独断と偏見で選んだ、最近のフローなどのソフト測定

新井田

貴文

（筑波大学）
QCD相転移やQGP生成のモデル化による重イオン衝突の時空発展の理解に向けた理論・実験共同研究会 ＠オンライン, 9/24/2021

粒子の集団運動（フロー）Niida and Miake AAPPS Bulletin(2021) 31:12

shaped distribution is simply expected from the overlapof two colliding nuclei when collisions are non-central,with the shorter dimension of the almond shape alignedwith the reaction plane. As a result, elliptic flow canbe interpreted as a result of medium expansion driven
by the asymmetric density profile. More precisely, gradients, which play the role of force in hydrodynamics, areanisotropic in- and out-of reaction plane, leading correspondingly to an anisotropic expansion. This expansion scenario has been justified by the similar expansion
out of an anisotropic medium system realized in the cold
atom experiments [48]. The key in this relation is theazimuthal structure of the initial distribution, which isasymmetric between in- and out-of reaction plane, analogous to that of elliptic flow. The extent of asymmetry is
characterized by a dimensionless quantity called ellipticity. With respect to the reaction-plane, it can be definedasnnformations induced by the extra fluctuations. A generalization of ellipticity to higher orders can be applied,which provides a mode decomposition with respect tothe azimuthal asymmetry of the initial state geometry.
If one takes the complex expression z = x + iy = rei forthe transverse coordinates, a standard generalization of
the n-th order eccentricity is defined in terms of the n-thorder moment of the density, as

Page 4 of 14

En ⌘ " n e

in n

=

{rn ein },{rn }{z n }={|z|n }

n > 1 , (16)フローは粒子の集団運動を表す。初期の空間異方
where {|z| } in the denominator plays the role of normaln

ization. The minus sign is conventionally taken so that
En is potentially aligned with respect to Vn , although thealignment is often broken due to the complexity induced
from the medium response. It can also be understood asa Fourier decomposition of the energy density in termsof azimuthal angle , with a rn -weight corresponding to
the fluctuation modes along the radial direction. For thecase of n = 1, since {z} vanishes by a re-centering of thedensity profile† , the non-trivial leading contribution is

性・密度揺らぎに対するシステムのレスポンス

momentum anisotropy called the elliptic flow. An important feature of the elliptic flow is that it is sensitive to the ε ∝v 。反応平面と粒子の相関とも言える。
{x y },(14)" =early stage of the collisions. Since the hot and dense region{x + y }where the curly brackets denote the average with respect
expands more in plane, the spatial anisotropy disappears 生成粒子の方位角分布のフーリエ係数で表される{r e }{z z }
to the initial state energy (or entropy) density distribu=,(17)
E ⌘" e =tion,{|z| }{r }quickly as it expands.
R‣ v1: directedflow,which captures a dipolar structure in the initial energy
dxdye(x,y) . . .指向型フロー
R
{.
.
.}
=
.
(15)
Experimentally, the azimuthal distribution is evaluateddensity. E is the dipolar anisotropy, which is rapiditydxdye(x, y)even. Note that in Eq. (16), E is complex with its mod‣The
v2reaction-plane: ellipticellipticity
flow," 楕円型フロー
is bounded by unity.
ule " characterizing the magnitude of asymmetry, whilein terms of a Fourier expansion [35],
It is clear that the elliptic asymmetry vanishes whenits phasedefines the orientation. The phaseis"= 0, corresponding to a density profile with absosometimes referred to as the participant plane of the!
#fluctuate from event toluteazimuthalsymmetry. Elliptic
asymmetry maximizes
initial state. Both " and‣v:triangularflow∞
3
event in heavy-ion collisions as the density profile flucwhen " = 1. To a good approximation, a linear rela"
d3 N
d2 N
tion between the ellipticity and v has been found [49].
tuates. Again, by definition in Eq. (16) and Eq. (17),E 3 =1+2vn cos(nφ) ,(2) ‣ vWhen
4, vevent-by-event
5, v6… fluctuations are taken into ac- E is bounded by unity, with a vanishing E indicatingd p
2π pT dpT dy
a vanishing n-th order anisotropy, while a maximized
count, the initial state geometry in heavy-ion collisions
RP
2

2

2

2

2

1

1

i 1

2 ⇤

3 i

3

3

1

n

RP
2

n

n

n

RP
2

n

n

RP
2

2

n

n=1

where φ is the azimuthal angle of produced particles with
φ: 粒子の反応平面（あるいはイベント平面）からの方位角
respect to the reaction plane. The second-order coefficient v2 quantifies the strength of the elliptic flow.
The top panel of Fig. 6 shows elliptic flow v2 for pions,
kaons, protons, φ, #, and $ in mid-central Au+Au col√lisions at 理論・実験共同研究会
sNN = 200 GeV [36–38]. In pT < 2 GeV/c,T. Niida, 重イオン衝突

depends not only on the background shape, but also de-

E1

E2

E3

n

anisotropy is achieved when |En | = "n = 1.

L. Yan, CPC42,042001(2018)

E4

E5

Fig. 2.
Characteristic shapes of the deformed initial state density profile, corresponding to anisotropies of E1 , E2 ,E3 , E4 and E5 (from left to right).

2

n η. The implementation of thisod. For the event plane method,
wo subevents. For the cumulant
p in η between all consideredults which are consistent within

data.

楕円型フロー vs. 衝突エネルギー
VI. FEMTOSCOPY OF PIONS

Two-particle correlations at low relative momentum canbe used to extract information on the space-time structure

ptic flow v2 as a function ofSTAR, PRC103, 034908 (2021)− m for pions and protons obRotating
systemprojectile-target
method,where
m isofmass
andCollective flow(v2>0 at √sNN <1.4 GeV)

W. Reisdorf et al.

e mass. It is compared to E895
pressure-gradient-driven expansion
e same method. We analyze the
Au + Au 400A MeV 0.25 < b0 < 0.45
(v2>0 at √sNN >4 GeV)or pions and protons, we require(v2<0)
use “squeeze-out”
tracks with 0.2 emission< pT < 2.0√
ptance in FXT mode at sNN =ly protons with higher values of(see Fig. 6). The proton resultsts [45].
IQMD
e divide v2 and mT − m (Fig. 12)
quarks (three for protons andare presented in Fig. 13. The
mber of constituent quarks at 4.5
Preliminary
bserved for Au + Au at higher
FIG. 14. The excitation function v2 for all charged particles orf thedata createdis correcthesystemfor and
Au +theAumodelseparately for protons and pions, measured by several experiments.
surprisingly,
larger confirmed
collecshaps
correct→ soft EOS
The STAR v
FXT
points for protons and for pions are near the region
楕円型フロー2の符号は、エネルギーを変えていくと、２回変わる。
e is no significant difference inwhere a change in slope occurs. Data are shown from FOPI [48,49],BUT
w behavior
whentoE895 [45], E877 [50], CERES [51], NA49 [52], PHENIX [53],Stopping
andflowcomparedcorrelated
n
Fig.
13
are
in
possible
conflict
PHOBOS [54], and from the STAR collider energies [46,47,55–57].
3
T.
Niida,
重イオン衝突理論・実験共同研究会
Consistent description required

Number of Constituent Quark (NCQ) スケーリング
5

LOW OF IDENTIFIED HADRONS IN Au + . . .

PHYSICAL REVIEW C 88, 014902 (2013)

STAR, PRC88, 014902 (2013)v2/nq

STAR, arXiv:2108.00908
3

Au+Au Collisions (10-40%)

0.08

0.04

27 54.4 (GeV)

π

0.08

200
54.4
27
14.5
7.7

0.06

v2/nq

v2/nq

[40]
(a) and Ultra-relativistic Quantum Molecular
11.5 GeV
19.6 GeV
0.1 7.7 GeV
Au+Au, 0-80%
mics (UrQMD)[25, 26], are also given for the abunη-sub EP++
producedhadrons ⇡ , K , p, and ⇤. The results
0.05
he cascade and baryonic mean-field modes of the0
and UrQMD model are shown as colored bands.
39 GeVkinematic selection
62.4 GeV
me collisioncentrality andcri0.1 27 GeV
s in the data are applied in the model calculations.
0.05
m the top panels in Fig. 2 the strength of the radependenceof v1 is shown to be proportional to0dron mass.
The
valuesofthemidrapidity
slope,
0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 22-m0)/nq (GeV/c) protons andford as dv1 /dy|y=0 , are the(mTlargest
(b)
panel
(a),
and
are
close
to
zero
for
pions
in
panel
11.5 GeV
19.6 GeV
0.1 7.7 GeV
0-80%
panel (c),Au+Au,dv
ηNCQスケーリングが成り立つことが-sub EP1 /dy|y=0 are positive and have small
0.05
dependence
amongkaons.
The
JAM
and
UrQMD
パートンレベルでの集団運動を示唆。
field calculation
includesaSkyrmepotential
energy0
y function [30]. Comparing to the cascade mode,
27 GeV
39 GeV baryons are
62.4 enhanced
GeV
0.1
pulsiveinteractions
among
T. Niida, 重イオン衝突 理論・実験共同研究会

K
p

0.06
0.04

0.02

0.02
(a) Positive particle(b) Negative particle

0

0

−0.02

0.02
0

0.2

0.4

0.6

0.8

0

0.2

0.4

0.6

0.8

2

(m - m0)/nq (GeV/c )T

3 GeVでは、”粒子”のNCQスケーリングが成り立たない。
FIG. 3. v2 scaled by the number of constituent quarks,
パートンではなく、バリオンが支配的。
v2 /n
q , as a function of scaled transverse kinetic energy
)/n
)
for
pions,
kaons
andprotonsfrom
Au+Au((mπT+: Δ m0qresonancepcollisions
in 10-40%
centralityofatΛ sNN = 3, 27, and 54.4 GeV
K+: associatedproduction
for p:
positivechargedparticles(leftpanel)
andnegativechargedspectator proton contribution
4
particles (right panel). Colored dashed lines represent the

3% for v1 and v2 , respectively. Assuming the sources areuncorrelated, the total systematic uncertainty is obtainedby adding uncertainties mentioned above in quadrature.

モデルとの比較STAR, arXiv:2108.00908
(a)

v1

0

0.2
p

Λ

0.4

Au+Au Collisions
sNN = 3 GeV 10-40%
π+ π-

0.2

Y. Nara et al., PRC61, 0249021 (1999)
S. Bass et al., Prog.Part.Nucl.Phys.41, 255 (1998)

v2

−0.5

p
Λ

−0.5

+

K

0.4

0
(d)0.04(e)0.04

0.02

0.02

0

0

0.02

0.02

0.04

0.04

0.06

JAM

UrQMD

0.08 Baryon-Mean-field Cascade
0 −1
−0.5

π+

-

K0S

K

0.4 < pT < 1.6 GeV/c

0.2 < pT < 1.6 GeV/c

0.4 < pT < 2.0 GeV/c

0.04 −1
0.02
0
−0.02
−0.04
−0.06
−0.08
−1

0

JAM: JET AA Microscopic Transportation ModelUrQMD: Ultra-relativistic Quantum Molecular Dynamics

0

−0.2
−0.4

(c)

(b)

(f)

0.06

K+

0.08

0

−1

−0.5

0

Particle Rapidity y
Baryonic mean-fieldを取り入れたモデル計算（JAM、UrQMD）は、定性的に実験データを再現。

FIG. 2. Rapidity(y)dependence
ofv2vなども）は再現できていない。
+ v2（π v1やΛ
1 (top panels) and v2
ただし、K(bottom
panels)ofprotonand⇤baryons(leftpanels),piT. Niida, 重イオン衝突 理論・実験共同研究会

5指向型フローv1
１次相転移に敏感な量としてv1は測定されてきた。

Λ, ΛH _l b ΛH t / +Qjmnc t q, N_prgaj

5
最近は、”even”成分、初期の”tilt”、電磁場の効果、coalescenceの研究がされている。

STAR,
PRL120,062301(2018)
0STAR, SQM2021/ ' U grf gl qr_rgqr

0

−0.05
−0.1

−0.01

qjmncqmdt / dm

−0.15
7

8 9 1020

H qcck dmj

−0.02

y =0

−0.03

dv 1 / dy |qa_jgl e gl rf c
amjjgqgml q9
0' ? l _jwqgqmdqw
sl bcpu _w9

10 - 40% Au+Au
Λ (uds)−0.04

K− (us) + 1 p (uud)3(a)

6 7 10

20 30

0.04

100

net Λ

200

net p − 1 p + s
3
net p − 1 net p + s
3−(s = K − 1 p)
3

0.02

0
(b)

10

sNN (GeV)

T. Niida, 重イオン衝突 理論・実験共同研究会

102→ Am_jcqacl a
npmacqqdmp f w
d
m
pk
_rg
m
l
g
l
r
”輸送クォーク"と"生成クォーク"に基づくcoalescence sumルール
ハイパー核を含む原子核のdv1/dy vs. 質量。
Af cl js F s/ 7RF Qrp_l ecl cqqgl Os_pi K _rrcp* K _w / 5 ç 00* 0.

ハイパー核生成プロセスはcoalescenceが支配的。

6

geo

TABLE II. Systematic error estimates 3.foin Fig. 20. First row considers using a 2–12
Fixed Target
2 cuts, 2fitT
hkT i ⇡
0.22 GeV/c
a 0–10% 0-5%
selection.
Track-merging
First
measurements
of
R
−
R
out
side
8
E895
labo
Coulomb
effectsarediscussed
in[57,78].
highest energies at RHIC [57,67] wereSTAR
E89
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STAR Collider

Figure 19 shows Rside vs. Rlong for several different data
+ +
STAR,
PRC103,034908sets. STAR FXT
and BESpoints use
low-kT , π(2021)
π and

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81.2

STAR Fixed Target
E866

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10

E895

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Lisa et al.
!4

HADES

<latexit

M. S. ABDALLAH!2 ET AL.

Central Collisions

low
2%
50 MeV/c variation in ⟨mT ⟩geometric size varyingof the initial
fit participant
range in region|q| and the subse- <boo
1%
⃗
fixe
quent emission region at freezeout.
varying track-merging cut
4%
sour
side
2. Evolutiontreatment
from oblate toof
prolatefreezeoutconfiguration REVIEW
Coulomb
effects
1%
PHYSICAL

Rside (fm)0

R2out-R2side (fm2 )Rout /Rside

Femtoscopy

2

Rout /Rside

sured at lower energies, contrary tothats
Rout
6
exp)
sourceδ(
7long lifetime [58,87]. This “puzzle”Rside[87
for2.70 GeV
1.1
understoodas arising from a number
4
thiso
z
variation in centrality
1%
atic
cations
that
tend
to
reducetheextende6
2%
50 MeV/c variation in ⟨mT ⟩trea
2
Figure20
suggeststwoother
2.76 TeVreasonsund
2.4 GeVvarying fit range in |q< 1%
Central Collisions⃗|
rang
observed.
Firstly,theenergyofcollisio
0 1
HADES
varying
track-merging
cut
4%
√
In a
4.5
GeV
5
=Coulomb
200 GeV)
may be too1%
hig( sNN of
200 GeVE895
acce
treatment
effects!2
STAR Fixed Target
zcom
energy for QGP formation; at such high11.5 GeV
E866
corr
lifetime
signalispredicted
todisappe!4 0.9Collider4tainSTAR Collider
because particles with heavier masses have smaller thermal velocities,
early femtoscopic data fromE895 andSTAR
to aE
rce volumes
are more strongly confined by collective flow. For longitudiRlong: ビーム軸方向のHBT半径
mos
2
ALICE
precisetodiscernthepeak
revealed
by
2
2
1
10
10
(left panel) this results in smaller values of Rlong for particles with higherway
4 First measurements
5
6
7 of Rout
8 − Rside a!
The STAR low energy measurements
Rout2 : ペア横運動量方向のHBT半径+粒子放出時間
are
1.2
s
(GeV)
R
(fm)
2
NN
long
highestenergies
at
RHIC[57,67]
weresI
m + pT . For radial flow (right panel) this confines heavier particles
sue.
Indeed,theentireSTAR
fixed-tar
Rside: RlongとR
outに直行する方向の半径
at lower
contrarythe to som
he surface,which
results
in both a reduced volume and an oﬀset ∆r in
is re
FIG. 19. sured
Rsidefor identifying
vs.
Rlong , energies,which
measuressuch energy-dependent2
FIG. 20. Top: The difference between the squared transverseR
ard direction.
outprolateness/oblatenessof the pion
emitting source
viewed [87]long lifetime[58,87].
Thiswhen“puzzle”
pion
from forbeside the beam. HADES [76], ALICE [77], and STAR
femtoscopic 1.1
radii are plotted as a function of the collision energy
understoodasarising
fromanumberof[80][78]
pointsincludesystematic
errors;
E895
[65]
show
statistical
20
GeV付近でR/Rのピーク。EOSのsoftest
point？
outBottom:
side The energy dependence of the ratio of thecentralzero-rapidity particles is determined by the distance one
can collisions.
move beativ
errors only. STAR
fixed thattarget data
correspondto pion thepairs extendedwithcationstend
to reducesysttransverseradii. The centrality and mT values for the high-statistics
TheSUMMARY
various⟨kT ⟩ = 0.22 GeV/c from 0–5 % centrality events.
VII.
collective velocity overwhelms the thermal velocity to force
the emission
Figure20 usedsuggests
two otherreasons
th
ary
,
and
k
cuts
in
the
different
experimentsarecentrality,pTTback to zero. The size can then be expressed as:4.5 GeVは（π中間子の）放出領域が“oblate”から”prolate”シェイプへ変化する中間点。
datasets are HADES [76] (0–10 %, 349 MeV/c); STAR fixed targetthediscussed in observed.
the text.In
Thethisgrey
curve
indicates
theresults
evolution
the fixe
Firstly,theof
energyofoffrom
collisions
1
first
set
√ energy is increased.
(this work) (0–10 %, 303 MeV/c); STAR collider [78] (0–10 %,326
calc
shape,
as the collision
Vtherm
s
=
200
GeV)
may
be
too
high
(
STAR
experiment,
wereportthattheNN
Rlong ≈= Vtherm ⟨t⟩.
(24)
MeV/c).
The
valuesfortheearlier
measurements
are
E895
[65]
(0–
dv/dz
7 e
energyfor
QGP
formation;
at
such
high
034908-13
protonsand"baryons
is
in
line
with
T. Niida, 重イオン衝突 理論・実験共同研究会
11 %, 330 MeV/c); E866 [66] (0–15 %, 295 MeV/c). Only statistical
HADES

カイラル磁気効果(CME)の探索~J / (Qe)µ5 B~
CMEは、磁場方向に電流が流れる現象(masslessクォーク物質＋カイラリティインバランス＋強磁場)同重体衝突 Ru+Ru vs. Zr+Zr‣ 同じ質量数、異なる電荷 (陽子数)‣ Ru+Ruの方が、10-18% 初期磁場が大きい‣ ほぼ同じ大きさなので、v2などによるBGが同じで、CMEシグナルだけ異なる

T. Niida, 重イオン衝突 理論・実験共同研究会

8two centrality columns are the actual centrality ranges which are slightly di↵erent because of integer edge cuts used for theo✏ine
i values, the mean number of participants (hNpart i), and the mean number ofcentrality determination. The mean hNtrko✏ine
i are all significantly smaller than 0.01. The
binary collisions (hNcoll i) are also listed. The statistical uncertainties on hNtrk
uncertainties on hNpart i and hNcoll i are systematic.
Centrality
Ru+Ru
Zr+Zr
o✏ine
o✏ine
o✏ine
o✏ine
hNtrk i hNpart i
hNcoll i Centrality(%) Ntrk
hNtrk
i hNpart i
hNcoll ilabel (%) Centrality(%) Ntrk
0–5
0–5.01258.–500. 289.32 166.8±0.1 389±100–5.00256.–500. 287.36 165.9±0.1 386±105.01–9.94 216.–258. 236.30 147.5±1.0
323±55.00–9.99 213.–256. 233.79 146.5±1.0
317±5
5–10
9.94–19.96 151.–216. 181.76 116.5±0.8
232±39.99–20.08 147.–213. 178.19 115.0±0.8
225±3
10–20
I. The Woods-Saxon parameters
used
in
the
Glaubersimulationsforthecentrality
determination.
19.96–30.08 103.–151. 125.84
83.3±0.5146±220.08–29.95 100.–147. 122.35
81.8±0.4
139±2
20–30
69.–103. Case-2
85.22
58.8±0.3
89.4±0.9
29.95–40.16
30–40
Case-130.08–39.89
[83]
[83]
Case-3[113] 65.–100. 81.62 56.7±0.3 83.3±0.8
39.89–49.86 44.–69.
55.91
40.0±0.1 53.0±0.5 40.16–50.07 41.–65.
52.41
38.0±0.1 48.0±0.4
40–50
R (fm)a (fm)
R (fm)a (fm) 25.–41.
Nucleus R (fm)249.86–60.292 26.–44.
25.8±0.1 2 29.4±0.2
50.07–59.72
32.66
24.6±0.1 26.9±0.2
50–60 a (fm)
12 34.58
96
60.29–70.04
15.–26.
20.340.46
15.83±0.03
15.6±0.1
59.72–70.00
14.–25.
19.34 15.10±0.03 14.3±0.1
60–70 0.46
5.085
0.158
5.085
0.053
5.067
0.500
0
44 Ru
70.04–79.93
8.–15.
11.47
9.34±0.02 8.03±0.04 70.00–80.88
7.–14.
10.48
8.58±0.02 7.12±0.04
70–80
96
the half-maximum
point of5.02
thegiven0.46
V19.96–49.86
equal
to5.02the 89.500.46
0.08
0.21796.7±1.0
4.96520.08–50.07
0.556 41.–147.
0z,tpc bin
20–50
44.–151.
60.9±0.385.68
58.9±0.3 90.3±0.9
40 Zr

ibutions are both calculated, and the overall size of Ru is found to be smaller than Zr because of aer neutron skin in the latter. The nucleon distributions are found to be well parameterized by thetributions (i.e. the neutron a parameter is significantly larger than that for the proton) [113].

粒子多重度と楕円型フロー

different non-flow contributions
0.08

0.08

STAR Isobar blind analysis√sNN = 200 GeV

0.06

0.06

Glauber Case-2

0.9

50

GlauberNtrk= npp [(1x)N0 part /2 + xNcoll ] ,Efficiency uncorrected tracks(|η|<0.5)

1.1

0.02

Ru+Ru
Zr+Zr

(6)

Ru+Ru / Zr+Zr

1.12

Ru+Ru

v2{EP}

v2{EP}v2{2}v2{SP}(∆ηsub=0.2)v2{2}v2{SP}(∆ηsub=0.2)

v2{2} (∆η>1)v2{2}(∆η>1)v2{SP}(TPC-EPD)

v2{SP}(TPC-EPD)

1

0

10

0

Zr+

v2{

v2{

1.1

TPC (|η|<1)
EPD (2.1<|η|<5.1)

1.05
1

1

n

(n +0.98k)80 70 60(npp
/k)
50
40
30 , 20·(npp , k;
PNBD200
100300n) =
400
n+k
Centrality
(%)
(n
+
1)
(k)
(1
+
n
/k)
pp
Nofflinetrk

0.02

Ru+Ru / Zr+Zr

Ratio

Ratio

Ratio

0.9

0.04

0

Ratio (NN) collisions, and x is the0verage pseudorapidity multiplicity density 1.1
in zero-bias nucleon-nucleon
on to 1.05
multiplicity from hard processes. The
1.1
1.08 multiplicity given by Eq. (6) is the average multiplicity.
Glauberuations 1are taken into account in the following
way. Ntrk
is considered to be accumulated by
1.06
1.04 NN collisions. In each NN collision, the multiplicity n 1.05
xNcoll (that Ru+Ru/Zr+Zr
is rounded to the closest integer)
0.95
1.02
Datanegative binomial distribution
nvolutionof the(NBD)
Glauber Case-3

v2

Zr+Zr

Ratio

〈 NtrkRatio

offlinev2〉

s we use STARthe Isobar
simpletwo-component model for
multiparticle
production[117]. Several alternablind
analysis
STAR
Isobarblind
analysis,
√s
=
200
GeV
1.1
NN
300
f multiparticle
production
have
been
developed
overtheyears,
such as Quark-Glauber [118], IP√sNN = 200 GeV
Efficiency uncorrected tracks (|η|<0.5)
250 improve the two-component model. These approaches
1.05
ento [120]and Shadowed Glauber [121], that
0.04
200 work we stick to the two-component nucleon based MC
d in future STAR analyses – for the current
1
r simplicity. The multiplicity density at a 150
given b, with the corresponding Npart and Ncoll from the
Ru+Ru/Zr+Zr
100
on for0.95
each setof the WS parameters, is parameterized
by the two-component model [117] as:
Data

(7)
80

70

60

50

40

30

20

10

0

80

70

60

Centrality (%)⌦ sharpness
↵
o✏ine
mma
function
the fluctuation
parameter
kmean
controls
theof the large multiplicity tail) from
the TPC inandthe pseudorapidity
acceptance|⌘| < 0.5
trk
FIG. 3. (Upper)
The efficiency-uncorrected
multiplicity N
from the TPC within |⌘| < 0.5 as a function ofllisions. The experimental distributions
beenandcorrected
centrality inhave
Ru+Ru
Zr+Zrforcollisions. The centrality bins are shifted horizontally for clarity. (Lower) The ratio of
stribution.
nd uncorrected
for tracking efficiency.
Fits to the inexperimental
the mean multiplicity
Ru+Ru collisions to that in Zr+Zr collisions in matching centrality. The points include statistical
同じ中心衝突度で~4%程度の粒子多重度の違い。
v2（BG）は~3%程度の違い。
FIG. 4. (Left)
Elliptic anisotropy v2 measurements using di↵erent methods in iso
ultiplicity
distribution
thisthen convolved with a binomial distribution to accountent Glauber modelusing two uncertainties
sets ofobtained
Woods-Saxon
parametersin issize.
that arein
withinthewaymarker. The Ru+Ru to Zr+Zr ratio of the experimental data, as wellfunctionof centrality using TPC and EPD detectors. In the upper panels, the solid anefficiency
andacceptance
of
the
TPC.
The
net
e↵ect
depends
on
the
TPC
hit
occupancy
andisshown in the upper right andThe
lower
right panels,
centralityof anrespectively.
event is defined by the percentile of the total cross section. The integer edge cuts are madefor Ru+Ru and Zr+Zr collisions, respectively. The data points are shifted along the
Glaubero✏inemetersis used forin
centrality
determination
as it[108].
providesthebest
so that the integralsof theNtrk
distributions
woulddistribution
be closest to the is5%thenor 10%fitted
mark. Forcentrality
to thethe0–20%experimentalarfunction
the multiplicity
The
final
Ntrk
the v2 ratios in Ru+Ru over Zr+Zr collisions. The statistical uncertainties are represeinterval the experimental data are used for integration, while the MC Glauber distributions are used for the remaining
on, with npp , k, and x as fit parameters. The fit is performed simultaneously for Ru+Ru and by
Zr+Zr
9 us
boxes. (Right) The same showing measurements for four particle correlations
T.
Niida,
重イオン衝突理論・実験共同研究会o✏ine
fit parameters
beZr+Zr
commontributions
P (N) forcedin Ru+Ruto
andcollisions.for
Theboth isobars. Since the peripheral collisions are a↵ected by
o✏ine
trk

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( v/v
2 2)
0.92
>
1
Predefined CME signature:
Ru+Ru / Zr+Zr
Zr+Zr( background/v2 )the trivial scaling expected from a purely
scenario. The flowing-resonance picture canbe (SE)Group-2<latexit

the conventional

112 = hcos( ↵ +112

ベースライン（ratio=1からのずれ）を理解する必要ある。

T. Niida, 重イオン衝突 理論・実験共同研究会

112 = hcos( ↵ +222 )i ,OSSS= 112
are the azimuthal angles of particles
of
112interest (POIs) and

,
Ru+Ru

Ratio (∆γ/v2)

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A.

Ratio (∆γ/v2)

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is the second-order flow plane.
0.92
Ru+Ru / Zr+Zr
and 2 , respectively.
scripts “1”,“1” and “2” in 112 refer to the harmonics associated with the ↵ ,Group-1 (EP)he flow plane is approximated with the EP ( EP ) reconstructed with 0.88
measuredparticles,the(3PC)
Full-TPC(|ηα,β,c|<1) and thenGroup-2
OS Group-3
SS (3PC)
0.2<
p
<
2
GeV/c
粒子が反応平面から±９０度方向に放出するとT
is corrected for the finite EP resolution [125]. The charge-dependent backgrounds in
112 = 112
112
y understood using the exampleOSof= resonancedecays.
hcos(90 90 +0)i = +1If resonances from1.04 the event exhibit elliptic flow,ughters could mimic a signal forSScharge
separation
the flow plane with a magnitude proportional= hcos(90+ 90 + 0)i =across1151]. Therefore, following Eq. (4), one should study the normalized quantity<latexit

nalysis, for which a magnitude of high significance must be observed for an affirmative observation of

γ-correlator
and mixed harmonics with second and third order event planes
1.04

correlator(Eq. (2))
with a more specific notation,
S. Voloshin,
PRC70.057901(2004)
STAR Isobar blind analysis, √sNN = 200 GeV

1

0.96

(8)

2

0.96

(9)

Group-3 (SE)0.88
a larger portion of the event, or even the full event, through the mechanismsof transverse momentum
Group-4 (SE)
(TMC) [38, 126] and/or local charge conservation (LCC) [51]. In the case of thecorrelator this
事前に定義したCMEシグナルは観測されず。
80
70
60
50
40
30
20
10
0
an be written as
TPC sub-event (∆ηsub=0.2)
0.2< pT < 2 GeV/c

Centrality (%)

2 )iFIG. 5. Ru+Ru over Zr+Zr ratio of the primary CME-sensitive observable10/v2 estimated using dIsobar CMEのサマリープロット
compilation of all results
1.02

39

predefined CME signature: ratio>1

STAR Isobar post-blind analysis, √sNN = 200 GeV, Ru+Ru / Zr+Zr, 20-50%

Ratio

1
0.98

(∆

e

trk fflin

up

-3
1/
No

G

ro

in
v)

r(m -5

G 2
ro
up

Ψ

R

σ -1

ro 3
up
-2

k

G

ro 2
up
-2

k

G

11

κ

G

2
p-

γ

ou

11
2 /v
2)
(∆
EP
γ
,T
11
P
2 /v
G C
ro
2)
up
-1
(∆
3P
γ
C
,T
11
P
2 /v
G C
ro
2)
up
-2
3P
(∆
C
γ
,T
11
P
G C
2 /v
ro
up
2)
-3
(∆
SE
γ
,T
11
P
G C
2 /v
ro
up
2)
-2
(∆
SE
γ
,T
11
P
G C
2 /v
ro
up
2)
-3
(∆
SE
γ
,T
11
P
G C
2 /v
ro
up
2
)
-4
(∆
S
γ
P,
12
EP
3 /v
G D
ro
3)
up
-2
3P
C
,T
P
G C
r

0.94

ro 2
up
-1

0.96

STARは５グループによるブラインド解析により、アイソバーにおけるFIG. 27. Compilation of post-blinding results. This figure is largely the same as Fig. 26 with the following di↵erences: numericalchanges in the results from the new run-by-run QA algorithm are treated as an additional systematic uncertainty added inquadrature, and two data points (open markers) have been added on the right to indicate the ratio of inverse multiplicitieso✏ine) and the ratio of relative pair multiplicity di↵erence (r) as explained in the text.
(Ntrk

CME探索を行ったが、”事前定義”したCMEシグナルは見えなかった。
粒子多重度の微妙な違いによって、ベースラインの変化（Ratioが１以
VI. POST BLINDING
下）が見られるので、その理解に向けて現在調査中。

Duringthe second step of our analysis (the isobar blind analysis) a potential issue was identified related to theT. Niida, 重イオン衝突
理論・実験共同研究会

11ハイペロンのグローバル偏極
STAR, arXiv:2108.00044

L12P ⇤ (%)

3FD
UrQMD, |~!th |/2
AMPT
Chiral Kinetic
UrQMD+vHLLE

10
8

¯
⇤ ⇤

beam fragment

6→L方向にスピンが偏極”グローバル”偏極と呼ぶ。

T. Niida, 重イオン衝突 理論・実験共同研究会

10

HADES preliminary
Ag+Ag 2.4 GeV

p
STAR Au+Au 20%-50%
STAR
Au+Au,
sNN = 3 GeV
PΛ (7.7)=7.34± 3.02 [%]Nature548.62 (2017)
pT > 0.7 GeV/c, 0.2 < y < 1 ΛΛ
10↵⇤ = 0.732
PRC76.024915 (2007)
3FD
UrQMD, |~!th |/2
AMPT

8

4

10

2

−1

3

10

p

0

Λ

PRC98.014910 (2018)
ΛΛ

ALICE Pb+Pb 15-50%

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

1

2

Λ

PRC101.044611 (2020)
Λ
Λ

6

0

2

1

12

scaled using ↵⇤ = 0.7320

初期の軌道角運動量L32STAR 20-50% Au+Au, 2021
STAR 20-50% Au+Au, ’07-’18
ALICE 15-50% Pb+Pb

4

reaction plane

STAR, PRL126, 162301 (2021)
PH [%]P H (%)B

6

AMPT PRC99, 014905 (2019)
0
Λ +Λ
Ξ
Ω

10 0

αΛ = 0.732 ± 0.014
α = -0.758 ± 0.012ΛαΞ- = -α + = -0.401 ± 0.010
γ =1 Ξ
Ω

10

102 2030 103sNN (GeV)40

50

sNN [GeV]

Centrality (%)

p

FIG. 3. Global hyperon polarization as a function of sNN
FIG. 4. The centrality dependence of P ⇤ is comparedin mid-central heavy-ion collisions. The trend of increasing
with hadronic and partonic transport[20], and three-fluidp
グローバル偏極は理論予測通り、3
GeV付近で最大値をとりそう。
P H withdecreasing sNN is maintained at the low energyhydrodynamic[40] calculations at impact parameters of 8 fm.
pof sNN = 3 GeV. Statistical uncertainties are represented
Statistical uncertainties are represented with lines while sysΞ(spin-1/2)やΩ(spin-3/2)の偏極測定が出始めている。
with lines
while systematic uncertainties are represented withtematic uncertainties are represented with boxes.
boxes. Previous experimental results[9–11, 17] are scaled[5]using 今の所、（初期磁場による）粒子・反粒子に違いはない。
the currently-accepted[31] decay parameter ↵⇤ = 0.732.
p
Calculations with a hybrid model (UrQMD+vHLLE)[22] andpmeasurements at collision energies sNN
7.7 GeV,chiral-kinetic transport[21] are compared to the higher- sNN
12p

reproduces the measurement well at

sNN = 3 GeV.

ities, while central values for J/ are set to be 1/3. Note that for the J/yzmeasurement, STAR can implement High Tower (HT) triggers
with the Barrel
Electromagnetic Calorimeter, like what was done in the past. These triggers will
select an enhanced sample and let STAR take advantage of high luminosity in
2023-2025, even though STAR’s overall DAQ rate is limited. In the estimationof error, we have assumed that a similar DAQ bandwidth (⇠ 90 Hz) would bexallocated for the J/ data stream as was allocated in the year 2016 and 2011.
What is also shown are preliminary results of ⇢00 for and K 0 , along withthe projected error with an extra ⇠ 10B MB events. It is important to note
that, with extra statistics, the finite global spin alignment of K 0 can be firmly
Polarization
the beam
direction
established and studied differentially - (currently
thealong
integrated
significancefore
K 0 is at the level of ⇠ 4 ).
from the “elliptic ﬂow”
PHYSICAL REVIEW C 103, 024903

偏極測定における課題

方位角依存性surementsof PH

ラピディティ依存性
HYDRODYNAMIC STUDY OF HYPERON SPIN …

AMPT model
D. Wei, W. Deng, X. Huang, PRC99, 014905 (2019)2

0.4

Λ and Λ combined10.2

PH [%]

3

1

0.4

-

+

-

+

00

Projection(run2023)
Au+Au 200 GeV
further constrainttotheequation
of
state
of
the
hot
medium,Λ +Λ
Ξ +Ξ
0.35 of the hot medium [58].
especially the vorticalsusceptibilityΩ +Ω
Λ , geometric model
The
flow
Data of spin, f2 , is even in rapidity. It is negative,Λ , PICRelliptic
hydro
0.3
Λ
Λ
Ξ , AMPT
inconsistence with our numerical result in Fig. 9; However,Ω , AMPT
0.25
one should be noticed that the experimental
data shows a opposite trend for the FTSdependence of0.2Py in mid-rapidity region
which should result in a positive f2 . Again, this discrepancy
0.15
williTPCbe examined in future works.

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

Au+Au 20-50 %STAR preliminary|Y| < 1

STAR 200 GeV
19.6 GeV
Au+Au 200GeV
62.4 GeV
200 20-50%
GeV- STAR data indeed show such a longitud
AMPT-IC+ MUSIC hydroon azimuthal
angle (sine fun
B. Fu et al., depending
PRC103, 024903(2021)

BUR2020, STAR Note SN0755

PH [%]

0.6

Py (%)

PH(%)

4 B. Tu (STAR), ISMD2018

ビーム軸方向の局所渦6

T. Niida, SQM2021

0
-

0.5

φ (QM18, ~800M MB evts)

φ projected error (~10B MB evts)

0

0

*0

K (QM19, ~350M evts)

0*0

K projected error (~10B MB evts)

J/ ψ projected error [~200M HT evts (~20B MB equivalent) ∪ ~10B MB evts]

−0.2

-1
0

0.5

1.0
0.5

1.5

φ

2.0 1 2.5

1.5

φ-Ψ

1 [rad]

0

η

2

0

4

η

10

20

30

40

50

60
70
80
Centrality(%)¯
Figure 54: (Left) Projections (along with preliminary
data)
for
diﬀerential
measurementsof⇤(⇤Figure 1: ⇢00 as a function of centrality, with projected errors based on ⇠∗ subFIG. 6. Azimuthal
distributionof (a)
P−y and(b)⟨cos(θ p10)⟩ billion
in 200Aand
19.6A
GeVandAu +AuJ/collisions
20–50%
centrality.
polarizationovertheextendrange
ofpseudorapidity
with
the
iTPC
FTS
detectors
events.
The
centralvaluesforare set attoof
beSTAR
at 1/3(no spinlor online) The azimuthal angle dependenceof⇤and
0 STAR data are taken from Refs. [6,8].
is scaledtension
by a factorof 0.33 todiﬀerent
make thealignment),
comparison
moreThe(b),thatthe calculated
Pzresolve
where
forexplicit.
andK, the central
valuesby
forcurves)
future measurements
will
help
betweentheoreticalmodel
predictions(shownofdifferentialな測定を見ると、多くのモデルが実験データを再現できていない。
on in rapidity
region|Y | < 1 for Au
Au collisionsatare set to be their corresponding values in current preliminary analyses.
‣ Largerpolarization
in +peripheral
collisionsasexpectedpolarization with ⌘. In addition, projections for the measurements of spin-1/2 ⌅ and spin-3/2 ⌦nd 200 GeV. The experimental
data [6] is also shown.
局所渦に関しては、BWモデルは定量的に再現している。今も議論が続いている。
particles are also shown. (Right) Spin alignmentThe
co-eﬃcient⇢00 ofasglobal
a functionof centrality,withdifferential study
spin alignmentof and K 0 will
also benefit‣ Azimuthal dependence: discrepancy
betweendata
andmodelssignificantly
fromextra statistics
statistics.
large
momentumandthese
forwardhas
been
described
in
Sec.
II
A.
For
the
AMPT
initialcondemonstratethat AtPz Run-23,
has atransverse
similarstructureintwprojected errors based on ⇠ 10 billion
events.
Theenhanced
combinedwith30x
y rapidity, an anti-quark that combines with an initial polarized quark is createdditionwithout
initialflow,
wedirectlysetuparisonruns, as J/
shown
by the lower
panelsof Fig.
(τ)=
u(τ0enable)=0
theexcellent
dileptoncapabilities
of
STAR,
will
us
to
measurealignment
along
with
in the fragmentation process and may carry the information of the initial quark.
‣ Unknown rapidity dependence= 0beand exploredobtain the initial energy density ⇤0
as described
alsothemeansthat ofthelongitudinalvorticitytoPthatu ηs (τ0 ) toz mainlyThis
impliesthatpolarization
anti-quarkcanbecorrelatedof13
themeasurements.
increasing
thesignificance
of
the
and
K
T. Niida, 重イオン衝突 理論・実験共同研究会
in Ref. [61]. The initial flow directly influences the initial
the vortical structure developed during the hydrod

relatively large, and the results are rather inconclusive; below I concentrate on the discu
global polarization results.
FIG. 3 (color online). Directed flow slope
1 =dy) near
global(dvpolarization
results.
19.6 GeV-0.02
midrapidity versus beam energy for intermediate-centrality
Figure 3 shows a comp
Figure 3and
shows
0.02
Au+Au collisions. The slopes for protons, antiprotons,
π ' a compilation of published[3, 12] and presented at this conference [10on prior
the average
global polarization of lambda and anti-lambda
hyperons
at mid-rapidity
in
on
the
averageglobalpolar
are reported, along with measurements by
experiments
0[17,18] with comparable but not identical cuts.
Statisticalcollisions
as errorsa function of collision energy. The blue solidcollisions
and dashedas
lines
are the resulafunctionof(bars)
andsystematic
errors(shaded)areshown
separately.
-0.02
11.5 GeV
dynamic calculation [7, 13], with and without accountingdynamic
for the hyperon
feed-downcSTARcalculation
[7,
13
0.02
respectively.
The procedure for the feed-down correction is outlined in [6] with Eq. 1 used
informative. We define the slope Fnet-p basedon expressing
respectively. The procedur
L. ADAMCZYK et al.
PHYSICAL REVIEWC
98,
014915(2018)
0matepolarizationof the higher spinresonances.
Note thatthe 014915
e↵ect of(2018)
the feed-dow
for ofall theprotonsasL. ADAMCZYK et al. the rapidity dependence of directed flow
PHYSICALREVIEWC
98,
mate of the polarization of
6 Page 8 of 14
Eur. Phys. J. C (2015) 75:406
7.7 GeVis rathermodest
–
at
the
level
of
⇠
15%.
½v1 ðyÞ%p ¼ rðyÞ½v1 ðyÞ%p̄ þ ½1 − rðyÞ%½v1 ðyÞ%
,
where
rðyÞ
-0.02
net-p
406
Page
8
of
14
Eur. Phys. J. C (2015) 75:406
STAR,
PRC98,
014915(2018)
dipoleweek ending-1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1
israthermodest
–
at
the
le
is
the
observed
rapidity
dependence
of
the
ratio
of
Two
contributions
tov
determinesthedirectionofinitialdipoleasymmetry!
1e Riemann problems at cell interfaces [30]. It is therefore
states) at thefreeze-out
andcompared
it
with
the
STAR
data
S.
Voloshin,
EPJ
Web
Conf.171,
07002(2018)PyH Y S I C A L R E V I E W L
E T TPRL112.162301
E1 R dipole
S
18 MAY 2012
dipoleRL
202301STAR,(2014)
portant108,
to check whether
the code(2012)
is not introducing, forfor charged particles collected in the centrality interval 40–
Twocontributions
tov1determines the direction of
initialdipoleasymmetry!
the
Riemann
problems at cell interfaces
[30].
ItThe
is therefore
states)angle
at the freeze-out
compared
it with the STAR dataflow.
dipole flow
!1 andcanbe approximatedby 3
1
PRL108.202301(2012)
initialgiven resolution, STAR,numerical errors
which are larger than
80 % [22].
Directed flow is an important observablefor sev- tilt + 0density asymmetry
10-40%
3 Centrality
dipoleFIG. We
2 (colorand Recently,
antiproton(left
importantto checkwhethertheatpanels)code
not introducing,for 3 forchargedparticles
collected
in[18]
the centrality
interval40–
1 ðyÞ
e effects induced by the physics.
refer toonline).
the global Protoneral reasons.
it hasv
been
studiedlowerisenergy[31]!
=
arctan(⟨r
sin
φ⟩/⟨r
cos
φ⟩)
+
π
where
r
and
φ
1,3
STAR,
Nature, 548, 62 (2017)
flow.
The
dipole
flow
angle
!
can
be
approximatedby3'
1
initialtilt+
densityasymmetryv
ðyÞ(rightpanels)forintermediate-centrality
and
π
a
given
resolution,
numerical
errorswhicharelarger
than
80
%
[22].
Directedflow
isanimportantobservableforsevðyÞ
betweenparticle
species
[31];
(ii)
if
the
differenceinvmerical errors genericallyasnumerical
viscosity.
withahybridfluid-transport
model
(see
also
Ref.
[32]).
At
RQMD
Au+Au 200GeV 110%-70% √arethe1 polar
coordinatesof1participants
anda weighted average
33ΛΛP.idealBozek
andI.-0.02
Wyskiel,
PRC81.054902(2010)We have thus calculated the T(10%–40%)-vorticity for different
physis NN
200
GeV,
it has been
with
an
3 +to
the=ateffects
inducedbycalculated
the 19.6,
physics.
We
refer
the
globaleral reasons.
Recently, it has beenstudied at lower energy[31]!
=
arctan(⟨r
sin
φ⟩/⟨r
cos
φ⟩)
+
π
[18]
where
r and φAu+Aucollisions
200,
62.4,
39,
27,
11.5,
1,3
α
=0.64
Λ
QGSM*
v1two
of nuclei,
protonsandantiprotons
is caused
STAR, PRC76.024915 (2007)
isHeinz
taken
overP.theKolb,
overlap
regionofwith
theviscosities(in fact η/s ratios),
in orderprovidean upperhydrocode
by Bozek
and Wyskiel[18].U.
Herein,we difference
0.5
numerical
errorsgenericallyas numericalviscosity.
withbetween
a hybrid
fluid-transport
model
(see
also
Ref.weight[32]). Atand7.7 toGeV.
The
plottedDerrors
are first
statistical
only.
and
J.Phys.G30:S1229(2004)
√
are
the
polar
coordinatesof participants anda weighted
2
AMPT
und for the numerical viscosity of ECHO-QGP in the ideal
extend thethe viscous
P.
Bozek
and
I.
Wyskiel,
PRC81.054902(2010)
ΛΛ average(a)antiproton
Wecalculation
have thus tocalculated
theregime.
T -vorticity
for different
physis
=
200
GeV,
it
has
been
calculated
with
an
ideal
3
+
1
-0.04
pointsinbeing
theenergyorentropydensity.
The
angle
!
NN
1,3
ode. The mean value of the T -vorticity is shown in Fig. 5
The amount of generated directed flow at the freeze-out by antiflow alone, then such difference is expected to be
STARwith
prelim.the(20-60%)UrQMDin orderisHeinz
taken
overP.theKolb,
overlap
region of two nuclei,
weightcal viscosities (in fact η/s ratios),
to provide
an upperDhydro code
first by
Bozek andVery
Wyskiel[18].U.
Herein,we andthedirectionofthelargestdensity
gradient.
schematically,
J.Phys.G30:S1229(2004)
d its extrapolation to zero occurs when |η/s| ! 0.002
depends, of course, on the initial conditions, particularlyon2
accompanied
strongly
negative
slopes.
In data,theboundcollisions,forηthe(seenumerical
in the ideal
extend theby
calculation
to the viscous
regime. vbeingΛΛ !
intermediate-centralitythe3),viscosity
protonslope
hydro*1hich is a very satisfactory value,For
comparablewith the one
the parameterSect.
as shownof
inECHO-QGP
Fig.
6.
The
the
energyorentropydensity.
The
angle
pointsinmfor aofparticularfluctuation
leadingtotheis modification
to vThe
1,3
Relative
contribution
from
the
tilt
1 (η)
mode.
The
mean
value
of
the
T
-vorticity
shown
in
Fig.
5
amountgenerated
directed
flow
at
the
freeze-out
ALICE
prelim.
(15-50%)tained in Ref. [4]. The good decreases
performance iswith
due to theuse
directedflow
also
depends
on
η/s
as
shown
in
Fig.
7
and
increasing energy and changes sign from
0.01(b) proton and antiproton v1 slopes islarge
difference
betweenproton0
positiveis shown
in Fig.
the directionof the largest density gradient. Very
and
its
to
zero
occurs ofwhen|η/s| dipole! 0.002 flow
depends,
of course,on the1(b).
initial conditions, particularly
on 1high-order reconstruction methods
that toare ableto com- between
could
then
beextrapolationusedmeasurethe viscosity
Λ schematically,Λpositive
negative
7.7
and to11.5
GeV,
shows
athe QCD>
andv
slopescanbestudiedby<px
1
nsate for the highly diffusive two-wave Riemann solver
plasmaalong
otherazimuthal anisotropy
coefficients.
which
is witha verysatisfactory
value, comparable
the onetheparameterηm (seeSect.participating3), asrange,
shown in-nucleonsFig.
6. modificationThe
seen
in thecentrality
whilestronglycontribution
negative
Thewithdifference
in5%–30%
the numberoffluctuation
leading totheto v1 (η) for a particular
Relative
from
the
tilt
minimum
between
11.5
and
19.6
GeV,
and
remainssmall
mployed [3].
It shouldbepointedoutthat,apparently,
thedirectedflow
obtained in Ref. [4]. The good performanceis due toin
thetheuse projectile
alsotarget
dependsnuclei
on η/s as
shown
in Fig.
7theand0 directed flow(quarks)
and
also
leads
to
v
slopes
are
found
for
protons,
antiprotons,
and charged
can be reproducedby pionour hydrodynamical
calculation
only
and negative up to 200 GeV,
while
the
and
antiproton
1
PRC98.014915(2018)
of high-order reconstruction methods that are STAR,
able 1to comcould then be used
to measure the viscosity ofpositive
the QCD dipole flow is shown in Fig. 1(b).
canbefor −3< y < 3. energies. In contrast,change in rapidity of the “fireball” center of mass relative
to 0 studied by <px> and v1 slopes
slopesarenegativeatallmeasuredpensateforthehighlydiffusive
two-wave
Riemannsolverplasma
along
with
other
azimuthalanisotropy
coefficients.
ALICE,(2013) range (30%–80%).
pions PRL111.232302
in a different centralityBothob-theThe differenceinnumberof participating nucleons
The dependence of v1 (y) on ηm and η/s makes it possible
Directed-0.5
flow, angular momentum, and thermal
Karpenko,
Becattini,
EPJ
C77(2017)213
±
that
of
nucleon-nucleon
system.
Insymmetric
collisions
such2
employed[3].
It should
apparently,
the directed flow
behaviornet
π there is no hint of the observed
to adjustthepnonmonotonic
ηm parameter
for a given
η/s value.forThis adjustπ
10 protonvorticity
10 be pointed out that,(c)primary
Λthat(quarks)
intheprojectile
andtargetnucleialso
leads-0.7*dv/d η to theservations
suggestthat
additional
mechanisms
than
1
canbe
be reproducedby our hydrodynamical
calculation
only
mentUrQMD
cannot be properly
fit because,
as
would
a
consequenceoffluctuations
in
the
STAR,
PRC98.014915(2018)
protons in the well-tested
model.called
Issea precision
et al., inaa differenceΛ including feed-down
0.01
we
have
mentionedinthe
Introduction,
severaleffects
in
the
for
−3
<
y
<
3.
th the initial conditions reported
at
the
end
of
Sect.
3
changeinthe
rapidityof the “fireball” center of mass relative to 0
transport model
study
incorporatinga momentum-dependentnumberassumed
in[11,31]
areneededtoexplaincentralityofparticipating
nucleons
event
by
event
[19],
while
Eur.
Phys.
J.
C
(2015)
75
:406
Page
9
of
14
406
ALICE,PRL111.232302(2013)-1directed-0.5
0 (both
0.5charged1 -15 Directed-0.5 flow,0 angular
0.5momentum,
1 and thermal
have calculated theflow of pions
The dependence of v1 (y) on ηm and η/s makes it possible
Ka
mean field, report qualitative reproduction [40]F.ofBecattini
protonin asymmetricthatofnucleon-nucleon
system.
Insymmetric
collisions
such
3
collisions
thepositionofthecenter
of
mass
2
et
al.,
Eur.
Phys.
J.
C
(2015)75:406
dependenceofthedifference
betweenthev
ðyÞslopesofto adjust the ηm parameter for a given η/s value. This adjust- 1
vorticityy (see Fig. 3), but
y
10
10
10
0.04
3200
0
directed flow from E895
[17]
and
NA49
[18]
week ending
participating
nucleons
will beshiftedcalledon average,
dependingment cannot
be properlya precision
fit because,
as
Data
a
difference
would
be
a
consequenceoffluctuations
in
the
3000
W L E T T E R Sthis model yields a 0.03
protonsandantiprotons.
s[GeV]
19 DECEMBER
2008
positivedvthe
at conditions
all beamreported
energies
UrQMD
1 =dy
we case,have mentioned
in the Introduction,
severaleffectsin theNN
Withinitialaton
thecentrality.
end ofSect. In3 thisone
would
expecttheoverallshapep
ﬃﬃﬃﬃﬃﬃﬃ
ﬃ
2800
0.02
numberofparticipating
nucleons
event
by
event
[19],
while
v
の起源：初期の傾きと非対称な密度分布012STAR,studied
PRL101.252301(2008)
Eur.
Phys.
J.
C
(2015)
75
:406
Page
9
of
14
406
GeV
and
below).
(calculationssNN ¼ 17.2, 8.8
IG. 2 (color).
Model
of
pion
(left
panel)
andproton10
we have calculated the directed flow ofof
pions
(both
chargedThe
excitation
functionofprotonv1 ðy Þ slope
10
2600
(η)
to
be
mostlyunchanged,buttheentire
v
(η)
curve
to
v
0.01
1
1
ﬃﬃﬃﬃﬃﬃﬃﬃ
p
√
s
(GeV)
0 v ðyÞ for
inBetterasymmetriccollisions
thepositionofthetilted
center sourceof mass ofNN
F. Becattini
et al., Eur.
Phys.
J. C (2015)75:406
The 10%–70%
energy dependenceofprotondv1 =dy at
involves
an0
description
of
v
with
the
1
2400
ight panel)AuþAu
collisions
s
¼
0
F
(¼
dv
=dy
at
midrapidity)ispresented
in
Fig.
4.
Values1NN
be shiftedin thedirectionof rapidity
where
more
participants
渦の起源：初期の軌道角運動量・速度プロファイル
0.04
3200
Figure3.
Averageglobalpolarizationof lambda hyperons as a function of collision energy. Boxe1vやvと比べると、
interplay
betweenthedirectedflowofprotons
associated2
3
2200
participating
nucleons
will be shifted on average, depending
-0.01
0
FIG.
4
(coloronline).
Directed
flow
slope
(dv
=dy)
near
3000
0.03
move,
as
schematicallyindicated
in
Fig.
1(c).
00 GeV. The
QGSM*
model
presents
thebasicquark-gluon
stringwhich accounts for vorticity.
y =with
0 baryon number transported from the initial beam
1 uncertainties.
systematicfor2000 F are extracted via a polynomial fit of the form Fy þ
CM
-0.02
on
centrality.
In this case, one would expect the overall shape-2 parton recombination [30]. The hydro* model presents Finally,
midrapidity
versusthat
beam
energyforintermediate-centrality
2800vの傾きとグローバル偏極が同じような
0.02
we
note
the
dipole
flow
is
found
to
be
less
1
03
0
1800
odel with
rapidity to the vicinity-0.03of midrapidity, and the directed flow
Cy
,
where
y
¼
y=y
for
which
are
normalv1(エネルギーや粒子種依存性)はAu+Au.
Panels(a), (b)and(c)
reportmeasurement
for spectators
anti-v (η)2600
beam
of
to
be
mostlyunchanged,buttheentire ofv1 (η)
curve to1600
0.01
sensitive
to theshear3 viscosity
over 5entropy
η/s[20]-than
1vslope2 of system
ofexpansion
protonsfromparticle-antiparticle
pairs
produced
near
v
seems
to
follow
the
trend
P
30%
- 60%
-0.04
1
H
e hydrodynamic
from
a-4tilted
source
[11].
3.5
4
4.5
2
2.5
v
has
been
extensively
measuredasfunctions01
protons,
protons,andnet proton
protons, respectively,
along decreases
with
-2
-3
-1
0
1
2
3
4
Betterd
2400rapidly with
ized
at
%
1.
The
v
ðy
Þ
slope
η
0
1
エネルギー依存性に見える。
andv,
thereforeit
providesabetterconstraintonthegeometrybeshiftedinthedirectionofrapiditywheremoreparticipantsmmidrapidity.
The
importanceofthesecondmechanism
3-4 Data AMPT
Figure 3. Average global pol
Y (rapidity)
UrQMD
calculations subject to the same cuts and fit conditions.
ﬃﬃﬃﬃﬃﬃﬃﬃ2200 PH(LHC) ~ PH(RHIC-top)/2
pexpect
定量的に再現できていない。
->-0.01of theincreasingenergy,reachingzero
aroundsNN¼schematically
9 GeV. Its indicated in Fig.systematicandsystemin theinitialstate.
increases strongly
with flow
beamenergy.
A formeans
tocompareddistinuncertainties
are
shown
as shadedbars.
Dashedsize,
collisionenergy,andspecies…
move,
as20001(c).
Fig. fluctuations
9Systematic
Angularmomentum(inh¯units)
ofparticle
the plasma
with Bjorken
which
acc
6ofDirecteddifferent
valuesof η parameter
withuncertainties.
Fig. 8 DirectedFig.
pions atflow
η/sof=pions
0.1 andηm = 2.0
conditionsare
as a afunctionof the fit
parameter
ηm
38
η/s
= 0.1
comparedfor
with FAIR/NICA
STARwould
data [22] 2020
-0.02
guish 200
betweentheNiida,
twomechanisms
thus be initialT.
GeV
curvessmoothtocollisions
guide
the theeye.initial dipolelike asymwithAu+Au
STAR
data
[22]Workshop
In
Pb+Pb
and
Au+Au
we point
note thatsign changes
to negative as shown byFinally,
the 1800
data
at the dipole flow is found to be less
In Fig.
protonv1 ðyÞ are plotted together with
-6 2, pion and200
GeV Cu+Cu
-0.03
90000
ﬃﬃﬃﬃﬃﬃﬃﬃ
metry inp
thedensity distribution at midrapidity is caused purely 1600
FIG.
1.
Cartoonillustrating
different
contributions
tothedirected
sensitive
to theshear
viscosity
over 5entropy η/s [20]-thanvslope¼ 17
GeV,
measuredbyhavetheanNA49
experiment[15].
sNN -0.04
2
80000
62.4 GeV
Au+AubetweenRQMDvve model calculations,
namely,[12],haveUrQMD
1
3
3.5
4
4.5
2
2.5
comparison
data and calculations
been delib- by the fluctuations,
while
Cu+Au
collisions
intrinsic
-4
-2
-3
-1
0
1
2
3
4
flow and their effect ontheGeV(pseudo)rapidity
dependence
ofsincemeanvaim
1 . was162301-5 70000
ηm
62.4
Cu+Cu
and
v
,
thereforeit
providesabetterconstraintonthegeometry
eratelyneglected
in
this
work.
However,our
モデルは、少なくともvとグローバル偏極の両方を再現すべき。
3
1
None
of
modelsreproduce
all
the
data
quantitatively!
-8(a) showsAsimilar
trend
has
been
observedatlowenergieswithaY(rapidity)28], Panel
AMPT
[29],
QGSM
with
partonrecombination
densityasymmetry
due
to
the
asymmetricsizeofcolliding60000
the effect of tothe“tiltedsource,”while
panelsof (b)
and
->
expec
obtaina somewhat
realisticevaluation
the vorticities,
140andfluctuationsofthesystemintheinitialstate.
50000
T. (c)
Niida,
重イオン衝突理論・実験共同研究会
Fig. with
9 AngularThemomentum(in h¯ units) of the plasma with Bjorken
In additiondifferent
to6thedirected
flow
ofdhp
the
“tiltedsource”
Fig.
Directedflowof pions
for different
valuesof ηm parameterof0ηm forwhich we obtain
the best nuclei. slightly-4 effectsweofhave-2chosen the value
i=dy[32,33].
energyquantity
include additional
asymmetricdensity
distribution
and
0

渦とv1

Directed flow and vorticity/global
Directed flowpolarizationand vorticity/global polariz

|Jy|

v1

m

units)

v1 (%)

v1|Jy|

dv1/dy|y=0

v1 (%)

PH [%]

PH [%]

+'%()+'-)#',*%'$*

まとめ
フローと粒子相関に関する最近の実験結果（ほぼSTARしかカバーしていない）を紹介しましたQCD相転移やバリオン高密度領域における物性解明のために、低エネルギー領域
でフローやfemtoscopyの精密測定が進んでいる。
ブラインド解析によるアイソバーCME探索がついに終了。事前定義したCMEシグ
ナルは観測されず、さらなる調査が必要。完全にCMEを否定したわけではない。
グローバル偏極の新しいデータ（低エネルギーや粒子種依存）が出始めている。

T. Niida, 重イオン衝突 理論・実験共同研究会

15バックアップ

T. Niida, 重イオン衝突 理論・実験共同研究会

16species identity.

Analysis procedure
D.

Methods for isobar blind analysis

The detailed procedure for the blind analysis of isobar data is outlined in Ref. [88] and is strictly followed by the
analysts. Shown in Fig. 1, the blind analysis procedure includes a mock-data challenge to perform a closure test andthree main steps: 1) isobar-mixed analysis, 2) isobar-blind analysis, and 3) isobar-unblind analysis [105].

started ~Jan/2019

started end of May/2021

Step-1

Step-2

Step-3Isobar Mixed
analysis

Isobar Blindanalysis

Isobar Unblind
analysis

Follow blind analysis as recommended by
BNL NPP PAC

Code freezing(Each run is
Ru+Ru & Zr+Zr)

QA with ⇠ 1% data
(Each run is
Ru+Ru or Zr+Zr)

Final analysis(Ru+Ru & Zr+Zr
12 12
separated)‣ No species info. until final step

Step-0
Mock Data
challenge
Test data structure(Au+Au data)

correction
factoris determinedby makingthe thelocationof thehalf-maximum
pointof thegiven
Vz,tpcbin binequal
to thecorrection
factoris determinedby makinglocationof thehalf-maximum
pointof thegiven
Vz,tpcequal
to theFIG. 1. Flowchart
illustrate
ofoftheblind analysis [105]. This is based on the procedure for the isobar blind
one oneat at1 <to< 1<cm(thesteps
center
the
TPC).
1V<
Vz,tpc1thecm(the
centerof isobar
the
TPC).
z,tpc
analysis outlined in Ref. [88].
STAR
Isobarblindblind
analysis
STAR
Isobarblindblind
analysis
STAR
Isobaranalysis
STAR
Isobaranalysis
1.1 1.1-2-2
In the zeroth 10step
analysis,in a mock-data challenge.
√sNN√s=NN
200
GeVGeV the analysts participated√sNN√s=NN
200
GeVGeV= 200= 200
10 preceding the blind

-6

10

Ratio

Ru+Ru
Ru+Ru

10-6

Ru+Ru/Zr+Zr
Ru+Ru/Zr+Zr

0.950.95

DataData2
2
GlauberCase-2(χ /ndf=2.22)
GlauberCase-2(χ /ndf=2.22)
GlauberCase-3(χ2/ndf=2.19)
GlauberCase-3(χ2/ndf=2.19)

10-8 10-8

Ratio

)

offlineP(NtrkP(Ntrkoffline)

The purposeof this step is to familiarize the analysts with the data structures
1.051.05 that have been designed for the blind analysis andthe techniques toaccess the data. Feedback is also provided to the ABC to ensure feasibility of the analysis blinding
10-4 10-4p
1 1in 2018 after the isobar run) are used for this step.
process. Data for Au+Au collisions at sNN = 27 GeV (collected
DataData
GlauberCase-2GlauberCase-20.9 0.9‣ Codes frozen before the unblind step
‣ Analyzed by 5 independent groups‣ Case for CME is pre-defined
13
STAR, Nucl.Sci.Tech.
32(2021)5,48“Methods for a blind analysis of isobar data collected by the STAR collaboration”

Ratio

2
2

0

0

100 100

200 200

Ratio)

offlineP(NtrkP(Ntrkoffline)e-range droplet macroscopic model and the folded-Yukawa single-particle microscopic model [116]. The
Efficiency
uncorrected
tracks
Efficiency
uncorrected
tracks
Efficiency
uncorrected
tracks
Efficiency
uncorrected
tracks1.1 1.196-2 -2 of its additional
of 96
Ru,
becauseprotons,islargerthan
thatof(|η|<0.5)(|η|<0.5)(|η|<0.5)(|η|<0.5)
10 10
44
40 Zr. The neutron and proton density
1.051.05
taken to be the same for both R and a, so Ru
is larger than Zr. The third set (Case-3) isCentrality
from recent determination-4
10-410sed on energy
densityfunctional theory (DFT),1 assuming
the nuclei are spherical [85, 113]. The proton
1‣ Donestributions are
bothZr+Zr
calculated, and the overall sizeRu+Ru/Zr+Zr
of
Ru is found to be smaller than Zr because
of by
a non-CME analyzers-6 -6 Zr+Zr
Ru+Ru/Zr+Zr
0.950.95
10 10
Data
DataData
Data
icker neutron skin GlauberinGlauber
thelatter.
The
nucleondistributions
are found to be well parameterized by the
GlauberCase-3GlauberCase-3Case-2(χ /ndf=2.22)
Case-2(χ /ndf=2.22)
0.9 0.9
GlauberCase-3(χ /ndf=2.19)
GlauberCase-3(χ a/ndf=2.19)-8
Unknown deformation parameter, tried 3 cases of
distributions10-8(i.e.
theneutronparameterissignificantly
larger than that for the proton) ‣[113].
102
2

300 300

400 400

00

offlineNoffline
trkNtrk

100 100

200 200

300 300

offlineNoffline
trkNtrk

400 400

Woods-Saxon parameters below

E II. The Woods-Saxon parameters used in the Glauber simulations for the centrality determination.
FIG.FIG.
2. 2.
Distributionsof thenumberof charged
particles(N (N ) fromthe the
TPCTPCin thepseudorapidity
acceptance|⌘| <‣ Case-3 (β2=0) best describes the data. Potential
Distributionsof thenumberof charged
particles) fromin thepseudorapidity
acceptance|⌘|0.5< 0.5
in Ru+Ru(upperleft left
panel)
and
Zr+Zr(lowerleft left
panel)
collisions.
TheTheexperimental
havehave
beenbeencorrected
for for
Case-1[83]
Case-2[83] distributions
Case-3[113]
in Ru+Ru(upperpanel)
and
Zr+Zr(lowerpanel)
collisions.
experimental
distributions
corrected
uncorrected
for tracking
efficiency.
FitsFits
to theexperimental
variationsin theluminosityand andthe thevertexposition
V V , and
, and
uncorrected
for tracking
efficiency.
to theexperimental
variationsin theluminosity
vertexpositionroom for improvement.
R
(fm)
a
(fm)
R
(fm)
a
(fm)
R
(fm)
a
(fm)
Nucleus22
2 in
distributions(graycircles)are performedby thetwo-component
Glaubermodel
using
two twosets setsof Woods-Saxon
parametersin
distributions(graycircles)are performedby thetwo-component
Glaubermodel
usingof Woods-Saxon
parameters
Table
II (blue
crossesfor Case-2
and and
red redcrossesfor Case-3).
TheTheRu+Ru
to Zr+Zr
ratioratioof theexperimental
data,
as well
Table
II96
(blue
crossesfor Case-2
crossesfor Case-3).
Ru+Ru
to Zr+Zrof theexperimental
data,
as well
Ru
5.085
0.46
0.158
5.085
0.46
0.053
5.067
0.500
0
as thoseof44
theGlaubermodel
fit forand andCase-3are areshown
in theupper
rightrightand andlower
rightrightpanels,respectively.
as thoseof theGlaubermodel
fit Case-2
for Case-2
Case-3shownin theupper
lower
panels,respectively.
96simulation
TheTheGlauberwiththe theCase-3
nucleardensityparameters
is usedfor centrality
determination
as itasprovides
the thebest
Glaubersimulation
with
Case-3
nucleardensityparameters
is usedfor centrality
determination
it0.556
provides
best
Zr
5.02
0.46
0.08
5.02
0.46
0.217
4.965
0
40
description of the experimental data.
o✏ine
o✏ine
trk trkz,tpcz,tpc

description of the experimental data.

o✏ineFigure2 shows
the theluminosity
andandVz,tpccorrected
distributions
P (NPtrk) in)Ru+Ru
andandZr+Zr
collisions.
TheTheFigure2 shows
luminosity
Vz,tpccorrected
distributions(Ntrk
in Ru+RuZr+Zr
collisions.
T.
Niida,
重イオン衝突理論・実験共同研究会
o✏ineo✏ine for multiparticle production [117].
ysis we use the simple two-component modelo✏ine

Several alterna-

17

Elliptic/triangular flow
2125

different non-flow contributions
0.08
0.08

STAR
Isobarblind
analysis
STAR
Isobarblind
analysis

v2

0.02

v3

0.02

0.01
00

Ratio

Ratio

1.2
1.1
1.1
1.05

Zr+Zr

Ru+Ru
TPC (|η|<1),
EPD (2.1<|η|<5.1)
v2{EP}
v2{EP}v2{2}v2{2}v2{SP}(∆ηsub=0.2)
v2{SP}(∆ηsub=0.2)
v3 {2}(TPC),
Ru+Ru
v2{2} (∆η>1)v2{2}(∆η>1)
v3 {2}(TPC),
Zr+Zr
Ru+Ru
v2{SP}(TPC-EPD) v3 {SP}(TPC-EPD),
v2{SP}(TPC-EPD)

0.06
0.02

0.04

v2
v3

v2 {2}(TPC), Ru+Ru
v2 {2}(TPC), Zr+Zr
v2 {SP}(TPC-EPD), Ru+Ru
v2 {SP}(TPC-EPD), Zr+Zr

√sNN
= 200
GeV
√sNN
= 200
GeV
0.2< pT < 2 GeV/c

0.01

Zr+Zr
Zr+Zr v3{2}0.02

v {SP}(∆η3v3 {SP}(TPC-EPD), Zr+Zr

00

Ru+Ru
/ Zr+Zr
Ru+Ru/ Zr+Zrv2 {2}TPC (|η|<1)
v2 {SP}
EPD(2.1<|η|<5.1)
v3 {2}
v3 {SP}1

1.11.2
1.051.1

Ru+Ru
v3{2}
Ru+Ru

=0.2)

sub
v2{4}v3{2} (∆η>1)

Ratio
Ratio

v2

0.06
0.04

0.02

STAR
Isobarblind
analysis
STAR
Isobarblind
analysis

NN = 200 GeV√s√s
NN = 200 GeV

0.06

0.04 00.08

v {SP}(∆η

=0.2)

3
sub
v2{4}
v {2}(∆η>1)
3

v2{EP}(Ψv2{EP}(Ψv3{SP}(TPC-EPD)
v3{SP}(TPC-EPD)
ZDC)
ZDC)

Ru+Ru
Ru+Ru/ Zr+Zr/ Zr+Zr

TPC (|η|<1)
TPC (|η|<1)
ZDC (|η|>6.3)
EPD (2.1<|η|<5.1)1

0.98080 7070 6060 5050 4040 3030 2020 1010

0.98080 7070 6060 5050 4040 3030 2020 1010

Centrality(%)
Centrality(%)

v2 ratio deviates from unity in 0-5%,
while v3 deviates in opposite
direction. Could be related tonuclear structure difference
between the two species.

1

1
00

v2 differs by ~2-3%, indicating
different shape and CME
background for a given centrality

Centrality(%)
Centrality
(%)

0 0

p
FIG.
v2 measurementsdi↵erent
methods
in isobar
collisions
at sNN of= TPC
200 GeV
as a
FIG.4.10.(Left)(Left)Elliptic
Ellipticanisotropy
and triangularanisotropies using
measured
for thetwo systems
using
the combinationand EPDs.
unctionof centrality
TPC and
EPD detectors.
the represent
upper panels,
the solidand (Right)
open symbols
represent
The boxes
represent using
systematic
uncertainties
and theInlines
statisticalerrors.
Compilationof vmeasurements
3 using di↵erent
or
Ru+Ruandandcuts
Zr+Zr
collisions, respectively.
TheResults
data points
are shiftedalong thex axis inforopenclarity.
The lower
panelsshow
methods
on pseudorapidity
separation.
are shownfor individual
systemssymbolsfor Zr+Zr
andsolid
Ru+Ru Resultsover Zr+Zr
collisions.
statisticalare represented
by lines The
and systematic
uncertainties
hev2 ratios
symbols
forinRu+Ru.
are also
shown Thefor theratio ofuncertainties
Ru+Ru to Zr+Zr
in open symbols.
centrality bins
are shifted
Niida,(Right)
重イオン衝突理論・実験共同研究会
y T.boxes.
The sameshowing measurements for four particle correlations using TPC and EP determined from ZDC.

18

OBSERVABLES FOR ISOBAR BLIND ANALYSIS

CME observables

fically focuses on the following approaches and corresponding observables. The
ults from the two isobar species to search for a statistically significant16di↵erence
wing subsections describe these approaches and corresponding observables which
γ-correlator
condhigher-orderof short-range
the correlator,
2) di↵erential
measurements
S. Voloshin,
PRC70.057901(2004)
but inandreality
it could be harmonics
dominated by
two-particle
correlation
backditytogap 112 ,⌘weandinvariantmass mbetween
and quantify
backgrounds,
3)
ilar
focus
on the di↵erence
the opposite-signsame-signinv ) to identify‣ Well-studiedandcharge sensitive correlator
ration across spectator and participant planes, and 4) the use of the R observable‣ Δγ/v2 is commonly used to cancel v2-driven backgroundfirst three approaches are based on the aforementioned
three-point correlator and
= os
(12)
ss .
ch. For each observable/approach, we predefine a set of the CME signatures prior
Derivedmeasurements
magnitudeofhighsignificancemustbeobservedforanobservationofdue to the LCC and TMC have a similar characteristic structureaffirmativethat involves
the, 38, 51, 126]. This motivates the study of the normalizedofscaledby‣ γ113quantity: wrt Ψ3 whichisuncorrelatedwith B-field direction‣ two-particle correlator δ112. and third order‣ pseudorapidity(13)⌘ second
mixed harmonics112
withevent planes dependencev2‣ invariant mass
TMC/LCCTMC/LCCquires 112(Eq.
to be(2))
largerthan
112 specific. Whilea reliable estimate of 112
isorrelator
witha morenotation,‣ wrt spectator/participant planes(and)
betweenisobarcollisions
might
give
a
more
definite conclusion on the112112
112 = hcos( ↵ +22 )i ,(8)

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R-correlator
e variations in the OS
correlator
to understand the background mechanisms in 112 [26],N.N. Ajitnand et al., PRC83.011901(2011)SS= 112
hal angles of particlesofflow separation
plane.
2 is the second-order112interest (POIs) and ‣Alternative
N. Magdy et al., PRC97.061901(2018)measure for charge
and 2 , respectively.
2” in 112 refer to the harmonics associated with the ↵ ,‣Similar to Δγ in sensitivity(14)to CME based on AVFD model study
=
hcos(
+
2
3
)i
.
123
↵
3
oximated with the EP ( EP ) reconstructed with measured particles, and then theOS
SS
S. Choudhury etinal., arXiv:2105.06044
=
nite
EP
resolution[125].
The
charge-dependent
backgrounds
112
112
112
insensitive to the CME, because the correlation is negligible between the magnetic
heof resonance decays. If resonances from the event exhibit
elliptic flow,
ane,example
3 . However, background due to flowing resonances along the
3 plane can
19
T.
Niida,
重イオン衝突理論・実験共同研究会
aanalogy
signal toforEq.
chargeseparation(4) onecan write: across the flow plane with a magnitude proportional