RHICビームエネルギースキャ
ンの（私見を交えた）最新結果と今後の展望
益井宙（筑波大）

第１７回Heavy Ion Pub

H. Masui, Heavy Ion Pub, Sep/13/2013

1 /31

QCD相図の探索
M. CHENG et al.
0.4
0.6

PHYSICAL REVIEW D 77, 01451

0.8

1

1.2

1.4

4

εSB/T

Tr0

16

1.6

0.35
0.30

14
12

0.25

10

0.20

4

ε/T : Nτ=4
6
3p/T4: Nτ=4
6

8
6
4

0
100

0.10
0.05

T [MeV]
200

300

400

500

Nτ=4
6
fit: p/ε
HRG: p/ε
2
cs

0.15

M. Cheng et al,
PRD77, 014511 (2008)

2

p/ε

600

700

0.00
0

1/4

ε
1

2

3

[(GeV/fm

4

5FIG. 9 (color online). Energy density and 3 times the pressure as function of the temperature (left) and the ratio p=! as fu
the fourth root of the energy density (right) obtained from calculations on lattices with temporal extent N" # 4 and 6. Temper
energy density scales have been obtained using the parametrization of r0 =a given in Eq. (22) and r0 # 0:469 fm. The small ve
in the left-hand figure at high temperatures shows the estimate of the systematic uncertainty on these numbers that arises
normalizationof the pressure at T0 # 100 MeV. The dashed curve (HRG) in the right-hand figure shows the result for p=! in
超高温では自由度がハドロンからクォークへ”転移”
resonance gas for temperatures T < 190 MeV.

•• ”圧力”を変えるとどうなる？
minimalvalue of about !c " ’ 0:09 that is reached at2s min! * !1–2" GeV=fm3 . The dependence of p=! on the energy density can be parametrized in the high temperature

We note that for T & 2Tc the results obtained
asqtad action [11] for the entropy density are
H. Masui,Ion Pub,
Sep/13/2013
2 /31
agreementwith Heavy
the results
obtainedwith thep4fat

QCD相図の探索
M. CHENG et al.
0.4
0.6

PHYSICAL REVIEW D 77, 01451

0.8

1

1.2

1.4

4

εSB/T

Tr0

16

1.6

0.30

14

p/ε

0.25

12

?

10

6
4

4

0.15
0.10

M. Cheng et al,
PRD77, 014511 (2008)

2

0.05

T [MeV]
200

300

400

500

Nτ=4
6
fit: p/ε
HRG: p/ε
2
cs

0.20

ε/T : Nτ=4
6
3p/T4: Nτ=4
6

8

0
100

0.35

600

700

0.00
0

1/4

ε
1

2

3

[(GeV/fm

4

5FIG. 9Pressure(color online). Energy density and 3 times the pressure as function of the temperature (left) and the ratio p=! as fu
the fourth root of the energy density (right) obtained from calculations on lattices with temporal extent N" # 4 and 6. Temper
energy density scales have been obtained using the parametrization of r0 =a given in Eq. (22) and r0 # 0:469 fm. The small ve
in the left-hand figure at high temperatures shows the estimate of the systematic uncertainty on these numbers that arises
normalizationof the pressure at T0 # 100 MeV. The dashed curve (HRG) in the right-hand figure shows the result for p=! in
超高温では自由度がハドロンからクォークへ”転移”
resonance gas for temperatures T < 190 MeV.

•• ”圧力”を変えるとどうなる？
minimalvalue of about !c " ’ 0:09 that is reached at2s min! * !1–2" GeV=fm3 . The dependence of p=! on the energy density can be parametrized in the high temperature

We note that for T & 2Tc the results obtained
asqtad action [11] for the entropy density are
H. Masui,Ion Pub,
Sep/13/2013
2 /31
agreementwith Heavy
the results
obtainedwith thep4fat

QCD相図の探索
M. CHENG et al.
0.4
0.6

PHYSICAL REVIEW D 77, 01451

0.8

1

1.2

1.4

4

εSB/T

Tr0

16

1.6

0.30

14

p/ε

0.25

12

?

10

6
4

4

0.15
0.10

M. Cheng et al,
PRD77, 014511 (2008)

2

0.05

T [MeV]
200

300

400

500

Nτ=4
6
fit: p/ε
HRG: p/ε
2
cs

0.20

ε/T : Nτ=4
6
3p/T4: Nτ=4
6

8

0
100

0.35

Phase diagram of water from wikipedia
http://en.wikipedia.org/wiki/Phase_diagram

600

700

0.00
0

1/4

ε
1

2

3

[(GeV/fm

4

5FIG. 9Pressure(color online). Energy density and 3 times the pressure as function of the temperature (left) and the ratio p=! as fu
the fourth root of the energy density (right) obtained from calculations on lattices with temporal extent N" # 4 and 6. Temper
energy density scales have been obtained using the parametrization of r0 =a given in Eq. (22) and r0 # 0:469 fm. The small ve
in the left-hand figure at high temperatures shows the estimate of the systematic uncertainty on these numbers that arises
normalizationof the pressure at T0 # 100 MeV. The dashed curve (HRG) in the right-hand figure shows the result for p=! in
超高温では自由度がハドロンからクォークへ”転移”
resonance gas for temperatures T < 190 MeV.

•• ”圧力”を変えるとどうなる？
minimalvalue of about !c " ’ 0:09 that is reached at2s min! * !1–2" GeV=fm3 . The dependence of p=! on the energy density can be parametrized in the high temperature

We note that for T & 2Tc the results obtained
asqtad action [11] for the entropy density are
H. Masui,Ion Pub,
Sep/13/2013
2 /31
agreementwith Heavy
the results
obtainedwith thep4fat

RHICビームエネルギースキャン• QCD相構造の研究‣ 高バリオン密度 ~ 低エネルギー

重イオン衝突➡ Beam Energy Scan !

• 経緯‣

2008年: テスト実験 @ √sNN = 9.2 GeV(PRC81, 024901, 2010)‣2009年：BES Phase-Iの提案 (arXiv:
1007.2613)‣

2010年 : RHIC BES @ 7.7, 11.5, 39 and
62 GeV‣2011年 : 19.6 and 27 GeV‣

2012年 : 5 GeVでテスト実験（1 good
event）
H. Masui, Heavy Ion Pub, Sep/13/2013

3 /31

目的

• RHIC 200 GeVやLHCで観測されたQGP生成シグナルはどこで消失するか？
‣ 言い換えると、シグナルはどこから見え始めるか？

➡ これまでのQGP生成シグナルと期待される観測量の系統的測
定• 一次相転移のシグナルを観測する• QCD特異点を発見する➡ 観測量は？

H. Masui, Heavy Ion Pub, Sep/13/2013

4 /31

QGP生成のシグナル

H. Masui, Heavy Ion Pub, Sep/13/2013

5 /31

QGP生成のシグナル
PHYSICAL REVIEW C 72, 014904 (2005)

大きな方位角異方性
Polynomial Fit

0.08

クォーク数スケーリング

v2/n

0.06

クォークの非閉じ込め？

0.04
K S0

0.02

+

K +K

-

Λ+Λ

systematic error

0Data/Fit

p+ p

1.8
1.6
1.4
1.2
1
0.8
0.6
0.4

π ++π -STAR,
PRC72, 014904 (2005)

0

0.5

1

1.5

2

2.5

pt/n (GeV/c)
FIG. 33. (Color online) (Top panel) Identified particle v2 fromminimum bias collisions. The vertical axis and horizontal axis havebeen scaled by the number of constituent quarks (n). Pions are notplotted. A polynomial curve is fit to the data. The possible systematic
error is indicated by the gray band. (Bottom panel) The ratio of v2 /n
to the fitted curve.

coalescence model to describe the production of pions whose
masses are significantly smaller than the assumed constituent
quark masses [30].
At the end of Sec. V B we estimated that the v2 values
from two-particle correlations could be systematically high by
between about 10 to 20%. This was based on the integrated
values for charged particles and we do not know yet how thisH. Masui, Heavy Ion Pub, Sep/13/2013

5 /31

QGP生成のシグナル
PHYSICAL REVIEW C 72, 014904 (2005)

大きな方位角異方性
Polynomial Fit

0.08

クォーク数スケーリング
クォークの非閉じ込め？

0.04
K S0

0.02

+

K +K

-

Λ+Λ

systematic error

0Data/Fit

p+ p

1.8
1.6
1.4
1.2
1
0.8
0.6
0.4

π ++π -

0

A. ADARE et al.

0.5

1

1.5

2

2.5

PHYSICAL REVIEW C 82, 011902(R) (2010)

pt/n (GeV/c)

ηR

AA

FIG.
panel) Identified particle v2 from
1.2 33. (Color online) (Topπ 0, PRL 101, 232301(2008)
minimum bias collisions. The verticalaxis and horizontal axis haveηbeen scaled by the number of constituent quarks (n). Pions are not1plotted. A polynomial
is fit toBias
the data.
possible
Au+Aucurve
MinimumsNNThe= 200
GeV systematic
error is indicated PHENIX
by the gray band. (Bottom panel) The ratio of v2 /n
0.8
to the fitted curve.
π 0 RAA or

RAPID COMMUNICATIONSSTAR,
PRC72, 014904 (2005)

0.6

coalescencemodel to describe the production of pions whose
0.4
masses are significantly smaller than the assumed constituent
quark0.2masses[30].
PHENIX,At thePRC82,
end of011902(R)Sec. V B(2010)
we estimated that the v2 values
from two-particle
correlations could be systematically high by
0
0
2
4
6
8This10
14on 16
18 20 22
between about 10 to 20%.
was12
based
the integratedp (GeV/c)values for charged particles andT we do not know yet how thisχ2 Contour (Lines show 1 and 2 σ)

0.9
0.8Intercept at 20 GeV/c

v2/n

0.06

0.7

0-20%

0.6
0.5

20-60%

0.4

0.3
高運動量メソンの抑制

0-5%

0.2

パートンエネルギー損失
0.1

-0.01

0
0.01
Slope [ (GeV/c)-1 ]

0.02

0.03

H. Masui, Heavy Ion Pub, Sep/13/2013

5 /31

QGP生成のシグナル
PHYSICAL REVIEW C 72, 014904 (2005)

大きな方位角異方性
Polynomial Fit

0.08

クォーク数スケーリング

v2/n

0.06

クォークの非閉じ込め？

0.04

PHYSICAL電荷異方性の揺らぎ
REVIEW C 81, 054908 (201

OF CHARGE-DEPENDENT AZIMUTHAL . . .
K S0
+

0.02

K +K

-

1.8
1.6
1.4
1.2
1
0.8
0.6
0.4

π ++π -RAPID COMMUNICATIONSSTAR,
PRC72, 014904 (2005)

0.5

1

1.5

2

2.5

PHYSICAL REVIEW C 82, 011902(R) (2010)

pt/n (GeV/c)

ηR

AA

FIG.
panel) Identified particle v2 from
1.2 33. (Color online) (Topπ 0, PRL 101, 232301(2008)
minimum bias collisions. The verticalaxis and horizontal axis haveηbeen scaled by the number of constituent quarks (n). Pions are not1plotted. A polynomial
is fit toBias
the data.
possible
Au+Aucurve
MinimumsNNThe= 200
GeV systematic
error is indicated PHENIX
by the gray band. (Bottom panel) The ratio of v2 /n
0.8
to the fitted curve.
0.6

coalescencemodel to describe the production of pions whose
0.4
masses are significantly smaller than the assumed constituent
quark0.2masses[30].
PHENIX,At thePRC82,
end of011902(R)Sec. V B(2010)
we estimated that the v2 values
from two-particle
correlations could be systematically high by
0
0
2
4
6
8This10
14on 16
18 20 22
between about 10 to 20%.
was12
based
the integratedp (GeV/c)values for charged particles andT we do not know yet how thisχ2 Contour (Lines show 1 and 2 σ)

0.9
0.8Intercept at 20 GeV/c

0

A. ADARE et al.

π 0 RAA or

カイラル磁気効果？

Λ+Λsystematic error

0Data/Fit

p+ p

STAR,
PRC81, 054908 (2010)

0.7

0-20%

0.6
0.5

20-60%

0.4

0.3FIG. 7. (Color online) !cos(φa + φβ − 2$RP )# in Au + Au a
高運動量メソンの抑制√

0-5%= 200 GeV calculated using Eq. (Cu0.2+ Cu collisions at sNN
パートンエネルギー損失
The
error bars show the statistical errors. The shaded areas refle
0.1
-0.01
0
0.01
0.02
0.03
the uncertainty in the
Slopeelliptic[ (GeV/c) ]flow values used in calculations, w
H. Masui, Heavy Ion Pub, Sep/13/2013 5 /31
-1

観測量

• QGP生成シグナルの消失‣ 方位角異方性のクォーク数ス

ケーリング‣ 高横運動量ハドロンの抑制‣ 電荷異方性の揺らぎ• 一次相転移のシグナル (?)‣ 指向的方位角異方性‣ 同一粒子相関の方位角異方性• QCD特異点の発見‣ (保存量の)揺らぎ

H. Masui, Heavy Ion Pub, Sep/13/2013

6 /31

Solenoidal Tracker At RHIC
TOF

BEMC

TPC
VPD

EEMC
BBC

• 大きなアクセプタンス• 高精度の粒子識別
H. Masui, Heavy Ion Pub, Sep/13/2013

7 /31

QGP生成シグナル
はどこで消えるか？
H. Masui, Heavy Ion Pub, Sep/13/2013

8 /31

%

unted for by mean field potentials where the K and
eel an attractive force while the Kþ and p feel alsive force.

compared to the particles. At sNN ¼ 11:5 GeV
difference becomes negative for the antiparticle(mT % m0 ) <1 GeV=c2 but the overall trend is still si
pffiffiffiffiffiffiffiffi
to the one of the particles andSTAR
to PRL110,sNN 143201¼ 62:4
GeV.
(2013)

クォーク数スケーリングの破れ

see also PRC88, 014902 (2013)

v2

0.2

11.5 GeV

62.4 GeV

(a)

(b)

0.1

p
Λ
Ξ
Ω

v2(B)-fit

0

Au+Au, 0%-80%

11.5 GeV

p
Λ
+
Ξ
+
Ω

(c)

-

π
K
0
Ks
φ

η-sub EP

62.4 GeV

(d)

π+
+
K
0
Ks
φ

0.05
0
-0.05
0

1

2

3

0

1

2

3

0

1

2

3

0

1

2

3

mT-m0 (GeV/c2)

3 (color online). The upper panels depict the elliptic flow v2 as a function of reduced transverse mass (mT % m0 ) for par
pffiffiffiffiffiffiffiffind (b), and antiparticles, (c) and (d), in 0%–80% central Au þ Au collisions at sNN ¼ 11:5 and 62.4 GeV. Simultaneous
mesons except the pions are shown as the dashed lines. The difference of the baryon v2 and the meson fits are shown in thels.

142301-5

H. Masui, Heavy Ion Pub, Sep/13/2013

9 /31

%

unted for by mean field potentials where the K and
eel an attractive force while the Kþ and p feel alsive force.

compared to the particles. At sNN ¼ 11:5 GeV
difference becomes negative for the antiparticle(mT % m0 ) <1 GeV=c2 but the overall trend is still si
pffiffiffiffiffiffiffiffi
to the one of the particles andSTAR
to PRL110,sNN 143201¼ 62:4
GeV.
(2013)

クォーク数スケーリングの破れ

see also PRC88, 014902 (2013)

v2

0.2

11.5 GeV

62.4 GeV

(a)

(b)

0.1

p
Λ
Ξ
Ω

v2(B)-fit

0

Au+Au, 0%-80%

11.5 GeV

p
Λ
+
Ξ
+
Ω

(c)

-

π
K
0
Ks
φ

η-sub EP

62.4 GeV

(d)

π+
+
K
0
Ks
φ

0.05
0
-0.05
0

1

2

3

0

1

2

3

0

1

2

3

0

1

2

3

mT-m0 (GeV/c2)•

3 (color online). The upper panels depict the elliptic flow v2 as a function of reduced transverse mass (mT % m0 ) for par
pffiffiffiffiffiffiffiffi
メソン・バリオンの分岐
クォーク数スケーリングnd (b), and antiparticles,(c) and (d), in 0%–80% central- Au
þ Au collisions at sNN ¼ 11:5 and 62.4 GeV. Simultaneous
mesons except the pions are shown as the dashed lines. The difference of the baryon v2 and the meson fits are shown in thels.
‣ 粒子・反粒子の違いはなし

142301-5

H. Masui, Heavy Ion Pub, Sep/13/2013

9 /31

%

unted for by mean field potentials where the K and
eel an attractive force while the Kþ and p feel alsive force.

compared to the particles. At sNN ¼ 11:5 GeV
difference becomes negative for the antiparticle(mT % m0 ) <1 GeV=c2 but the overall trend is still si
pffiffiffiffiffiffiffiffi
to the one of the particles andSTAR
to PRL110,sNN 143201¼ 62:4
GeV.
(2013)

クォーク数スケーリングの破れ

see also PRC88, 014902 (2013)

v2

0.2

11.5 GeV

62.4 GeV

(a)

(b)

0.1

p
Λ
Ξ
Ω

v2(B)-fit

0

Au+Au, 0%-80%

11.5 GeV

p
Λ
+
Ξ
+
Ω

(c)

-

π
K
0
Ks
φ

η-sub EP

62.4 GeV

(d)

π+
+
K
0
Ks
φ

0.05
0
-0.05
0

1

2

3

0

1

2

3

0

1

2

3

0

1

2

3

mT-m0 (GeV/c2)•

3 (color online). The upper panels depict the elliptic flow v2 as a function of reduced transverse mass (mT % m0 ) for par
pffiffiffiffiffiffiffiffi
メソン・バリオンの分岐
クォーク数スケーリングnd (b), and antiparticles,(c) and (d), in 0%–80% central- Au
þ Au collisions at sNN ¼ 11:5 and 62.4 GeV. Simultaneous
mesons except the pions are shown as the dashed lines. The difference of the baryon v2 and the meson fits are shown in thels.
‣ 粒子・反粒子の違いはなし@11.5 GeV (スケーリング前)
142301-5• メソン・バリオンで同程度のv
2

H. Masui, Heavy Ion Pub, Sep/13/2013

9 /31

%

unted for by mean field potentials where the K and
eel an attractive force while the Kþ and p feel alsive force.

compared to the particles. At sNN ¼ 11:5 GeV
difference becomes negative for the antiparticle(mT % m0 ) <1 GeV=c2 but the overall trend is still si
pffiffiffiffiffiffiffiffi
to the one of the particles andSTAR
to PRL110,sNN 143201¼ 62:4
GeV.
(2013)

クォーク数スケーリングの破れ

see also PRC88, 014902 (2013)

v2

0.2

11.5 GeV

62.4 GeV

(a)

(b)

0.1

p
Λ
Ξ
Ω

v2(B)-fit

0

Au+Au, 0%-80%

11.5 GeV

p
Λ
+
Ξ
+
Ω

(c)

-

π
K
0
Ks
φ

η-sub EP

62.4 GeV

(d)

π+
+
K
0
Ks
φ

0.05
0
-0.05
0

1

2

3

0

1

2

3

0

1

2

3

0

1

2

3

mT-m0 (GeV/c2)•

3 (color online). The upper panels depict the elliptic flow v2 as a function of reduced transverse mass (mT % m0 ) for par
pffiffiffiffiffiffiffiffi
メソン・バリオンの分岐
クォーク数スケーリングnd (b), and antiparticles,(c) and (d), in 0%–80% central- Au
þ Au collisions at sNN ¼ 11:5 and 62.4 GeV. Simultaneous
mesons except the pions are shown as the dashed lines. The difference of the baryon v2 and the meson fits are shown in thels.
‣ 粒子・反粒子の違いはなし@11.5 GeV (スケーリング前)
142301-5• メソン・バリオンで同程度のv• クォーク数スケーリングは粒子・反粒子間では破れている
2

H. Masui, Heavy Ion Pub, Sep/13/2013

9 /31

バリオン・反バリオンの差
PHYSICAL REVIEWPRL 110, 142301 (2013)

Mo
duce
the m
0.04
theorythe ptheory0.02
possibthat t
0
Coulo
(only
0
20
40
60
baryo
sNN (GeV)
out
FIG. 2 (color online). The difference in v2 between particles
obser! (see legend) as a(X) and their corresponding antiparticles (X)粒子・反粒子の差は低エネルギーでより大きいIn
pffiffiffiffiffiffiffiffi
function of sNN for 0%–80% central Au þ Au collisions. The"v
f2
バリオンの差はメソンに比べて大きいdashed lines in the plot are fits with a power-law function. The
if diff
error bars depict the combined statistical and systematic errors.
H. Masui, Heavy Ion Pub, Sep/13/2013 10
a/31fun2

v2(X)-v (X)

0.06

•
•

STAR PRL110, 143201 (2013)see also PRC88, 014902 (2013)

Au+Au, 0%-80%
η-sub EP

-

+

Ξ -Ξ
p-p
Λ-Λ
K+-K
π+-π-

(反)粒子毎のスケーリング

PHYSICAL REVIEW C 88, 014902 (2013)

C FLOW OF IDENTIFIED HADRONS IN Au + . . .

(a)

0.1 7.7 GeV

Au+Au, 0-80%
η-sub EP11.5 GeV

19.6 GeV

39 GeV62.4 GeVSTAR PRC88, 014902 (2013)

v2/nq

0.05
0
0.1 27 GeV
0.05
0
0

0.5

1

1.5

20

0.5 1 1.5 2 0(m -m0)/nq (GeV/c2)

0.5

1

1.5

2

T

(b)

0.1 7.7 GeV

Au+Au, 0-80%
η-sub EP11.5 GeV

19.6 GeV

0.05

v2/nq

• (反)粒子毎に見るとスケーリングはよく成り立つ？
0‣ 7.7 GeVでもQGP ? スケーリングはハドロン相起源？
0.1 27 GeV

0.05

39 GeV62.4 GeV

H. Masui, Heavy Ion Pub, Sep/13/2013

11 /310.05(反)粒子毎のスケーリング
0

0

0.5

1

1.5

20

0.5 1 1.5 2 STAR
0 0.5
1.5
PRC88, 1014902(2013)2(m -m0)/nq (GeV/c2)T(b)0.1 7.7 GeV

Au+Au, 0-80%
η-sub EP11.5 GeV

19.6 GeV

39 GeV62.4 GeV

v2/nq

0.05
0
0.1 27 GeV
0.05
0
0

0.5

1

1.5

20

0.5 1 1.5 2 0(m -m0)/nq (GeV/c2)

0.5

1

1.5

2

T

• (反)粒子毎に見るとスケーリングはよく成り立つ？

FIG. 19. (Color online) The NCQ-scaled elliptic flow, v2 /nq versus (mT − m0 )/nq , for 0%–80% central Au + Au collisions forparticles (a) and corresponding antiparticles (b). Only statistical error bars are shown. The dashed lines show the results of simultan
with Eq. (17) to all particles except the pions.

‣ 7.7 GeVでもQGP
スケーリングはハドロン相起源？
the breakdown of NCQ?scaling
would be a necessary signaturescaled distributions versus (mT − m0 )/nq . The correspfor a QCD phase transition from partonic to hadronic matter.
Because particles and antiparticles have the same number ofquarks, the NCQ scaling transformation of v2 does not change

scaled plots for v2 (pT ) are shown in Fig. 24 in the App
The NCQ scaling should only hold in the tramomentum
range of 1.5 < pT < 5 GeV/c [44,48].
H. Masui, Heavy Ion Pub, Sep/13/2013

11 /31

Rcp抑制の消失
Open strange hadrons RCP

Feng Zhao, Thu. Resonances

Statistical error only
𝐊 𝟎𝐒 , Λ, Ξ, RCP :(0~5%)/(40~60%)

Hijing Simulation

Ω RCP in 19.6 and 27 GeV :(0~10%)/(40~60%)• 200 GeVでは大きな抑制
K R larger than unity for p > 1.5 GeV/c
R
は低エネルギーで増加(>1)•
R particle type (baryon/meson) difference at intermediate p (2~3 GeV/c)
becomes less obvious• バリオン・メソン分岐も低エネル17

𝒔𝑵𝑵   ≤  11.5 GeV,



CP

CP

STAR Preliminary

T

cp

T

ギーで消失
H. Masui, Heavy Ion Pub, Sep/13/2013

12 /31

そもそもジェットがいない？

HijingJet-quenching off• 低エネルギーではハード散乱断面積が小さい
atively
describes trend• Hijing + クローニン効果で定性的には合う
H. Masui, Heavy Ion Pub, Sep/13/2013

13 /31電荷異方性の消失
 cos(q + q - 2 s) 

0.002

ALICE, arXiv:1207.0900
0.001

2.76 TeV Pb+Pb

62.4 GeV Au+Au

200 GeV Au+Au

39 GeV Au+Au

27 GeV Au+Au

11.5 GeV Au+Au

7.7 GeV Au+Au

γos

0.0005

Opposite sign0-0.0005

Same sign

γss

-0
0.002
001
0.00151

2

 cos(q + q - 2 s) 

γ = 〈cos(φ1+φ2-2Ψ)〉1

20.00150.001

19.6 GeV Au+Au

0.00050-0.0005-0.001
80

STAR preliminary
70

60

50

40

30

20

10

00

70

60

50

40

% Most Central

30

20

10

00

% Most Central

70

60

50

40

30

20

10

0

% Most Central• 電荷異方性 (γ -γ ) @ 200 GeVosss‣ カイラル磁気効果？

• エネルギーと共に異方性の減少、11.5 GeV以下では消失
H. Masui, Heavy Ion Pub, Sep/13/2013

14 /31

Three Point Correlator

フロー起源？Phys. Rev. Lett.103,251601 (2009)

200 GeVAu+Au• γP is the differe
between unlik
like-sign corre

PRL103, 251601 (2009)• Blast wave mo
reproduces ob
difference betw
unlike- and lik
azimuthal corr•   cos(    2 RP ) 
1
2
dM
200 GeVの結果はBlast-wave
modelでも説明可能  (2     ) d d 
B( ,  )[cos 2 cos   sin
p







2
‣ 局所電荷保存＋フロー
Hui Wang for the STAR Collaboration

M2 

d

9

• 低エネルギーでも説明できるか？
H. Masui, Heavy Ion Pub, Sep/13/2013

15 /31

一次相転移のシグナル探索H. Masui, Heavy Ion Pub, Sep/13/2013

16 /31

~10年前の予想

ysics Letters B 458 (1999) 454–459

455
L. P. Csernai, D. Rohrich, PLB458, 454 (1999)
130

H.
Stocker, NPA750, 121 (2005)
H. Stöcker / Nuclear Physics A 750 (2005) 121–147

Ideal hydrodynamical modelwith 1st order phase transition

1.9√sNN (GeV)
13.8

4.5

Fig. 7. Measured SIS and AGS proton (dpx /dy)-slope data compared to a three-fluid hydro calculation. A l
Fig. 1. Upper part: Definition of the measure softening, S, deextrapolation of the AGS data indicates a collapse of flow at ELab ≈ 30 A GeV, i.e., for the lowest SPS- an
scribing the deviation of Px Ž y . or Õ1Ž y . from the straight line
upper FAIR-energies at GSI [59].
<
Ž
.<
<
<
behavior, ay, around CM. S is defined as ay y Px y r ay . The
1lower figure shows a typical example for fluid dynamical calculations with Hadronic and QGP EoS w3x. QGP leads to strong
softening, ;100%.

• 指向的異方性 (directed flow; v )は一次相転移で特徴的な振る舞い‣ v1で見えたらv2で見えてもおかしくない• 理想流体(一次相転移)の計算では~ 4.5 GeVくらいでv が最小

Fig. 8 of w4x, Fig. 6b of w5x and Fig. 6 of w7x at orslightly below 0.5 yrycm if QGP formation wasallowed during the calculation. In sharp contrast, thesolutions with hadronic EoS did not show this effect,
and the maximum and minimum of the Px curve

1

H. Masui, Heavy Ion Pub, Sep/13/2013

17 /31rgy loss in the TPC and from the time measurement by109
STAR’s time-of-flight barrel [25] in combination with the110
momentum.
111

sameproton
direction
flow. near mid-rapidity, which is arguedfultoinbi
as pconsistent with emission from a tilted source [18]. far
Thesportedresults certainly cannot be explainedbythebaryonstop
10-40%: v1 Slopeof Fig.
ping picturetha
0.1[15], since we observe
protons
E895: p large pion flow
p at 7.7 GeV. slope
is not opposite to proton flow NA49:
exceptIn pefo
where rSTAR:p for directed flowripheral collisions,anegative
slope
o
0.05
among
STAR: pprotons and pions at all energies
may have a di↵eren
this equSTAR: πorigin that is unrelated to a phase transition [27]. of this124

非単調的な振る舞い

143
144
145

112

0

146
147

113

148

114

149

dv1/dy’0.02

v1

39 GeV :π0-10%
10-40%
40-80%

39 GeV : p
0-10%
10-40%
0.02
40-80%

115

0

116

-0.02

142

150

-0.02

-0.5

0

0.5

1

153
-1

-0.5

0

0.5

1

27 GeV : π
0.02

0.04

0

0

0.02

v1

v1

0.02

-0.02

155

39 GeV(10-40%): p 0.04
39 GeV(10-40%): π - 156
STARpreliminary
STAR Data
STAR Data
0.02

157
158

0

0

-0.02

159

-1

-0.5

0

0.5

1

-1

-0.5

0

1

-0.04

-

19.6 GeV : p

19.6 GeV : π
0.02

0

0

-0.02

-0.02
-1

-0.5

0

0.5

1

0.04

-0.5

0

11.5 GeV : p

-0.02

-0.02
0.5

7.7 GeV : p

0.02

1

-0.02

-0.02
-1 -0.5

0

y

0.5

1

0 27 GeV : p

1
0.04

-1

-0.5

0

0.5

27 GeV : π -

162

1

-0.5

0

0.5

1

7.7 GeV : π -• net protonのdv /dy’は11.5 GeV付
近で最小

-1 -0.5

0

y

0.5

1
125

present
and ⇡tinguish
only sli
ically, ta proxy
protons
the netthe conrecent stentials

The
0.02
0.02
164
slope fo
(String Melting)165
comes n00166
and 19.
-0.02
-0.02
102
10
167
at 7.7√ sNN
168
In cont
-0.04
-0.04
-1
-0.5
0
0.5
1
-1
-0.5
0
0.5
1169
at all e
00.04 Directed flow slope (dv0.04
FIG. 3:/dy)
near
mid-rapidityas1
19.6 GeV : π 170 of this r
19.6 GeV : p
1
a functionofbeam
energyfor
mid-central
Au+Au
collisions,
0.02
0.02
171
model
0
where the primed quantity y refers to normalized rapidity
172
trends a
0 slopes for protons, any/ybeam .0 The upper panel reports
tiprotons and pions, including measurements by prior ex-173 panel)
-0.02
-0.02
periments. The lower panel shows STAR’s measurement of174 ates str
this same
which is a representation175 ergy re-0.04 slope for net protons,-0.04
of the signal
number
to1176 roughly-1 for
-0.5initial-state0
0.5 baryon
1-1-0.5 transported
0
0.5
0.04
0.04
mid-rapidity, along
with
from
11.5
GeVthe: π -177 above t
11.5 GeV:1
p corresponding predictions
UrQMD
and AMPT models. The
systematic uncertainty on178 from th
0.02
0.02
the net-proton measurements are shown as a shaded band179 influenc
0centered0 on dv1 /dy 0 = 0.
180transpo181
hadron
-0.02
-0.02
182
sign ch-0.04-0.04
The directed
flow excitation
functionfor protons, an-183 /31
H. Masui,Heavy Ion
Pub, Sep/13/2013
18 ence be
163‣ 低エネルギーの陽子以外

0.02
0

0.5

• v の傾き(dv /dy’)は負
1

-1

0

161

-0.04

v1

0

160

v1

0

-0.5

1

11.5 GeV :π

0

-1

0.5

-

0.02

p- p
0
URQMD

-0.5

-0.02

AMPT
AMPT(S)

-1

0.02

-1

AMPT(D)AMPT(S)Net Proton
UrQMD

v1

0.02

0.5

dv1/dy’-0.020.02

v1

154

-0.05

-

27 GeV : p

v1

152

STAR preliminary
-1

v1

151

0

-1

-0.5

0

0.5

1

-1

-0.5

0

0.5

1

初期異方性の時空発展
P. F. Kolb et al, PRC62, 054909 (2000)• 幾何学的異方性は状態方程式
⌦ 2
↵
2
y
x
"x = 2hy + x2 iに敏感• 一次相転移のシグナル（かもしれない）

with 1st order phase transition

H. Masui, Heavy Ion Pub, Sep/13/2013

19 /31

幾何学的異方性は単調減少
Excitation function for freeze-out eccentricity, εF
Kt = 0.15-0.6 GeV/c*Model centralities
correspond to data

εF

0.4

0.3

E895 - PLB 496, 2004 (7.4-29.7%)
CERES - PRC 78, 2008 (10-25%)
STAR (-0.5<y<0.5, 10-30%)
STAR (-1<y<-0.5, 10-30%)
STAR (0.5<y<1, 10-30%)
URQMD
Hybrid[BM]+UrQMD
Hybrid[HG]+UrQMD
2D hydro EoS-Q
2D hydro EoS-H
2D hydro EoS-I

0.2

0.1

0
STAR preliminary
1

•

10

102

3

sNN

10

p
パイ中間子で測った幾何学的異方性はエネルギーと共に単調
Figure 3: Freeze out eccentricity, " f , as a function of sNN for data and models [9] (color online).

減少、CERESのデータは再現できず

60

61
62

4. Summary‣ ラピディティ依存性はSTARのアクセプタンス内では見られないTo summarize, ⇤-⇤ correlation function is presented. Fits to data with di↵erent potential
models suggest that ⇤-⇤ interaction is attractive. A negative scattering
length gives indication
H. Masui, Heavy Ion Pub, Sep/13/2013

20 /313相転移のシグナルか？
εF

dv1/dy’124

flow but deviate at a qualitative level from the observed141 anism increases strongly with beam energy, and it is helpproton flow.
142
ful in interpretation to distinguish between the two as
143
far as possible. We define Ftransp , the v1 slope for trans144
ported baryon number (labelled p p̄ in the lower panel
10-40%: v1 Slope
forasfreeze-out
eccentricity,εF145
of Fig. 3 andExcitation
sometimesfunctionreferred tothe slope for
net
0.1
146
protons) based on an equationin which the measured
E895: pE895 - PLB 496, 2004 (7.4-29.7%)
Kt = 0.15-0.6 GeV/c
0.4
CERES -,PRC 78, 2008 (10-25%)
147
slope
for
protonsiswritten
F
=
rF
+
(1
r)F
p̄
transpNA49: p*Model centralities
STAR (-0.5<y<0.5, 10-30%)
148
where r is the observedcorrespondratio of to
antiprotons
to protons
STAR (-1<y<-0.5, 10-30%)
data
STAR: pSTAR (0.5<y<1, 10-30%)
0.05
149
among
the
analyzed
tracksateach
beam
energy.
While
STAR: p
URQMD
150
this
equationdefinesF,asimplified
interpretation
Hybrid[BM]+UrQMD
0.3
transpSTAR: πHybrid[HG]+UrQMD
151
of this observable is suggested by the observation inthe
2D hydro EoS-Q
0
2D hydro152
present analysis that v1 (y) is almost the same for⇡ + EoS-H
hydro EoS-I
153
and ⇡ and for K + and K — in fact, they are 2D
indis0.2
154
tinguishable within errors at the higher energies, and are
-0.05
155
only slightly di↵erent at 11.5 and 7.7 GeV [37]. Specif156
ically, the suggested interpretation is that Fp̄ serves asSTAR preliminary
0.1 or baseline for the directed flow from produced157
a proxy
158
protons, and this interpretation guides our inference that159
the net-proton quantity Ftransp isolates as far as possible
0.02
160
the contributionof the initial-state baryonic matter. The
0
Net Proton
161
recent study of Xu et al. addresses issues of hadronic poSTAR preliminaryp- p162
tentials that might arise in interpretation of Ftransp [38].
dv1/dy’

123

0

URQMD

2

3

10
10
The1 lower panel of Fig. 310reveals that the inferred
v1
sNN
164
slope for transported baryon number (net protons) be(String Melting)165
comes negative with good statistical significanceat 11.5p
FigureFreezeout eccentricity,
functionof andsNN fordata and models [9] (color online).
166
and3:19.6
GeV,
while it is" zero27 GeV
positivef , as aat
2
10
10
167
at 7.7 GeV and above 27 GeV, including at 200 GeV.
√ sNN
168
In contrast, the UrQMD model shows a positive slope
169
at all energies for this observable. Thus there is no hint60
4. Summary
FIG. 3: Directed flow slope (dv1 /dy 0 ) near mid-rapidity as170 of this remarkable non-monotonic behavior in a hadronica function of beam energy for mid-central Au+Au collisions,
171
model that
hascorrelationa good recordof reproducing
observed
61
To summarize,⇤-⇤functionis presented.
Fits to data with di↵erent pot
where the primed quantity y 0 refers to normalized
rapidity172
trends
at
least
at
a
qualitative
level
[31].
Figure3(lowery/ybeam . The upper panel reports slopes for 62
protons,
an- suggest that ⇤-⇤ interaction is attractive. A negative scattering length gives indic
modelstiprotons and pions, including measurements by prior ex-173 panel) also reveals that the AMPT model likewise devi63
towards non-existence of bound H-dibaryon. A clear source asymmetry signal is observ
periments. The lower panel shows STAR’s measurement of174 ates strongly from the measured data. The beam en64
pion-kaoncorrelation
the o↵setis roughlyof the source size. The azim
175
ergy region function
where weandobservethe double
sign halfchangethis same slope for net protons, which is a representation
with maximum
stopping,
and liesof the signal for initial-state baryon number transported
to176 roughly coincides
65
HBT measurementshows a monotonic
decreasefor freeze
outjusteccentricity as a function of
mid-rapidity, along with corresponding predictions from the177 above the region where the spectator matter separates
66
energy.
1
UrQMD and AMPT models. The systematic uncertainty on178 from the participants quickly enough so that it no longer
67
the net-proton measurements are shown as a shaded
band179 influences flow in the midrapidity zone [39]. Nuclear
0
centered on dv1 /dy = 0.
180transport models ought to clarify whether or not purely
H. Masui,Iondouble
Pub, Sep/13/2013 21 /31
181
hadronic physics could accountfor the Heavyobserved
AMPT
AMPT(S)163• 相転移のシグナルだとすると、HBTの結果はどう説明する？
‣ そもそもHBTは相転移に敏感ではない？

• 逆にHBTを信じたらv の結果をどう解釈する？

QCD特異点の探索
H. Masui, Heavy Ion Pub, Sep/13/2013

22 /31

高次モーメント(キュムラント)• 特異点では(無限に大きな系で)‣ 感受率と相関長が発散 → でも実験では測れない• 観測量‣ 保存量のモーメント (キュムラント) → 保存量の揺らぎ‣ モーメントの積 (キュムラントの比) ↔ 感受率の比⌦

2 = ( N )
3
S =
⇠
2

2

↵

2

⌦

3

↵

⇠ ⇠ , 3 = ( N ) ⇠ ⇠
4
3
4
2
, K =
⇠
2
2
2

4.5

⌦

, 4 = ( N )

4

↵

2

3 h( N )i ⇠ ⇠ 7* M. A. Stephanov, PRL102, 032301 (2009)- 感受率は格子QCDで計算可能。高次モーメントは相関長に敏感*• 保存量揺らぎのエネルギー依存性‣ QCD特異点近傍で大きく変化するはず
H. Masui, Heavy Ion Pub, Sep/13/2013

23 /31非ガウス揺らぎ
From Wikipedia• 三次のモーメント = Skewness S - 分布の非対称性• 四次のモーメント = Kurtosis K - 分布の鋭さ• ガウス分布では両方0• 高次モーメントの測定 → 非ガウス揺らぎの測定
H. Masui, Heavy Ion Pub, Sep/13/2013

24 /31

Net-protonの揺らぎ

Moment Products: Energy Dependence !

•! データDeviations below Poisson !
expectations are observed beyond‣ 検出効率補正なし*
statistical and systematic errors in
0-5% most central collisions for κσ2
and比較した基準値
Sσ above 7.7 GeV.

•!

!
peripheral collisions, the !
‣ For
ポアソン分布deviations above Poission expectationsareobserved below 19.6 GeV.!
‣ (負)二項分布*!

••! UrQMD model show monotonic !
UrQMDは単調増加
behavior
for the moment products, in!
which non-CP physics, such as!
精密測定(特に低エネルギー)
baryonconservation, hadronic
scattering effects, are implemented.!

が必要* under investigation (not shown here)

H. Masui, Heavy Ion Pub, Sep/13/2013

25 /31

Net-chargeの揺らぎ
Higher Moments of Net-charge• データ‣ 検出効率補正なし*• Net-charge fluctuation – related tofreeze-out
parameters
比較した基準値•

Bazavov et al, PRL 109 (2012) 192302‣ ポアソン分布• Data - efficiency uncorrected *(負)二項分布*• ‣Datacompared to various expectations- Poisson- (Negative-)Binomial *• net-proton同様もっとデータが• Need precision measurements.

必要* Currently under investigation* under investigation (not shown here)

Aug. 19th, 2013

Future Trends Workshop, Beijing

X. Dong

18

H. Masui, Heavy Ion Pub, Sep/13/2013

26 /31QCD特異点はどこに？

Moment Products: Energy Dependence !

• 期待されていた大きな変化! Deviations below Poisson !
は見られず
expectations are observed beyond
statistical and systematic errors in‣ mostポアソンからのずれは小さい
0-5%
central collisions for κσ2
and Sσ（最大20%程度）
above 7.7 GeV.
!

! For peripheral collisions, the !
- 検出効率の補正なし
deviations above Poission expectationsare‣observed
below 19.6 GeV.!
モデルによっては、特異点で二!

! UrQMDmodel show monotonic !
桁くらい増加するという予想もbehavior for the moment products, in!
whichあるnon-CP physics, such as!
baryon conservation, hadronic
scattering
effects, are implemented.! ≠ netそもそもnet-proton•

baryon（北沢さんの講演）• PHENIX≠STAR (net-charge)‣ acceptance ? centrality ?
H. Masui, Heavy Ion Pub, Sep/13/2013

27 /31

BES-Iのまとめ• QGP消失シグナルの観測 (11.5 GeV付近、それ以下)‣ クォーク数スケーリングの破れ (粒子・反粒子間)‣ 高横運動量ハドロン抑制の消失‣ 電荷異方性の消失• 一次相転移のシグナルのヒント？？
‣ net-protonのdv1/dyは非単調的な振る舞い‣ 幾何学的異方性には見られず• QCD特異点探索、低エネルギーでの精密測定が必要• BES-IIでは20 GeV以下に絞ってデータ収集
H. Masui, Heavy Ion Pub, Sep/13/2013

28 /31

Potential for luminosity improvement for low-energy RHIC

BES phase-II proposal

February 10, 2012averageluminosity
per store luminosity
Average(cm-2 s-1)
per store

will also come with heavy beam losses which was already an issue in RHIC operation at lower
energies even for nominal bunch intensities. On the contrary, the use of electron cooling should help
to minimize beam losses and make operation easier with longer stores in addition to a significant
luminosity improvement.
Simulationsof luminosity evolution with time for the three cases
A. Fedotov andM. Blaskiewicz
for luminosity
for low-energy
presented in Fig. 9Potential
are shownin Fig.improvement
10, for completeness.

• BES phase-II (2017-)は20

RHIC operation with long bunches

1 10

26

1 10

25

1 10

24

1 10

23

√sNN = 7.7 GeV

1 10

22

w/o e-coolingw/o e-cooling, long bunches
e-cooling + long bunches

GeV以下を重点的に探索‣ 11.5と19.6 GeVにはバリオン化学ポ

テンシャルに100 MeVのギャップ

0

0.5

1

1.5

• Electron cooling + longer

bunchesで最大10倍のルミノ
シティ！

2Gold Target
z-vertex cut (m)vertex cut [m]2.4 inch(6.10 cm) OD

Diagram is 1:1 Scale•

STAR
固定標的実験
- ~ 3 GeVまで
Side View:
Target Mount‣ リング状の金標的をSTARの衝突点

Beam Pipe:
Aluminum
OD:  3”  (7.62  cm)Thickness: 60 mil (1.5 mm)
sc
ID:  3.88”  (7.47cm)

Gold forAnnulusFig. 9. Average (per store) luminosity
111 bunches of Au ions in RHIC at =4.1 and spacethick cooling and long bunches ( s=4.5 m, *=2 m,charge tune spread Q =0.05: 30
1) milelectronから2m前方に設置

m, Ni=5e8) - blue, dash curve; 2) without cooling ( s=1.5 m, *=6 m, n,95%m,
Ni=5e8)–Mountred,Sleeve:solid curve; 3) without
cooling
1.8 inch (4.57
cm) IDbut longer bunches with higher bunch intensity
Target‣ コライダーモードと両立可能
Aluminum( s=4.5m, *=6 m, n,95%m, Ni=1.5e9) – magenta, middle curve (maxi mum luminosity was
OD:  3.8”  (9.65  cm)dividedby a60factorof 4 to account for a very short luminosity lifetime – in simulations, theThickness:mil (1.5 mm)
ID:  3.68”  (9.35  cm)luminosity
was decreased by a factor of 4 after first 3 min as shown in Fig. 10).
Length:  1.2  “  (3.04  cm)n,95%

Target Sheet:Gold

3 inch (7.62 cm) Aluminum Beam Pipe

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まとめ• QGP生成シグナル消失➡ ハドロン相互作用が低エネルギーではより重要• net-protonのv スロープに非単調的振る舞い
1‣ HBTには見えない（v2にも見えない）• 保存量揺らぎの測定にはもっとデータが必要• BES phase-II‣ 20 GeV以下を重点的に探索、RHICでの固定標的実験も提案中‣ バルク観測量の精密測定、特に揺らぎの測定

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Back up

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net-charge, PHENIX vs STAR

Higher Moments oAug. 19th, 2013

Future Trends Works

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