tion
unit
of
fluxtheperspeed,
changechargesorelectrons.
unit
angularvelocity
tensity
per anthus
laled
the
momentof inertia
thetheoreticalcylindel'wilhout
the
glass
tube
(5) fortheagrees
angularvelocityw theofacquil'es
thel'eversal
intrinsic
intensity
7• andofthe
which
very
wel!
with
tbecylinder
one by1,:13.
10initial
If itmagnetic
is given
acceleration
anthan thesmallestreadableangulartionsubstancemuststate.
have
far
less
been
quantity.
center of theaboutiron rodits
per axis,
unit eachto d*ensity at the gaussparallel to the axis of rotation,
proportional
Itlongitudinalcannotdenied tbat theseviews
caIl forth
littlemirror
Qobserve,=be0,0102.
X
found
to be
aWe
magnetisation,which
we suppose
to somehavetoobjections.
tile=
individual
consistof afortogauss/r.p.s.
we —the magnetizaand (likesupposethemay
angularconclusion
Io'3.1 10-7to
aresimplicity
forcedtheresultwe
H/11
As velocity,a system,ofwhichallthat
precedesX1.9were
7, Ispeed,
(36.
must
however,that
wecannotassignonrsatmumeasu10-5
and
X
per
rer.p.s.,
maxwells/cm.2
r.
s.
p.
of
tion
to
the
directedtheearth)
oppositely
One
of
these
is
even
more
serious
than
it
was
in
AMPÈRE'S
days;
numberconstantofelectrons
in
fixed
orbits
withaveragerevolvingIs.
DenotingbyQ
themomentofinertia'Ofthecylinder,tion\'aluesteel' spectively.
the intensity
rotationwhichthatmagnetic
of woulda rodbe of
produces therein an intrinsic magnetic
producedrements a greater preci&ion than of 10% ,Fromexperiments
made
for
a
different
purorientaits
velocities
will
This
is
on
the
that
the
electronabout
assumption
alone
is
an
nucleus,changenegative
effective.
chargedoppositelyantheelectricaroundcurrent
bycirculating
itandis writing
difficult }. tofor concei\'ecirculation 1,13of electricity
and acting in a direction
velocity
intensity proportional to the angular(he abovea coefficient. 10-7, wefree from all
Lebedew in 1912 it can be shown that andIf the pose aby minuteofas
rotation.
substance
the direction
It
seems
to
us
th
at
wItbin
these
hmits
the
theoretICal conclusions
tion in insuchtocontributemomentum,aangularway
allsubstances
would
to
be
acted
According
the
this,
upon
preciselybyin non-magnetic
suLbstancesbynotan
more
than a current
electric
be produced
resistance and therefore continuing for ever. lndeed, according towhichpro-would
to istheintensity
rotating bodymagnetic,
magnetization,
opposite
therefore
axis of thecylinder.
minuteminutevelocity.
fraction oftothethe
magnetization
we havemagnetic
moment,parallelportional
to thea intensity,
shouldrestult; otherQw by= J&dt2J.Is .
havebeen fairly eonfirmed
OUl' obseryations
..
the
same
for
intensity
directionasinextent).
theangularofrotation,requiredaroundtherodsameflowingby theMAXIDlLL'S equations circulating electrons must lose their energy
iniron
observedisatsame
producedthespeed.
to
wise
not
a
minute(except
very
is in the direction
increment
momentum of eachof thesystemangular3
IfThisall ofsomeor experiments
positive
Preliminary
mentioned
not, ofhavecourse,orbital
possible to motions,obtain iron proporTheexperiments
bave beenout in bodytIle "Physlkalisch-TechNow,
if the thesatllration
vailleofcal'rled
ofa themagnetisation
per cmtherefore
is 1000,in ($1and in5.the ionsIt isalso
theoryproposedmagnetic
wonld
byradiation;
moleculesof theandmagneticof theaxistoofappeared,
the corresponding
rotation,rods entirely free incrementfrom magnetization,obnotereferredthoughanddoubtfully,
with
will
still
but
the
tionality
angularvelocity
evidently
it is now
uniton changes
Toobtaintheintrinsic
magnetic
intensity
speedaccording
perexist,
Lvi ofthanksin questionin thedirection
toshowof a servations
were always
ofcoefficient
We want to exprNothing
ess our
fOl" having
the appanische
Reichsanstalt".
mlade
case
the effectdirection
momentis rotatedeitherin thisor in thegradually
lose
their
magnetic
moment.
thekindopposite
rod
flux.
iron
90
residual
with
large
at
a
speed
of
about
Togetherthechange
of
which
is
not
a
high
estimate,
we
have
Is
1000.
The
momentinQ will beonly
in magnitude
even differential
ofnecessary
reducedormeanandpertheunitchanged indeflection
sign,
halfarethe
to inmultiply
the revolving
or negative.
revolution
flux proportional
revolutions
per seconid.
Later
observations
mtus
placed at theour hypotbesis,
dIsposition.seems' irreconcilable
as the particles
to the an-gularIfvelocity,
thepositive
7,8
ever lnndly
been observed,
with atensitiesondifferent
substances
differ
for
same
value
Q.
actingtheofmay
intrinsic
unit
deflection,intheintensity
Ho,
given
per
speed,
by)29,
electrons are all negative, in conformity with most of the experimental
of inertia
is Q of !;theMR2,and we find
0,1 cmfnndamental
lawsforof R
electromagnetism_generalvalidityThisfollows
statedimmediately infromequation,inthis above,
obtainwe
given
way)ted.the asIn
direction.equationin whichfor thetheMaxwell's
will also
becomemagnetized
evidence,cylinder2,torque when the conditions here assumed are put in.
w = 0,6 . 10Again, the law of CURIE-IJANGBVIN
requiresthat tbe magneticitinaaroundelectric
current
anflowingwouldbeitmagnetizedbyTocomparetoBarnett’s
results,
II The erst term0.of thismm.
gauss
Physics.
"Onapossible
influenceoftheon
Einsteinequation has been given5 gauss
and,
de
Haas
previously
c.
(1.
by
),
—= —imparted
26theI.
' (I3)Io
I6 X Ioto it. ThisX derived
050 1".into theirofamolecule
shaLLbeindependentofthetemperatul'e,
andmoment
X
X
3.
that
of
angularvelocityanangularvelocitythatcaneasilybeobserved.
formolarbutÃ isdirection
incorrectlyopposite
equationsainsteadofmolecular
16
magnetar.p. s.
mm.
P.S. paper,
saZarmultiply
p/tenomena".
By
ZEEMAN.
2𝝅Prof.
the sun.
andunlessthe earth
directionof magnetization
to the All
corresponds
the termsof their equationsof reducethe body
magnetbeing employed.
to zeroshall stillexist
at the byabsolnte
zero.P. Theenergy of the revolving
flux-density
for the University
from $fa9
and x3, madeSimilarly,
we obtain
magnetic of
Louisiis originallymagnetized.
at the Tulane
experiments(2. Preliminary§ 3. lil
DesC1'iption
0/of t!temet/wd.
electrons would,
therefore
be meetinga truezero
point25,energy.
(OommunicatedtheSeptember1915). In tbe' thoughrotationin thethe intrinsic
intensity toofshow,
peranaunitat speed
to me appeared
the timeproduced
this ideabyoccurredof many
physicists
however, the existenceof an energy ofopinionJapan,
GlobalScience Week, Tsukuba,
September
28, 2017
page
21
S.A.may
Voloshincentralthe minuterotor, thethe assumption
part ofdoubtf'ully,of the sort in Tsukuba
question, on
e8ectquantity
a veryAt first sightit seems
that equation (5)be tested in the

V

=

=

=

.

=

=- .

I

~

—

—.

=

=

Downloaded from http://science.sciencema

and body
state
are theearthYs
the andintensity was compensatedsame as if thewere at rest
themagnetic
thatis both
indispensable,accordingly
exactlysystem were
—
T'
T"=
to
the
be
an
shouldbyelectric
current
flowing inbeinga verysufficiently
large
nieither
thatupon by a torqueemphasized
acted
due to an extraneous magnetic Geld
constant. If we pass on to smaller ol'dinates thisview
Inbalanced
of
this
coil,
was
alternately
rotated
by
an
air
motor
neglectoftheother.
with strength JI equal to the intrinsic magnetic intensity of rotation.
<}uantity seems to decrease "e1'y rapidly. lL must be remarked llOWmeritlies
theageiieies
the
of
and
two
sets
peculiarbrought
to
rest,
the
changeof flux forT"
The complete expression foris known (and can readily be shown
ever
book.
of first
different speeds and different directionstlmt
this excellentof ro-the small ordmates cannot be measul'ed with sufficientfromprinciples) to be
W. E. CASTLE
precision.
tation being determined by thefluxmeter.We shal1 therefore use tbe first foul' ordinntes on1.1. The
JULY 30, 1915]—~Q sin 0 —jgQ sin
163
T" = —T' = SCIENCE
cos 0,
The0 fluxmeter
was compensated for extraneous

Barnett and Einstein-de Haas effects

¹.

—.

~

t,

Downloaded from http://science.sciencemag.org/ on March 21, 2017mean of the nllmbel's deduced 696
from them is
698
ARTICLES
SPECIALwasandelectromotive
readmirrorforces,byin much of
the inertia
but thewith anatsame way, ofrior be8encouraged.
new excess
methods are
wheredenotes Nothe
ofsugthe mademomentabout
system2
apparatus,
but tempt at improvement inandthese desirable enids,
gested for securing
scalefailed
to to0.1
mm. at the scaledistance 8- "Evpel'imental prooj
BY ROTATIONMAGNETIZATION
the an axis
its orbital
overwiththe
momentPhysics.
of 0,124.
tlie e.1Jistence oj Ampèl'e's confirm thiscoresult
any certainty;
and of inertia
reasons why velocity
excellentofstatement
is made ofangular11
1 b2m, =meters.
Afterallsuspected
sourcesofsystefurther
investigationwas
postponed
until
they
shouldbesought.
—in thisb
ABOUT
six years ago
I publishedjourthat diameterof theorbit
about
AB theVol.
making
If
angle
SecondSeries.
October,
VI.90(4)rgzgwith,were 0.yeliminated,were available.
molecula1'
CU7'7'ents."
By
Prof. eA. EINSTl!.IN and Dl'. W. J. DE HAAS.
Chapter VI. was originally written as a pro- better facilities
matic
aneffectwaserror
the made, again with Mirs.
that onI havein which
it wasa noteRecently
iseugenics
circularthe nalorbitof the more
rabid shown
sort,
test
againstleft corresponding
precisely withFnrther
that (Comlllunicatedpre-it follows fromthe curve
Barnett's
experiments
which haveassistance,by Prof.
H. A. thatsomewhat
modified
its
and
in
even
presentof magnetism
moderntheoryanymagnetic
3''
yieldeddefiniteandresults.
In
theconclusive
the ——mr' =tomr'form presents a rather strong contrast
dicted by the above(6)theory and inexplic8 =magnetized
2 by a sort
1,85
substance
shouldbecometwo nearly similar rods ofissue withthe final experiments
2Q)
It takes
preceding chapter.
§ 2. Consequencem0/ theexistence 0/ a magnetic
moment
2
on
able
other
any
hitherto
proposed.
theorysteel
shafting
were
mounted
with
their
axes
of
view
mechanistic,
development,
fatalistic,
•
/a/
=
145,4
0,320.10seton(Communicatedinthemeeting
of
April
23,
1915).
of moleculargyroscopic
processbeing
8
Eliminating
and
from
3f
we
get
magnetic magnetic intensity of rotathat horizontal and perpendicularwhich would assign to heredity all the ills(5),of momentum.
Theto theintrinsic
Rotation
intomeridian,f inand any
two similar coils of insulated
the indi- produce
heir to, and would
flesh isrotation.
deprive slhould
Q tion per unit speed, and the change of fluxm were mounted—'aboutTHE
their0 centers.
—
—
and
'rhe
momentof thebyvibrating
was determined
his career
tointrinsic
altervidual of all ability
an7"
substance= —intensitysinmagnetic
0x + ,0 2 wirecos. TheseW"henit had ofbeeninertia
discovered
OBRSTED systemthat magnetic
actionsy(7)(werei connected coin series
with oneatanothercharacter or to deviate from the course which coilsrod
d*ensitythecenter
of
the
iron
per
unit
e
to
axis
paralleltotheof
proportionalrotation,AnychangetIle bymomentof momentum.2ID?
of tbea bymagnetizedbymeaburing
theofchangeoffrequenC'y
pl'oduced
additionfate had marked out for him in the constitu- and with a Grassot fluxmeter, and were oppoaregauss/r.p.s.
exertednot
onIypermanent
lllagnets,
but byalso
electric of
X
3.1
were
found
to
be
10-7
speed,—
sitely
wound
so
that
any
variations
in
the
inat
his
had
of
This
tion
germ-plasm.
protestthemagnetizaand
theangularvelocity,(like
Dividing this expression byp, sin 0, as in the case of an ordinary magto ofa inertia,
coupledeterminedbytIle vector
body
gives
rise seemedsmall
momentis aC'curately
lmown.
noX
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GlobalScience Week, Tsukuba,
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page
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SUMMARY
Vorticity: an important piece in the picture of heavy ion collisions---

The global polarization measurements indicate thermal vorticity values of theorder of a few percent at lower RHIC energy, strongly decreasing with collisionenergyPolarization seems to be stronger for particle emitted in-plane
The split between lambda and lambda-bar polarization is likely due to the strong
magnetic fields of the order of eB ⇠ 10 2 m2⇡
Polarization seems to be stronger for particle emitted in-plane
Elliptic (and higher harmonics) flow leads to a nontrivial azimuthal structure inpolarization along the beam direction.

Very rich and extremely interesting physics! … (StatMech of vortical fluids ofnonzero spin particles, spin structure of hadrons, etc…) as well as very important
ingredient for the interpretation of existing data (e.g. elliptic flow)
A lot more to come! (RHIC special Au+Au run at 27 GeV,… Measurements withcold atoms… )page 22

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

S.A. Voloshin

EXTRA SLIDES

page 23

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

S.A. Voloshin

Asymmetric collisions: Cu+Au

page 24

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

S.A. Voloshin

Asymmetric collisions: Cu+Auy!
x

page 24

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

S.A. Voloshin

Role
of
µ
B
Polarization of fermionsin a vorticular fluid

ICTS-USTC-16-05

Ren-hong Fang,1 Long-gang Pang,2 Qun Wang,1 and Xin-nian Wang3, 4[nucl-th] 14 Apr 2016
Interdisciplinary Center for Theoretical Study and arXiv:1604.04036v1
Department of Modern Physics,
University of Science and Technology of China, Hefei, Anhui 230026, China
2Frankfurt Institute for Advanced Studies, Ruth-Moufang-Strasse 1, 60438 Frankfurt am Main, Germany
3
Key Laboratory of Quark and Lepton Physics (MOE) and Institute of Particle Physics,
Central China Normal University, Wuhan, 430079, China
4
Nuclear Science Division, MS 70R0319, Lawrence Berkeley National Laboratory, Berkeley, California 94720
leading order in spatial gradient expansion. The polarization density of fermions can be calculated
from the axial vector component of the Wigner function and is found to be proportional to the local
vorticity ω. The polarizations per particle for fermions and anti-fermions decrease with the chemical
potential and increase with energy (mass). Both quantities approach the asymptotic value !ω/4
in the large energy (mass) limit. The polarization per particle for fermions is always smaller thanthat for anti-fermions, whose ratio of fermions to anti-fermions also decreases with the chemical
potential. The polarization per particle on the Cooper-Frye freeze-out hyper-surface can also be
formulated and is consistent with the previous result of Becattini et al..

In non-central high-energy heavy-ion collisions, the large orbital angular momentum present in the colliding system
can lead to non-vanishing local vorticity in the hot and dense fluid [1–6]. The vorticity induced by global orbital
angular momentum in the fluid can be considered as local rotational motion of particles [3, 4, 7, 8]. It is closely
related to the rapidity dependence of the v1 flow and shear of the longitudinal flow velocity inside the reaction plane[5, 9, 10].
As a result of spin-orbital coupling, quarks and anti-quarks can become polarized along the normal direction of thereaction plane [1, 2, 5]. Through hadronization of polarized quarks and anti-quarks, hyperons can also be polarized in
the same direction in the final state [1, 2, 11]. Measurements of such global hyperon polarization is feasible throughthe parity-violating decay of hyperons [12, 13]. Such measurements will shed light on properties of the vorticular
structures of the strongly coupled quark-gluon plasma (sQGP) in high-energy heavy-ion collisions.
Quark and anti-quark polarization in a vorticular fluid is also closely related to the Chiral Magnetic and VorticalEﬀects [14–19]. From the solutions of Wigner functions for chiral or massless fermions in a quantum kinetic approach
one can derive the axial current j5µ = ρ5 uµ + ξ5 ω µ + ξ5B B µ , where ρ5 is the axial charge density, uµ is the fluid velocity,ω µ ≡ 12 ϵµσαβ uσ ∂α uβ is the vorticity 4-vector, and B µ = 21 ϵµνλσ uν Fλσ is the 4-vector of the magnetic field with Fλρbeing the strength tensor of the electromagnetic field. The coeﬃcients ξ5 and ξ5B are all functions of temperaturesand chemical potentials µ and µ5 [19]. In a three-flavor quark matter with u, d and s quarks and their anti-quarks,
ξ5B = 0. In other words, the axial current in a three-flavor quark matter is blind to the magnetic field and solely
induced by the vorticity. Such an axial current leads to the Local Polarization Eﬀect [19] which is also connected tothe spin-vorticity coupling for chiral or massless fermions [20].
In this paper, we will extend our Wigner function method for massless fermions to massive ones and formulate thepolarization of massive fermions induced by vorticity. In Section II, we will give a brief introduction to the Wigner
function method and derive the equations for the Wigner function components for massive fermions based on Ref.
[21, 22]. The Wigner function components can be determined perturbatively by gradient expansion. In Section III,we will derive the Wigner function at the leading order by definition. Using the projection method we can extract
each component of the Wigner function at the leading order. We will propose the first order solution for the axial
vector component in Section IV by extending the solution for massless fermions. In Section V, we will show that theaxial vector component can be regarded as the spin density in phase space. We can obtain the polarization density
after completion of momentum integration of the axial vector component in Section VI. We will also formulate thefermion polarization on the freezeout hypersurface by extending the Cooper-Frye formula. We will give a summaryof the results in the final section.
We adopt the same sign!conventions" for fermion charge Q as in Refs. [19, 20, 22, 23], and the same sign convention
for the axial vector Aµ ∼ ψ̄γ µ γ 5 ψ as in Resf. [19, 20, 23] but diﬀerent sign convention from Ref. [22].

Fermions become polarized in a vorticular fluid due to spin-vorticity coupling. Such a polarization
can be calculated from the Wigner function in a quantum kinetic approach. Extending previous
results for chiral fermions, we derive the Wigner function for massive fermions up to the next-toleading order in spatial gradient expansion. The polarization densityof fermions canbe calculated
Nonzerobaryonpotential isfrom the axial vector component of the Wigner function and is found to be proportional to the local
unlikely
vorticity ω. The polarizations per particle for fermions and anti-fermionsdecreasethewith reason
the chemicalfor the
potential and increase with energy (mass). Both quantities approach
the asymptotic!ω/4
differencein valuepolarizationofin the large energy (mass) limit. The polarization per particle for fermions is always smaller thanlambda and lambda-bar
that for anti-fermions, whose ratio of fermions to anti-fermions also decreases with the chemical
potential. The polarization per particle on the Cooper-Frye freeze-out hyper-surface can also be
consistentpreviousL.
resultBecattini
et al.. Ann.
F. withB.,Phys.Rev.Lett.
V.theChandra,Del
Zanna,
E. (2009),
Grossi,Phys. 338 (2013) 32[16] formulated
D. T. Sonand
andisP.
Surowka,
103,of
1916010906.5044.

Polarization four-vector in the LAB frame
I.
INTRODUCTION¯⇤ /P⇤
v:1604.04036v1 [nucl-th] 14 Apr P2016

1[17] D. E. Kharzeev and D. T. Son, Phys.Rev.Lett. 106, 062301 (2011), 1010.0038.
[18] S. Pu, J.-h. Gao, and Q. Wang, Phys. Rev. D83, 094017 (2011), 1008.2418.
I. Wang,
INTRODUCTION[19] J.-H. Gao, Z.-T. Liang, S. Pu, Q.
and X.-N. Wang, Phys.Rev.Lett. 109, 232301 (2012), 1203.0725.
AtGao
first
in thegradients:[20] J.-h.
andorderQ. Wang,
Phys.
Lett. B749, 542 (2015), 1504.07334.
In non-central
high-energy
heavy-ion collisions,the large
orbital angular[21] H.-T.
Elze, M. Gyulassy,
and D. Vasak,Nucl.Phys.
B276, momentum
706 (1986).present in the colliding system
can lead[22]to non-vanishingvorticity
the hotanddensePhys.
fluid [1–6].
The(1987).
vorticity induced by global orbital
D. Vasak, M. local
Gyulassy,
andinH.-T.
Elze,
Annals173, 462
angular [23]momentumin theS.fluid
be considered
as localrotationalmotion ofparticles
4, 7, 8].
It is closely
J.-W. Chen,Pu, can
Q. Wang,
and X.-N.
Wang,
Phys.Rev.Lett.
110,
262301[3,(2013),
1210.8312.
related totheP.rapidity
the v1Annals
flow andshear245,of thelongitudinal
flow velocity inside the reaction plane[24]
Zhuangdependence
and U. W.ofHeinz,
Phys.
311
(1996), nucl-th/9502034.
[5, 9, 10].[25] S. Ochs and U. W. Heinz, Annals Phys. 266, 351 (1998), hep-th/9806118.
As a resultF.
of Becattini,spin-orbitalV.coupling,
quarksandZanna,anti-quarks
canbecomepolarized
alongthe32normal
directionof theChandra,L. Deland E.
Grossi,AnnalsPhys.
338,(2013),
1303.3431.
Eur. Phys. J. C (2015) 75:406reaction [26]
Page
3
of
14
plane [1, 2, 5]. Through hadronization of polarized quarks and anti-quarks, hyperons can also be polarized406
inthe same direction in the final state [1, 2, 11]. Measurements of such global hyperon polarization is feasible throughthe parity-violating decay of hyperons [12, 13]. Such measurements will shed light on properties of the vorticular
One can write the relation
between-vorticity
and quark-gluon
kinewhichtohigh-energy
spin 1/2 heavy-ion
fermions,collisions.
n F being the Fermi–
structuresof theTstrongly
coupledplasma applies(sQGP) inmatical vorticity by expanding
theanddefinition
Dirac–Juttner
distributionfunction,
Quarkanti-quark(5):polarization in a vorticular
fluid is also
closely related
to the Chiral Magnetic and VorticalEﬀects [14–19]. From the solutions of Wigner functions for chiral or massless fermions in a quantum kinetic approach
one can derive
the axial current j5µ = ρ5 uµ + ξ5 ω µ + ξ5B B µ , whereρ5 is the axial charge density, uµ is the fluid velocity,"
1!
1(∂ν T ) u µ − (∂ωµµT≡) u12 ϵνµσαβ+ uTσ ∂ωαµν!µν =uβ ,is the vorticity 4-vector, nandB µ = 12 ϵµνλσ uν Fλσ is theFλρ. 4-vector of the magnetic field with(12)
F =
β(x)·
p−µ/T
2
e The coeﬃcients+ 1ξ5 and ξ5B are all functions of temperatures
being the strengthtensorof the electromagnetic
field.
Same
formulaobtained witha perturbative
expansion of the solution of the Wigner fun
and chemical potentials µ and µ5 [19]. In a three-flavor quark matter with u, d and s quarks and their anti-quarks,
implying
projectionof!,Colloquium,
page 25that the double-transverse
Voloshine.o.m.
Wayne
23, 2017 quarkξ B = 0. In otherwords,inStatethe axial
current inMarcha three-flavoris blindsubsection,
to the S.A.
magnetic
solelySimilarly
to thematter
previous
onefieldcanandreadily6
Global hyperon polarization
at local thermodynamic equilibrium with vorticity,(1)where EP ismagnetic
the firstfieldharmonic(directed flow) eventand feed-down

Global hyperon polarization at local therm
magnetic field andFrancesco Becattini,1 Iurii Karpenko,2 Michael Annan

1
Dipartimento di Fisica, Universita‘ di Firenze, and2
INFN, Sezione di Firenz
Physics Department, The Ohio State Unive
4
Wayne State University, Detroi
3(1)

The system created in ultrarelativistic nuclear collliquid. In non-central collisions, due to the large orbita
with the highest vorticity ever created under laborato
a highly vorticous fluid are expected to be globally p
along the system angular momentum. Vorticity-inducantiparticles, but the intense magnetic field generated
in polarization. In this paper we outline the therm
polarization phenomenon for particles with spin andstudy of this phenomenon, estimating the e↵ect of fee
polarization transfer in two-body decays and, particu
We find that accounting for such e↵ects is crucial whe
the experimental data.

INTRODUCTION

PACS numbers: 25.75.Ld, 25.75.Gz, 05.70.FhI.

1r ⇥ v,
2

Heavy ion collisions at ultrarelativistic energies createa strongly interacting system characterized by extremely
high temperature and energy density. For a large fractionof its lifetime the system shows strong collective e↵ects
and can be described by relativistic hydrodynamics. In
particular, the large elliptic flow observed in such collisions, indicate that the system is strongly coupled, withextremely low viscosity to entropy ratio [1]. From thevery success of the hydrodynamic description, one canalso conclude that the system might possess an extremely
high vorticity, likely the highest ever made under the laboratory conditions.
A simple estimate of the non-relativistic vorticity, defined as

!=

FI
flo
th
in

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017

no
(s
ap
po

w
in
at
th
w
of
th

ev
wa
of

page 26

1can be made based on a very schematic picture of thecollision depicted in Fig. 1. As the projectile and target
spectators move in opposite direction with the velocity
close to the speed of light, the z component of the collective velocity in the system close to the projectile spectators and that close to the target spectators are expected
to be di↵erent. Assuming that this di↵erence is a fraction of the speed of light, e.g. 0.1 (in units of the speed oflight), and that the transverse size of the system is about
5 fm, one concludes that the vorticity in the system is of
the order 0.02 fm 1 ⇡ 1022 s 1 .

1 sometimes the vorticity is defined without the factor 1/2; we use
the definition that gives the vorticity of the fluid rotating as awhole with a constant angular velocity ⌦, to be ! = ⌦Decay
Cplane (e.g. determined by the deflection of projectile++
parity-conserving: 1/2 ! 1/2 0
1/3
2Francesco Becattini,1 Iurii Karpenko,(1)Michael Annan Lisa,3 Isaac Upsal,3 and Sergei A. Voloshin4
spectators)
and
R
is
the
corresponding
event
plane
EP
1
parity-conserving: 1/2 ! 1/2+ 0
1
Dipartimento di Fisica, Universita‘ di Firenze, and INFN, Sezione di Firenze, Florence, Italy
arXiv:1610.02506v1[nucl-th]
8
Oct
2016
2 Ref. [11] for the discussion of the detector
resolution (see
INFN, Sezione di Firenze, Florence, Italy
3/2+ ! 1/2+ 0
parity-conserving:
1/3
3
Physics Department,
The Ohio State University, Columbus, Ohio 43210, USA
acceptancee↵ects).
+4
parity-conserving: 3/2 ! 1/2 0
1/5Wayne State University, Detroit, Michigan 48201, USAItshouldbepointedoutthatinrelativistic
heavy
ion
0
0
Nonrelativistic
statisticalmechanics⌅ !⇤+⇡+0.900The system created in ultrarelativistic nuclear collisions is known to behave as an almost ideal
collisions
theelectromagnetic
field
may
also
play
a
role
liquid. In non-central collisions, due to the large orbital momentum, such a system might be the fluid⌅ !⇤+⇡+0.927
with thehighestvorticity everthe
createdunder laboratoryof
conditions.
Particles
emerging fromsuchindetermining
polarization
producedparticles.
If
0
p(T,
µi ,vorticous
B, !)+ µpolarized· spins
B+! · J)/T⌃ !⇤+-1/3
i Qi +
a highly
fluid/
are exp[(
expected to beE
globally
withµ
their
on average
pointing ]
we
keep
the
assumptionof
local
thermodynamic
equilibalong the system angular momentum. Vorticity-induced polarization is the same for particles andantiparticles,
the intensein thesecollisions
may leadto the splitting
rium,butone
can magnetic
apply fieldthegenerated
formulae
(30),
(31).
However,in polarization. In this paper we outline the thermal approach to the calculation of the globalTABLE I. Polarization transfer factors C (see eq. (36)) foras S(S+1)
yet,
it is!notclear with
if thefreedomwillpolarization
phenomenon
for particles
spin spin
and wedegrees
discuss theof
detailsof the experimental
important decays X ! ⇤(⌃)⇡
S⇡
study ofrespondthis phenomenon,
estimating
the
e↵ect
of
feed-down.
A
generalformulaisderivedforthe
3 to Ta variation of thermal vorticity as quickly aspolarization transfer in two-body decays and, particularly, for strong and electromagnetic decays.
variationof e↵ects
the electromagnetic
relaxWe findto
thataaccounting
for such
is crucial when extractingfield.
vorticityIf
andthemagnetic
field fromthe experimental
data.
which could make this measurement difficult. Similarly
ation times
were sizeably di↵erent, one would estimate
difficult will be the detection of the global polarization
thermalvorticityand magnetic field from the measured
PACS numbers:
25.75.Ld,
25.75.Gz, 05.70.Fhwith the help of other strong decay channels, e.g. propolarization (see Section VI) at di↵erent times in the proposed in Ref. [41].
I. cess.
INTRODUCTION
The magnetic moments of particles and antipartiS.A. Voloshin

6
Global hyperon polarization
at local thermodynamic equilibrium with vorticity,(1)where EP ismagnetic
the firstfieldharmonic(directed flow) eventand feed-down

Global hyperon polarization at local therm
magnetic field andFrancesco Becattini,1 Iurii Karpenko,2 Michael Annan

1
Dipartimento di Fisica, Universita‘ di Firenze, and2
INFN, Sezione di Firenz
Physics Department, The Ohio State Unive
4
Wayne State University, Detroi
3

The system created in ultrarelativistic nuclear collliquid. In non-central collisions, due to the large orbita
with the highest vorticity ever created under laborato
a highly vorticous fluid are expected to be globally p
along the system angular momentum. Vorticity-inducantiparticles, but the intense magnetic field generated
in polarization. In this paper we outline the therm
polarization phenomenon for particles with spin andstudy of this phenomenon, estimating the e↵ect of fee
polarization transfer in two-body decays and, particu
We find that accounting for such e↵ects is crucial whe
the experimental data.

INTRODUCTION

PACS numbers: 25.75.Ld, 25.75.Gz, 05.70.Fh

I.

(1)

Heavy ion collisions at ultrarelativistic energies createa strongly interacting system characterized by extremely
high temperature and energy density. For a large fractionof its lifetime the system shows strong collective e↵ects
and can be described by relativistic hydrodynamics. In
particular, the large elliptic flow observed in such collisions, indicate that the system is strongly coupled, withextremely low viscosity to entropy ratio [1]. From thevery success of the hydrodynamic description, one canalso conclude that the system might possess an extremely
high vorticity, likely the highest ever made under the laboratory conditions.
A simple estimate of the non-relativistic vorticity, defined as

1r ⇥ v,
2

FI
flo
th
in

Tsukuba
Week,
Tsukuba,[31] R. h.
Fang, L.Global
g. Pang,Science
Q. Wang
and X.
n. Wang, Japan, September 28, 2017
no
(s
ap
po

w
in
at
th
w
of
th

ev
wa
of

rement in Au+Au
Phys. Rev.
page collisions,”
26

!=

1
can be made based on a very schematic picture of thecollision depicted in Fig. 1. As the projectile and target
spectators move in opposite direction with the velocity
close to the speed of light, the z component of the collective velocity in the system close to the projectile spectators and that close to the target spectators are expected
to be di↵erent. Assuming that this di↵erence is a fraction of the speed of light, e.g. 0.1 (in units of the speed oflight), and that the transverse size of the system is about
5 fm, one concludes that the vorticity in the system is of
the order 0.02 fm 1 ⇡ 1022 s 1 .

1 sometimes the vorticity is defined without the factor 1/2; we use
the definition that gives the vorticity of the fluid rotating as awhole with a constant angular velocity ⌦, to be ! = ⌦Decay
Cplane (e.g. determined by the deflection of projectile++
parity-conserving: 1/2 ! 1/2 0
1/3
2Francesco Becattini,1 Iurii Karpenko,(1)Michael Annan Lisa,3 Isaac Upsal,3 and Sergei A. Voloshin4
spectators)
and
R
is
the
corresponding
event
plane
EP
1
parity-conserving: 1/2 ! 1/2+ 0
1
Dipartimento di Fisica, Universita‘ di Firenze, and INFN, Sezione di Firenze, Florence, Italy
arXiv:1610.02506v1[nucl-th]
8
Oct
2016
2 Ref. [11] for the discussion of the detector
resolution (see
INFN, Sezione di Firenze, Florence, Italy
3/2+ ! 1/2+ 0
parity-conserving:
1/3
3
Physics Department,
The Ohio State University, Columbus, Ohio 43210, USA
acceptancee↵ects).
+4
parity-conserving: 3/2 ! 1/2 0
1/5Wayne State University, Detroit, Michigan 48201, USAItshouldbepointedoutthatinrelativistic
heavy
ion
0
0
Nonrelativistic
statisticalmechanics⌅ !⇤+⇡+0.900The system created in ultrarelativistic nuclear collisions is known to behave as an almost ideal
collisions
theelectromagnetic
field
may
also
play
a
role
liquid. In non-central collisions, due to the large orbital momentum, such a system might be the fluid⌅ !⇤+⇡+0.927
with thehighestvorticity everthe
createdunder laboratoryof
conditions.
Particles
emerging fromsuchindetermining
polarization
producedparticles.
If
0
p(T,
µi ,vorticous
B, !)+ µpolarized· spins
B+! · J)/T⌃ !⇤+-1/3
i Qi +
a highly
fluid/
are exp[(
expected to beE
globally
withµ
their
on average
pointing ]
we
keep
the
assumptionof
local
thermodynamic
equilibalong the system angular momentum. Vorticity-induced polarization is the same for particles andantiparticles,
the intensein thesecollisions
may leadto the splitting
13
rium,butone
can magnetic
apply fieldthegenerated
formulae
(30),
(31).
However,in polarization. In this paper we outline the thermal approach to the calculation of the globalTABLE I. Polarization transfer factors C (see eq. (36)) foras S(S+1)
yet,
it is!notclear with
if thefreedomwillpolarization
phenomenon
for particles
spin spin
and wedegrees
discuss theof
detailsof the experimental
important decays X ! ⇤(⌃)⇡
nd X. N. Wang,“Globallypolarized
quarktional
Schoolon
Elementary
Particles,
Hercegnovi(GorS⇡
study ofrespondthis phenomenon,
estimating
the
e↵ect
of
feed-down.
A
generalformulaisderivedforthe
3 Phys.
to T
aRev.
variationofas1968).
quickly as
in non-centralpolarization
A+A collisions,”
donand,andthermal
Breach, Newvorticity
York,
London,transferin two-bodydecaysparticularly,forstrongand electromagnetic
decays.
2301 (2005) Erratum:[Phys.
Rev. Lett.
[28] L.electromagnetic
Landauandextracting
E. M. Lifshits,
Statistical
Physics,
2ndfromaaccounting
variationof e↵ects
thefield.
IfandtherelaxWe findtothatfor suchisD.
crucialwhen
vorticitymagnetic
field2006)] doi:10.1103/PhysRevLett.94.102301
Ed., Pergamon Press, 1969.
the experimental
data.
which could make this measurement difficult. Similarly
ation
times
were
sizeablydi↵erent,
one Theory
would
estimate
079].
[29] A. Vilenkin,“Quantum Field
At Finite
Tempern, “PolarizedPACS
secondaryparticlesin25.75.Gz,
unIn A Rotating
System,”D 21, 2260
difficult will be the detection of the global polarization
thermalvorticity
andaturemagnetic
field
fromPhys.
the Rev.
measurednumbers:
25.75.Ld,
05.70.Fhh energy hadron-hadron collisions?,” nucl(1980). doi:10.1103/PhysRevD.21.2260
with the help of other strong decay channels, e.g. propolarization (see SectionVI) attimes
thepro[30] F. Becattini
anddi↵erent
L. Tinti, Annals
Phys.in
325,
1566(2010)
t al. [STAR Collaboration],“Globalpolardoi:10.1016/j.aop.2010.03.007[gr-qc]].
posed in Ref. [41].
I. cess.
INTRODUCTION
The magnetic
momentsof particles[arXiv:0911.0864
and antipartiS.A. Voloshin

Azimuthal distributions relative to the RP
STAR

~
L

For the technical reasons (correction for theBBCfinite RP resolution, treating acceptanceeffects,etc.) it is easier to perform the analysis
Ĵ sys in ! *pp θ *
azimuthal space

p~⇤

cos

✓⇤

⇤

= cos ✓p sin(p)

quark-gluon
plasma✓pp~projectilepΛ

forward-going
beam fragment

eterbeam direction

pa

ct

pa

ra

m

~b
im

⇤!p+⇡

Figure 3: A sketch of the immediate aftermath of a Au+Au⇤ co
8 hsin( 1p )i
PH The= average vorticity points alongs
at midrapidity is suggested.
⇡↵
Res( 1 )dN / 1 + ↵ P cos ✓⇤H Hd cos ✓⇤
tum of the collision, Jˆsys . This
direction
estimated
experimSTAR,
PRC76, is024915(2007)

8 forwarddeflection
theandbackward-going
fragments an
PH = of⇡↵
hsin(
)i
RP
p
T. H
Niida, QCD Chirality Workshop 2017
hyperons are depicted as spinning tops; see text for details. O
are not drawn to scale: the fluid and the beam fragments havethe radius of each BBC is about one meter.
frame, thenpage 27

Tsukuba Global Science Week, Tsukuba, Japan, September 28, 2017⇣
dN
1
S.A. Voloshin=
1 + aH |~PH | cos q

Azimuthal distributions relative to the RP
STAR

~
L

For the technical reasons (correction for theBBCfinite RP resolution, treating acceptanceeffects,etc.) it is easier to perform the analysis
Ĵ sys in ! *pp θ *
azimuthal space

p~⇤

cos

✓⇤

⇤

= cos ✓p sin(p)

quark-gluon
plasma✓pp~projectilepΛ

forward-going
beam fragment

eterbeam direction

pa

ct

pa

ra

m

~b
im

⇤!p+⇡

Figure 3: A sketch of the immediate aftermath of a Au+Au⇤ co
8 hsin( 1p )i
PH The= average vorticity points alongs
at midrapidity is suggested.
⇡↵
Res( 1 )dN / 1 + ↵ P cos ✓⇤H Hd cos ✓⇤
tum of the collision, Jˆsys . This
direction
estimated
experimSTAR,
PRC76, is024915(2007)

8 forwarddeflection
theandbackward-going
fragments an
PH = of⇡↵
hsin(
)i
RP
p
T. H
Niida, QCD Chirality Workshop 2017
hyperons are depicted as spinning tops; see text for details. O

K ⇤0 ! ⇡ + K! K + K+

page 27

dN / (1d cos ✓⇤

not drawn to scale:2the ⇤fluid and the beam fragments have⇢00 ) +are(3⇢1) cos ✓00
the radius of each BBC is about one meter.

⇢00 frame,= 13 then 83 hcos[2( ⇤pTsukuba Global Science Week, Tsukuba, Japan, September 28, 2017RP )]i⇣dN
1
S.A. Voloshin=
1 + aH |~PH | cos q