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@QM14
NEW
@QM14
1.2
0.2
charm andbottom quarks
0.2
ALICE0D0+,D+,*+D*+ average
ALICE
D ,D , D average
Syst. from data
Syst. from data
Syst. from B feed-down
Syst. from B feed-down

-0.1
1.8
-0.1

0.2
0.2

v

AA

0
1.6
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|<0.5
Average|y|<0.5
0 1.62Average
4 D 6, D ,, D*
8D , |D*
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14
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00
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elastic(*)
TAMU
elastic(*)
pDjordjevic(GeV/c)02
4 0-7.5%
6 centrality
8 centrality
10
12
14
16
0
0-7.5%(**)
Djordjevic (**)
T
pCao,
(GeV/c)Qin, Bass(*) (*)
Cao,
Qin, Bass
1.4 1.4
T
1.6

and R

)

AA

2

R

AA

D

NN

0

2
2

+0

++

measurements together start to provide contraints
for the models
1.2 1.2[]

1

0.8 0.81

0.8 0.8

1markers:
pp p pp-extrapolated
referenceRaphaelle
Bailhache Open Open
markers:
p -extrapolated- 10
0.8
0.8- referenceTT1

0.6 0.6

0.4 0.4 0.6

0.4

0.2 0.2 0.4

0.2

quark energy loss

00

0.6 0.6

0.8
0.6

0.8
0.6

0.6
0.4

0.4 0.4

0.4
0.2

0.2 0.2

0.2
0 0.2 00
235 035 402 40 40 5 0 5 10104 15 615 208 25201025 12
25 3014 30 1600
ALI−PREL−77100
ALI−PREL−77100

2

4

6

8

10

12

p14 (GeV/c) 2 c) 4
p16 (GeV/
0
0
T

T

0.2

+

T

WHDG
rad+coll
WHDG
rad+coll
1.6(*) (*)

1

1

0.4

D ,D
|y|<0.5
AverageD ,,D*
D ,, D*, |y|<0.5
1.6 1.6 Average
4
6
8
10
12
14
16
30-50%
centrality
30-50%
centrality(GeV/16c)
4681012 p T 14
p (GeV/ c )1.4 1.4[]

R

1

with pp ref. from scaled cross section at s = 7 TeVwith pp ref. from FONLL calculation at s = 2.76 TeVBAMPS el.
BAMPS el. + rad.
TAMU
POWLANG
MC@sHG+EPOS,Coll+Rad(LPM)

0.6

ALICE
Preliminary
ALICE
Preliminary
Pb-Pb,s=
TeVTeVPb-Pb,NN s 2.76
= 2.7600

Pb-Pb, sNN = 2.76 TeV, 0-10% central

0.8

1.8 1.8

In MC@sHQ+EPOS
Plane MC@sHQ+EPOS
1.6
1.6 (*) (*) ALICE
Prompt D , D
Vitev,
rad+dissoc
Vitev,
rad+dissoc
2
AAOut
Of Plane
0
0
|
y
|<0.5
1.4
In
Plane
POWLANG(*)1.4 (*) Pb-Pb, sALICE
WHDG rad+coll= 2.76 TeV
POWLANG
Prompt D , D
NN
POWLANGOut
Ofuncertainties
Plane
BAMPS
el. (*)el.
Syst.
BAMPS
(*) Pb-Pb,|y|<0.5
1.4
1.4
WHDG
s
=
2.76
TeV
Cao,
Qin, rad+coll
Bass
Centrality
30-50%
BAMPS
el.+rad(*) (*)
Correlated
NN
BAMPS
el.+rad
MC@sHQ+EPOS
POWLANG
1.2 A 872 (2011) 265; MC@sHQ+EPOS,
1.2
WHDG: Nucl. Phys.
Coll+Rad(LPM):
Phys.
Rec.
C89
(2004)
014905;TAMU
elastic:
arXiv:1401.3817
Syst.
uncertainties
Uncorrelated
BAMPS
Cao,
Qin,
Bass
Centrality
30-50%(*) predictions
for38
0-10%
(*) predictions
for 0-10%
Correlated
Anticorrelated[nucl-th]; POWLANG:
Eur. Phys. J. C71 (201) 1666,
J.Phys.
G(2011)
124144; BAMPS: Phys. Rev. C 84 (2011)024908;TAMU
elasticJ. Phys. G38
MC@sHQ+EPOS
1.2
1.2
Uncorrelated
GlobalnormalizationUrQMD
BAMPS Ser. 426 (2013)(**) predictions
for 0-5%(2011) 124152 Phys.
Lett.
B
717
(2012)
430;arXiv:1310.3597v1[hep-ph];
UrQMD:
arXiv:1211.6912[hep-ph];J.
Phys.Conf.
(**)
predictions
for
0-5%
1
1
Anticorrelated
TAMU elastic
012032; Cao, Qin, Bass: Phys.
Rev. C
88
044907Filled Filledmarkers: pp(2013)
rescaled
reference
markers: pp rescaled
reference
Globalnormalization
UrQMD

D

1.2 1.2

cribed2R
AA
R

2 WHDG rad+coll
WHDG
rad+coll Preliminary
POWLANG
ALICE
ALICE Preliminary
Cao, Qin, BassPOWLANG
1.8
MC@sHQ+EPOS,
Cao,
Qin,
Bass
Pb-Pb,
s sColl+Rad(LPM)= 2.76
TeVTeV TAMU elastic
Pb-Pb,= 2.76
NNColl+Rad(LPM)
BAMPS
UrQMD
NN
MC@sHQ+EPOS,
TAMU
elastic
0
+0
++
+
BAMPS
UrQMD

Centrality 0-20%
Centrality 0-20%
WHDG rad+coll
WHDG rad+coll
POWLANG
POWLANG
Cao,
Qin, BassCao, Qin, Bass Coll+Rad(LPM)
MC@sHQ+EPOS,
MC@sHQ+EPOS, Coll+Rad(LPM)
BAMPS
BAMPS
TAMU
elastic
TAMU elastic
UrQMD
UrQMD

ALICE Preliminary

Average(30-50%)
AverageRAA
RAA(30-50%)

0.4
0.4

AA

R
AA
R

K=3.5

*+

NN
NN

Average(0-7.5%)
AverageRAA
RAA(0-7.5%)02+

Centrality 30-50%
Centrality 30-50%

0.6
0.6

0.1
0.1

0

0

0
+
*+
ALICE
|y |<0.5
ALICEDD, D, D, D, Daverage,
average,|y |<0.5

6

08 0 10
0 02

6
8
10
ALI−PREL−77088

ALI−PREL−77088

2124
12

14 6

16 8

p4 (GeV/6c)
T

14

16

p (GeV/ c)0
TAMU0elastic
2elastic
4 6 8 10 12 14 16 18
TAMU
Djordjevic
p (GeV/c)
Djordjevic
TCao, Cao,
Qin, Bass
Qin, Bass
ALI−PREL−77686
WHDG
rad+coll
WHDG
rad+coll
0.5
MC@sHQ+EPOS
MC@sHQ+EPOS
ALICE
Preliminary
Vitev,Vitev,
rad+dissoc
rad+dissoc
POWLANG
ALICE, v 2{EP, |6d| > 0.9}
POWLANG
0.4 BAMPS
BAMPSel. syst
el. error
BAMPS
el.+rad
BAMPS
el.+radel.
BAMPS

Heavy flavour decay electron v 2

0.40.4

Pb-Pb, ssNN==2.76
2.76 TeV
TeV
Pb-Pb,
NN

0.3
0.2
0.1
0

MinJung Kweon, Inha University

A. A.
Festanti
Festanti

Pb-Pb, s NN = 2.76 TeV
20-40% Centrality Class, |y| < 0.7

810 1012 1214
-0.1 1416 1618 1820 20
0
2
4
6

8
10
12
14
p (GeV/c) byp (GeV/c) Davide
Summarized
CaﬀarriTTp (GeV/c)T
Figure 11: (colour online) Model comparisons for average D meson v2 in the 30–50% centrality
class (upperALI−PREL−77576
0left), average
D mesonRAAModelin thecomparisons
0–20% centrality
class (upper-right)
D 30–50%
RAA in-planeand out-of-plane
Figure11: (colour
online)for average
D meson v2[13],in thecentrality
class (upperTAMU
elastic:
arXiv:1401.3817
MC@sHQ+EPOS:
PRC
89(2014)
014905TAMU
elastic:
arXiv:1401.3817
MC@sHQ+EPOS:
PRC
89(2014)
0149050inthe
30–50%
centrality
class(lowerpanels).
The
seven
model
calculationsaredescribed
in
the
text:
WHDG
left),
average
DarXiv:1307.4098
meson
RAA in the 0–20% centrality class (upper-right)[13], D PRC
RAA 80in-planeand054902
out-of-plane
Djordjevic:
Vitev,
rad+dissoc:(2009)
Djordjevic:
arXiv:1307.4098
Vitev,
rad+dissoc:
PRC
80(2009)
054902[18],centrality
POWLANG[19],
Cao,panels).
Qin, Bass
MC@sHQ+EPOS,
Coll+Rad(LPM)
[79],
BAMPS
[21],
in rad+coll
the30–50%
class(lowerThe[46],
seven
model
calculationsarein 124144
thetext: WHDG
Cao,
Qin,Qin,
Bass:
PRC
88 (2013)
044907
Cao,
Bass:
PRC
88
(2013)
044907
POWLANG:
JPG
38described(2011)
124144POWLANG:JPG
38 (2011)
TAMU
elastic[44], Nucl.
UrQMD
[45].
The
models
WHDG
rad+coll, POWLANG,TAMU elastic[79],and UrQMD are
rad+coll[18],
POWLANG
[19],
Cao,
Bass
[46],
MC@sHQ+EPOS,
Coll+Rad(LPM)
WHDG
rad+coll:
Phys.
A 872
(2011)265
WHDG
rad+coll:
Nucl.
Phys.
AQin,
872
(2011)
265
BAMPS:PLBPLB
717717(2012)
430430 BAMPS [21],BAMPS:(2012)
shown
by
two
lines
that
represent
their
uncertainty.
TAMU elastic [44], UrQMD [45]. The models WHDG rad+coll, POWLANG, TAMU elastic and UrQMD are

QM2014,
QM2014,
Darmstadt
shownby two Darmstadt
lines
that represent their uncertainty.

BAMPS el. + rad.
POWLANG
MC@sHQ+EPOS, Coll+Rad(LPM)
TAMU

T

Various observables provide
constraints for the models

Quark Matter 20140.08 from low to high pT ), which is close to that observed in data. The nuclear modification factor

1111

44

Heavy(Ion(Cafe(and(Pub( 2014/06/06(

Is'charm'quark'heavy'enough?

Transport theory: the Boltzmann equation
Time evolution of HQ phase-space distribution fQ (t, x, p)3 :dfQ (t, x, p) = C [fQ ]dt
Total derivative along particle trajectory
d
∂
∂
∂
≡
+v
+F
dt
∂t
∂x
∂p
Neglecting x-dependence and mean fields: ∂t fQ (t, p) = C [fQ ]Collision integral:!
C [fQ ] = dk[w (p + k, k)fQ (p + k) − w (p, k)fQ (p)]
"
#$
% "
#$
%
gain term3w (p, k): HQ transition rate p → p − kloss term

運動量変化 << HQの運動量

Approach implemented in codes like BAMPS (J. Uphoﬀ talk at this conf.)
Andrea Beraudo

Dynamics of heavy flavor quarks in high energy nuclear collisions

From Boltzmann to Fokker-Planck
Expanding the collision integral for small momentum exchange4 (Landau)
#
"
!
2
1
∂
∂
C [fQ ] ≈ dk k i i + k i k j i j [w (p, k)fQ (t, p)]
∂p
2
∂p ∂p
The Boltzmann equation reduces to the Fokker-Planck equation (approx.
to be quantitatively tested!)
%
$
∂
∂
∂
i
ij
A
(p)f
(t,
p)
+
(p)fQ (t, p)]
fQ (t, p) =
[B
Q
i
j
∂t
∂p
∂p
where
Ai (p) =Z

dk k i w (p, k) −→ Ai (p) = A(p) p i|{z}

衝突項から、A,B0,B1が独立に得られる

friction

B ij (p) =1
2

Z

dk k i k j w (p, k) −→ B ij (p) = p̂ i p̂ j B0 (p) + (δ ij − p̂ i p̂ j )B1 (p)|{z}momentum broadening

Problem reduced to the evaluation of three transport coeﬃcients
4

B. Svetitsky, PRD 37, 2484 (1988)
Andrea Beraudo

Dynamics of heavy flavor quarks in high energy nuclear collisions

The relativistic Langevin equation
The Fokker-Planck equation can be recast into a form suitable to follow
the dynamics of each individual quark: the Langevin equation∆p i= − ηD (p)p i + ξ i (t) , A(p)は一般にはEinstein!"#$! "# $∆tdeterm.

stochastic

with the properties of the noise encoded inδtt ′⟨ξ (pt )ξ (pt ′ )⟩ = b (pt )
∆t
i

j

ij

関係式を満たさないが、ここではA(p)を用いる。

b ij (p) ≡ κ∥ (p)p̂ i p̂ j + κ⊥ (p)(δ ij −p̂ i p̂ j )Transport coeﬃcients (to derive from theory):22⟨∆p∥ ⟩
1 ⟨∆p⊥⟩
Momentum diﬀusion κ⊥ ≡and κ∥ ≡;2 ∆t∆t
Friction term (dependent on the discretization scheme!)
%
&
∂κ
(p)
κ
(p)
κ
(p)
−
κ
(p)
1
d
−
1
⊥
∥
∥
∥
ηD Ito (p) =− 2 (1 − v 2 )+2TEp Ep∂v 2
2v2

fixed in order to assure approach to equilibrium (Einstein relation):
Andrea Beraudo

Dynamics of heavy flavor quarks in high energy nuclear collisions

The Langevin/FP approach: a critical perspective
Although the Langevin approach is a very convenient numerical tool andallows one to establish a link between observables and transport
coeﬃcients derived from QCD... it is nevertheless based on asoft-scattering expansion of the collision integral C[f ] truncated at second
order (friction and diﬀusion terms), which may be not always justified, inparticular for charm, possibly aﬀecting the final RAA (V. Greco et al.,arXiv:1312.6857 [nucl-th] and F. Scardina poster)2

2
t=0 fmt=2 fmt=4 fmt=6 fm

1.5
RAA(pT)

LV/BM

1,5

t=2 fm (BM)t=4 fm (BM)t=6 fm (BM)t=2 fm (LV)
t=4 fm (LV)
t=6 fm (LV)

1

0,5

1

0.5
Charm

0
0

1

2

3

4
p (GeV)

5

6

7

0
0

2

4
p (GeV)

6

8

チャームは十分に重くない？
Andrea Beraudo

Dynamics of heavy flavor quarks in high energy nuclear collisions

The Langevin/FP approach: a critical perspective
Although the Langevin approach is a very convenient numerical tool andallows one to establish a link between observables and transport
coeﬃcients derived from QCD... it is nevertheless based on asoft-scattering expansion of the collision integral C[f ] truncated at second
order (friction and diﬀusion terms), which may be not always justified, inparticular for charm, possibly aﬀecting the final RAA (V. Greco et al.,arXiv:1312.6857 [nucl-th] and F. Scardina poster)2

2
t=0 fmt=2 fmt=4 fmt=6 fm

1.5
LV/BM

LV/BM

1,5

t=0 fmt=2 fmt=4 fmt=6 fm1

0,5

1

ボトムは十分に重そう。

0.5

Bottom

Charm

0
0

1

2

3

4
p (GeV)

5

6

7

0
0

1

2

3
4
p (GeV)5

6

7

For beauty on the other hand Langevin≡Boltzmann!
Andrea Beraudo

Dynamics of heavy flavor quarks in high energy nuclear collisions

Heavy(Ion(Cafe(and(Pub( 2014/06/06(

Transport'coefLicient'on'the'latticeLattice-QCD transport coeﬃcients: setup
Non perturbative information on HF transport coeﬃcients can beobtained from lattice-QCD simulations, so far treating the HQ’s as static(M = ∞) color sources placed in a thermal bath.
One consider the non-relativistic limit of the Langevin equation:

dp i 輸送係数を非摂動的に定義しよう！
= −ηD p i + ξ i (t), with ⟨ξ i (t)ξ j (t ′ )⟩ = δ ij δ(t − t ′ )κdt
運動量拡散係数は、“力”のHence, in the p → 0 limit:! +∞! +∞ 時間相関で表される。
11dt⟨ξ i (t)ξ i (0)⟩HQ ≈dt ⟨F i (t)F i (0)⟩HQ
κ=
3 −∞
3 −∞
"
#$
%
≡D > (t)In the static limit the force is due to the color-electric field:!
F(t) = g dxQ † (t, x)t a Q(t, x)Ea (t, x)

κ is then given by the ω → 0 limit of the spectral density σ(ω) of theabove E-field correlator
D > (ω)1 σ(ω)
1T
≡ lim
σ(ω)
κ ≡ lim
∼
−βω
ω→0
ω→0
ω→0
3
31−e
3ω
Andrea Beraudo

Dynamics of heavy flavor quarks in high energy nuclear collisions

Lattice-QCD transport coeﬃcients: results
The spectral function σ(ω) has to be reconstructed starting from theeuclidean electric-field correlator⟨Re Tr[U(β, τ )gE i (τ, 0)U(τ, 0)gE i (0, 0)]⟩DE (τ ) = −⟨Re Tr[U(β, 0)]⟩虚時間方向の電場相関

according to

DE (τ ) =! +∞0dω cosh(τ − β/2)σ(ω)
2π sinh(βω/2)One gets (D. Banerjee et al., PRD 85 (2012)
014510; A. Francis et al., PoS LATTICE2011
202 and arXiv:1311.3759 [hep-lat])κ/T^3 ~ 2.4(6)は現象論から見積もられた値(~4)に比較的近い。
4

Gimp/Gnorm
continuum
NLO
κ/T3=2.4(6)3.5

κ/T 3 ≈ 2.4(6) (quenched QCD, cont.lim.)∼3-5 times larger then the perturbative result(W.M. Alberico et al, EPJC 73 (2013) 2481).
Challenge: approaching the continuum limit infull QCD (see Kaczmarek talk)!
Andrea Beraudo

Y.A., Hatsuda, Hirano (’09)

3
2.5
2
1.5
1

τT
0

0.1

0.2

0.3

0.4

0.5

Dynamics of heavy flavor quarks in high energy nuclear collisions

Heavy Quark Momentum Diffusion Constant – Tree-Level Improvement[A.Francis,OK,M.Laine,J.Langelage, arXiv:1109.3941 and arXiv:1311.3759]

lattice cut-off effects visible at small separations (left figure)Æ tree-level improvement (right figure) to reduce discretization effects

連続極限への補正を横軸方向
LO
LO
Gcont ( T ) = Glat ( T )で考える。

leads to an effective reduction of cut-off effect for all T

Heavy Quark Momentum Diffusion Constant – Model Spectral Function
4

Gim p/Gnorm

result of the fit to }model ()continuum
NLO
3
N/T =2.4(6)3.5
3with three parameters: w,A,B

連続極限の虚時間相関関数から

2.5

κを読み取る。スペクトル関数の形を仮定。

2
1.5
1

WT
0

0.1

0.2

0.3

0.4

0.5

Model spectral function: transport contribution + NLO + correctiono3 w}model () t max A}NLO () + B ,2TnGmodel ( ) t

Z 
0

d
}model ()
|

cosh

¡1

2 c Tsinh 2T¢T

used to fit the continuum extrapolated dataÆ first continuum estimate of w :(still preliminary)

2T }E ()' 2.4(6)0

w/T 3 = lim

Heavy Quark Momentum Diffusion Constant – Model Spectral Function
4

Gim p/Gnorm

result of the fit to }model ()3.5

A }NLO() + B w3

3
2.5
2

NLO perturbation theory

1.5
3

A*NLO+B*Z
NLO
N Z/2T

1
0.5
0

w
2T

WT
0

0.1

0.2

0.3

0.4

small but relevant contribution
at T > 0.2 !

0.5Model spectral function: transport contribution + NLO + correctiono3 w}model () t max A}NLO () + B ,2TnGmodel ( ) t

Z 
0

d
}model ()
|

cosh

¡1

2 c Tsinh 2T¢T

used to fit the continuum extrapolated dataÆ first continuum estimate of w :(still preliminary)

2T }E ()' 2.4(6)0

w/T 3 = lim

Quarkonium• Andronic((plenary)(• Zhuang((parallel)(• Song((parallel)(• Kopeliovich((parallel)(• Topics(• Phenomenology(at(AA(collisions(• Transport(model(• QCD(sum(rule(and(heavy(quark(potenYal(• Quarkonium(at(high(pT(

Heavy(Ion(Cafe(and(Pub( 2014/06/06(• Talk(slides(from(

Heavy(Ion(Cafe(and(Pub( 2014/06/06(

Phenomenology'at'AA'
collisions

1.2

J/ ψ

ALICE (|y|<0.8, ±13% syst. uncert.)
Statistical Hadronization Model
Transport Model (Zhou et al./Tsinghua)
Transport Model (Zhao et al./TAMU)

1.4

RAA

J/ ψ

RAA

Model comparisons for the LHC
A.Andronic@GSI.de
10
Statistical Hadronization Modelとmidrapidity
forward rapidity
Transport Modelの現象論
1.2

1

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

Pb-Pb sNN=2.76 TeV
0
0

50

100

150

200

ALICE (2.5<y<4.0, ±15% syst. uncert.)
Statistical Hadronization Model
Transport Model (Zhou et al./Tsinghua)
Transport Model (Zhao et al./TAMU)

1.4

Pb-Pb sNN=2.76 TeV

250

300

350

400

Npart

0
0

50

100

150

200

250

300

350

400

Npart

Both model categories reproduce the data ...dσcc̄/dy values rather diﬀerent:
midrapidity: Stat. Hadr.: 0.3-0.4 mb
Transport: 0.5-0.75 mb (TAMU), 0.65-0.8 mb (Tsinghua)J/ψ vs. pT - data and models
13

A.Andronic@GSI.de

1.4
1.2

forward rapidity
R AA

R AA

midrapidity
ALICE Preliminary, inclusive J/ψ→e+ePb-Pb, sNN=2.76 TeV, |y |<0.8, centrality 0-40%
Transport model (Zhao et al., Nucl.Phys.A859(2011)114)
Transport model (Zhou et al., arXiv:1401.5845)

ALICE (arXiv:1311.0214), centrality 0% 20%, 2.5<y <41.2

global syst.= ± 8%

Transport model (K. Zhou & al, arXiv:1401.5845)
Transport model (X. Zhao & al., NPA 859 (2011) 114)

Primordial J/ψ (w/ shadowing)
Regeneration J/ ψ (w/ shadowing)
Primordial J/ψ (w/ shadowing)

0.8

Primordial J/ψ (w/ shadowing)

Regenerated J/ψ (w/ shadowing)

Regeneration J/ ψ (w/ shadowing)

0.6

0.6

0.4

0.4

0.2

0.2
0

Inclusive J/ψ → µ+µ-, Pb-Pb s NN = 2.76 TeV

1

1
0.8

1.4

2

4

6
p T (GeV/c )

0

0

1

2

3

4

5

6

7

8

p (GeV/c )T(re)generation models describe the LHC data well ...with a healthy fraction ofJ/ψ newly produced
LHCでのlow pTのJ/Ψは、
ALICE, arXiv:1311.0214 (& prelim., Book, HF 4)

regenerationが主な生成メカニズム。

Bottomonium at the LHC
20
RAA

A.Andronic@GSI.de

1.4

CMS PbPbsNN = 2.76 TeV

ϒ (1S), stat. unc.
ϒ (1S), syst. unc.
ϒ (2S), stat. unc.
ϒ (2S), syst. unc.

1.2
1interpreted as eﬀect of (almost:) fulldissoc. of Υ(2S), Υ(3S), χb

Lint = 150 µb-1

Transport models:|y| < 2.4

Emerick et al./TAMU, EPJA 48 (2012) 72µ

p > 4 GeV/c
T

Zhuang, HF 6
30-40%

0.8

40-50%(re)gen. component small (!10%),20-30%

50-100%

Stat. Hadr. model

5-10% 0-5%

0.4

Y
RAA

10-20%

0.6

CMS, Y(1S) (|y|<2.4, ±14% syst.), sNN=2.76 TeV

1.4

Statistical Hadronization Model

1.2
1

0.2

dσbb /dy=13.8 µ b

0.8
0.6

0
0

50

100

150

200

250

300

350

400

0.4

dσbb /dy=9.2 µ b

0.2
Npart基底状態より励起状態の方が、00

媒質効果を受けやすい。

CMS, PRL 109 (2012) 222301

50

100

150

200

250

300

350

400

Npart

Bottomonium at RHIC
A.Andronic@GSI.de

STAR, arXiv:1312.3675

PHENIX, arXiv:1404.2246(Zha, HF 4)(da Silva, HF 6)

2

AA

(b)

1.8

STAR Au+Au
STAR Au+Au, Centrality Integrated

1.6

STAR d+Au

1.4

Rϒ (1S+2S+3S) R

AA,dA

21

Strickland-Bazow Model

1.2
1

Emerick-Zhao-Rapp Model

Strong Binding Scenario

p+p Stat. Uncertainty

Weak Binding Scenario

p+p Syst. Uncertainty

1.2

0.8

1

0.6

0.8

PHENIX

0.4

0.6

0.2

0.4

STAR ϒ (1S+2S+3S)
sNN = 200 GeV

0.2
0

0

50

100

150

0
0

|yϒ |<0.5
200

250

300

350

50

100

150

200

250

300

350

400

Npart

複素ポテンシャルをそのまま使った計算もある。
Emerick et al./TAMU, EPJA 48 (2012) 72; Strickland, Bazow, NPA 879 (2012) 25

is the charmonium story SPS–RHIC repeating with bottomonium RHIC–LHC?

N

400
part

More bottomonium at the LHC
22

A.Andronic@GSI.de

1.4

R AA

R AA

ALICE arXiv:1405.4493 (Castillo, talk HF 6)
Pb-Pb s NN = 2.76 TeV, inclusive ϒ (1S), p T > 0-1

ALICE: L int = 69 µb , 0%-90% (open: reflected)
CMS: L int = 150 µb-1, 0%-100%

1.2

ALICE: L int = 69 µb-1, 0%-90% (open: reflected)
CMS: L int = 150 µb-1, 0%-100%

1
Total

Regenerated

Primordial

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0
-4

Pb-Pb s NN = 2.76 TeV, inclusive ϒ (1S), p T > 0

1.2

1
0.8

1.4

-3

-2

-1

0

1

2

Emerick et al./TAMU, EPJA 48 (2012) 72

3

4
y

0
-4

Boost-invariant plateau
Gaussian profile

-3

-2

-1

4πη/s = 34πη/s = 304πη/s = 24πη/s = 2

1

Strickland, Bazow, NPA 879 (2012) 25

24πη/s = 14πη/s = 1

34y

ラピディティー分布は、どのモデル
no model does very wellも説明できていない。
...recall the shocking RAA vs. y of J/ψ? (PHENIX, 2006)

Heavy(Ion(Cafe(and(Pub( 2014/06/06(

Transport'modelA Dynamic Transport Approach for Quarkonia in HIC

QuarkoniumのTransportの模型

ƽ QGP evolution

w PT PQ

0,

w P nPƽquarkonium motion (<0 + equation of state

J /\ , \ ', F c )gluon dissociation cross section by OPE
and quarkonium size by potential model

V (T ) V (0) r 2 (T ) / r 2 (0)detailed balanceƽcold medium effects (for instance, EKS98) modify not only the initialquarkonium distribution but also the regeneration!
ƽassumption: thermalized gluon and heavy quark distributions

HQの数が変われば、
regenerationの頻度も変わる。

（注）Bottomも熱平衡分布を仮定する
4のがどれくらい正しいのか？

Upsilon(1s) at mid rapidityd‫(׳‬1s)/dy=40 nb (PYTHIA, CDF(1.8TeV) and CMS(7 TeV))d‫(׳‬bb)/dy=20 ub (FONLL)
反応率を計算するために、ポテンシャル
CMS data: NPA910, 91(2013)（U or F）と束縛状態の波動関数が必要。

in central collisions:
1) T(2s)<T<T(1s) for both V=U and V=F, excited states are eaten up but
ground state is not affected, R_AA=0.5;
2) small regeneration.
ground state is not sensitive to the hot medium !
6

Upsilon(2s) at mid rapidity

ポテンシャルは、UのほうがFより深いので。
in central collisions:
1) initial production is eaten up by the hot medium, the small
regeneration becomes dominant!
2) for V=F, T(2s)~Tc, regenerated Upsilon(2s) is again eaten up by themedium !
3) the data favor V=U.
excited states are sensitive to the hot medium !
7

Pt Ratio (Upsilon)

the excited Upsilon states are sensitive to the hot medium !

Heavy(Ion(Cafe(and(Pub( 2014/06/06(

QCD'sum'rule'and'heavy'quark'potentialDispersion relation
左辺を有限温度のGluon凝縮で評価、右辺はスペクトル関数：Quarkoniumの媒質中のダイナミクス• Physical parameters

波動関数の原点~QとQbarが対消滅する確率。

8

J/Ψ wavefunction |Ψ(0)|波動関数の原点での値をポテンシャルモデルで計算。

Borel windowでの値：|Ψ(0)|~0.16-0.17@T=Tc

1. Both |Ψ(0)| and J/Ψ mass decrease with T
2. Width effect is small

11

5. Comparison of the results fromQCD sum rule & Schrödinger equation|Ψ(0)| as well as J/Ψ mass from QCD sum rule closely follow those
テ energy potential.
from free

QCD和則から求めた|Ψ(0)|は、V=Fとしたポテンシャルモデルと良く合う。
17

J/Ψ  wavefunction
from the complex Schrödinger equation

この計算では、ポテンシャル虚部にHTL摂動論

T=1.0 Tc の結果を用いている。10倍しても|Ψ(0)|はほとんど不変。しかし何故？？

Rothkopf, Hatsuda,
Sasaki (2012)（注）有限温度中の複素ポテンシャルを直接計算する研究もある。

Imaginary potential does not affect |Ψ(0)| !!
16

Heavy(Ion(Cafe(and(Pub( 2014/06/06(

Quarkonium'at'high'pT

High pTのQuarkonium

Charmonium propagation through a hot medium
Path integral technique
B.G.Zakharov & B.K. PRD44(1991)3466

q
z1

q

h (r)

z2

Gq̄q (z1 , 0; z2 , r)



d
i
dz

m2c
r?
E /2

Vq̄q (z, r? ) Gq̄q (z1 , r?1 ; z, r? ) = 0

The Green function Gq̄q (z1 , r1 ; l2 , r2 ) describes
propagation of the dipole between longitudinalcoordinates z1,2 with initial and final transverse(2D) separations r1,2 .

The imaginary part of the light-cone potential describes absorption,
Transport coefficient q̂ , the rate of broadening,v
2
ImVq̄q (z, r? ) =q̂(z) r?
is related to the medium temperature, q̂ ⇡ 3.6 T3
4( T > Tc ) and is to be adjusted to data.

ReVq̄q (z, r) corresponding to the binding potential, is known only in the rest
frame of the dipole, and it also depends on longitudinal dipole separation rL

It cannot be properly described with this 2-dimensional Schrödinger equation.
Debye screening corrections make it even more challenging.
4

B.Z.$Kopeliovich,$Quark$Ma5er,$2014

Solving the equation
ReUq̄q (r? , ⇣) =

M
V
p+

✓q

r2? + ⇣ 2◆

- rest frame potential

This is the main result, a simple replacement:rL ) ⇣In the rest frame the usual Schrödinger equation is recovered.

ImUq̄q (r? , ⇣) =1
v q̂ r2? controls absorption and is independent of ζ
4

Screened potential.
✓◆qVc̄c r = r2? + ⇣ 2 =µ(T) = g(T)T

r

Nf
1+
,
6

µ(T)

Lightcone座標でのポテンシャル？
⇣ このように定義すれば良いらしい。
⌘
1e µ(T)r↵ µ(T)re
r24⇡ 2
g (T) =
33 ln (19T/⇤M̄S )2

F. Karsch, M. T. Mehr and H. Satz, Z. Phys. C 37, 617 (1988)

The equation is solved numerically with q̂ = q0
7npart (˜⌧ , b̃) t0;
npart (0, 0) t

q0 = 1 fm
B.Z.$Kopeliovich,$Quark$Ma5er,$2014

問題設定は面白い。

これは波動関数ではないと、 Results 流体静止系にいるQuarkoniumの描像から連続的にどう移るか？
何回も言っているのに・・・。

in (r1 , ⇣1 )

1.

1.0

1.0

0.8

0.8

0.6

q0 = 0.5 GeV2 /fm
q0 = 1.0 GeV2 /fm
q0 = 2.0 GeV2 /fm
q0 = 3.0 GeV2 /fm
q0 = 4.0 GeV2 /fm

0.2
0.0
10−1

1

1.2

3.Total suppression: ReU 6= 0; ImU 6= 0.
2

4. q0 = 2 GeV /fm

10

0.2
0.0
10−1

102

1

10

Full
Melting
Absorption

1.2

2.

1.0

1.0

0.8

0.8

0.6

102

pT , GeV

S2

S2

3.

0.6

pT , GeV

1. Net melting: ReU 6= 0; ImU = 0.

q0 = 0.5 GeV2 /fm
q0 = 1.0 GeV2 /fm
q0 = 2.0 GeV2 /fm
q0 = 3.0 GeV2 /fm
q0 = 4.0 GeV2 /fm

0.4

0.4

Calculations are done for central Pb-Pb
collisions with realistic nuclear density.
No ISI effects are added.

2. Net absorption: ReU = 0; ImU 6= 0.

1.2

S2

⇥G(r2 , ⇣2 , z2 ; r1 , ⇣1 .z1 )

1.2

S2

Survial probability amplitude
Z
S(z2 , z1 ) = d⇣2 d⇣1 d2 r2 d2 r1 J/ (r2 , ⇣2 )

4.

0.6
0.4

0.4
q0 = 0.5 GeV2 /fm
q0 = 1.0 GeV2 /fm
q0 = 2.0 GeV2 /fm
q0 = 3.0 GeV2 /fm
q0 = 4.0 GeV2 /fm

0.2
0.0
10−1

1

pT , GeV
8

10

102

0.2
0.0
10−1

1

10

102

pT , GeV
B.Z.$Kopeliovich,$Quark$Ma5er,$2014

Photon'and'Dilepton'• Bratkovskaya((plenary)(• Ghiglieri((plenary)(• Topics(• Direct(photon(ﬂow(• Rate(in(NLO(perturbaSon

Heavy(Ion(Cafe(and(Pub( 2014/06/06(• Talk(slides(from(

Heavy(Ion(Cafe(and(Pub( 2014/06/06(

Direct'photon'Llow1. Hydro: Influence of e-b-e fluctuating initial conditions
Î From smooth Glauber initial conditions
光子のv2@RHIC, LHC
to event-by-event hydro with fluctuating initial conditions

テ
各Eventの完全流体発展から光子放射
 Jyväskylä
ideal hydro Ideal QGP and HG fluid

 Initial: ‚bumpy‘ ebe
MC Glauber EoS: lQCD
Talk by R. Chatterjee@
Chatterjee@QM‘
QM‘14,14,
PRC
PRC 88, 034901 (2013)

Î Fluctuating initial conditions: slight increase at high pT for yield and v2
small effect, right direction!
Elena Bratkovskaya (Uni. Frankfurt)

Quark Matter-20149

2. From ideal to viscous hydro: direct photons as a QGP viscometer?
The thermal photon emission rates with viscous corrections:

粘性による分布関数のゆがみの効果

equilibrium contribution

 (3+1)D MUSIC (McGill):
M. Dion et al., PRC84 (2011) 064901

 viscous QGP and HG fluid
 Initial: ‚bumpy‘ ebe from IP-Glasma EoS: lQCD

first order viscous correction

 (2+1)D VISH2+1 (Ohio State) :C. Shen et al., arXiv:1308.2111
arXiv:1308.2111,, arXiv:1403.7558; Talk by C. Shen @ QM2014

 viscous QGP and HG fluid
 Initial: ‚bumpy‘ ebe from MC Glauber /KLN
 EoS: lQCD

RHIC energy

Thermal photons:
QGP +HGÎ Effect of shear viscosity:
t!
n
a
t
or
* small enhancement of the photon yieldImp* suppression of photon v2* effect on v2 for photons is stronger than for hadrons
Elena Bratkovskaya (Uni. Frankfurt)

Quark Matter-201410

3. Influence of Glasma initial conditions with initial flow (3+1)D MUSIC - 2014:
J-F. Paquet et al. (2014)(2014)IPグラズマ初期条件

 viscous QGP and HG fluid (K/s=0.22)

ALICE (preliminary)
Au+Au, 2760 GeV

 Initial: ‚bumpy‘ ebe from IP-Glasma Îgenerate initial flow due to fluctuations of IC
IP-Glasma:
Schenke et al., PRL108
PRL108 (2012) 252301

 EoS: lQCD
 QGP photon rate: AMY
 HG photon rate: TGR for meson gas with viscouscorrections + Rapp spectral function for U-mesons
to account for the baryonic contributions

 MUSIC with IC-Glasma describes vn of

hadrons at RHIC & LHC,
however, missing v2, v3 of photons!

Î ‚Bumpy‘ ebe from IP-Glasma - small effectElena Bratkovskaya (Uni. Frankfurt)

Quark Matter-201411

4. Hydro with pre-equilibrium flow 初期条件における
 ‚Initial‘ flow: rapid increase of bulk v2 in fireball modelvan Hees, Gale, Rapp, PRC84 (2011) 054906

 pre-equilibrium flow in (2+1)D VISH2+1 - 2014:

有限フローの効果
ALICE (preliminary)
Au+Au, 2760 GeV

C. Shen et al., arXiv:1308.2111
arXiv:1308.2111,, arXiv:1403.7558; Talk by C. Shen @ QM‘
QM‘2014 viscous QGP and HG fluid (K/s=0.18)

 Initial: ‚bumpy‘ ebe from MC Glauber /KLN
 EoS: lQCD
 QGP photon rate: AMY
 HG photon rate: TGR for meson gas with viscous corrections• Generation of pre-equilibrium flow:using free-streaming model to evolve the partons
right after the collisions to 0.6 fm/c
+ Landau matching to switch to viscous hydroÎ quick development of momentum anisotropy
with saturation near TC
Î Pre-equilibrium flow:

 small effect on photon spectra slight increase of v2
Elena Bratkovskaya (Uni. Frankfurt)

Warning: results can be considered as
upper limit for the pre-equilibrium flow effect!
Quark Matter-2014

12

PHSD: photon spectra at RHIC: QGP vs. HG ?
Parton-Hadron-String Dynamicsの計算
 Direct photon spectrum (min. bias)

Linnyk et al., PRC88 (2013) 034904;
PRC 89 (2014) 034908

PHSD:
 QGP gives up to ~50% of direct photon
yield below 2 GeV/c! sizeable contribution fromhadronic sources– meson-meson (mm) andmeson-Baryon (mB) bremsstrahlungm+mÆ m+m+J
m+BÆ m+B+J
 m=SKUZ..*,…
B=p

!!! mm and mB bremsstrahlung channels
can not be subtracted experimentally !
Elena Bratkovskaya (Uni. Frankfurt)

Quark Matter-201416

Are the direct photons a barometer of the QGP?
 Do we see the QGP pressure in v2(J) if the photon productions is dominatedby hadronic sources?

PHSD: Linnyk et al.,
PRC88 (2013) 034904;
PRC 89 (2014) 034908

1) v2(Jincl) = v2(S) - inclusive photons mainly come from Sdecays HSD (without QGP) underestimates v2 of hadrons andinclusive photons by a factor of 2, wheras the PHSD modelwith QGP is consistent with exp. data
HSD(no QGP)Î The QGP causes the strong elliptic flow of photons
indirectly, by enhancing the v2 of final hadrons due tothe partonic interactions
direct photon v2 in PHSD
1/2

Au+Au, sNN =200 GeV, MB, |y|<0.35

0.3,
PHENIXiv2 = 6i v2 Ni(J)/Ntot(J)dir2) v2(Jdir) of direct photons in PHSD underestimates thePHENIX data :v2(JQGP) is very small, but QGP contribution is up to 50% of
total yield Î lowering flow

PHSD

v2

0.2

0.1

0.0
0.0

Direct photons (inclusive(=total) – decay):ÎPHSD: v2(Jdir) comes from mm and mB bremsstrahlung !
0.5

1.0

1.5

pT [GeV/c]

2.0

Elena Bratkovskaya (Uni. Frankfurt)

2.5

Quark Matter-201420

Heavy(Ion(Cafe(and(Pub( 2014/06/06(

Rate'in'NLO'perturbation22 processes
1 loop O(αEM ):K

Kinematically disallowed for light-like K(both quarks can’t be on-shell simultaneously)

2)• Cut two-loop
diagrams(αgEMLOdiagrams
2 loops O(α α ):EMs

Cut diagrams correspond to:
KCompton scattering:K

LO diagrams

∝

t

!

2
dq⊥

!

2
dq⊥

dσ
2
dq⊥

Cut diagrams correspond to:2↔2 processes(with crossingsand interferences):Compton scattering:
Pair annihilation:

P0

Z

P

t

K0

K

t∝

!

2 dσ
dq⊥
2
dq⊥

∝

dσ
2
dq⊥

Every time a scattering takes place, a quark can convert to a photo
2 = 0) t −→ 00, IR divergence: 0⇒ For 2(K 4
f (p)f (p )(1 ± f (k ))|M| (P !+ Pdσ! K K ) " #
2
k0 T
∝ dq>
ph. space
t
2 dσ
⊥
2
∝
ln
dq⊥
D dq
∝⊥
2
dq⊥
Λ2IR
Λ2IR
Every time a scattering takes place, a quark can convert to a photon⇒ For (K 2 = 0) t −→ 0, IR divergence:
"
#
!
k
T
dσ
0
2
∝ ln
dq⊥
D> ∝
2
2
dq
Λ2IR
ΛIR
⊥
Pair
0 annihilation: 0• Equivalence with kinetic theory: distributions x
matrix elements

HTLで赤外正則化• IR divergence (Compton) when t goes to zero

it is an HTL gluon in the Landau cut. In these diagrams the gluon is scattering o↵ light quarks(the hard lines at the bottom). The corresponding case with gluons is not shown.

{fig_colline

Collinear processes••

In terms of the two-point function these processes correspond to diagrams with thetwo nearly collinear fermion lines connected with arbitrary number of soft spacelike gluonsggwith same kinematics as Q. In [14, 15] Arnold, Moore and Ya↵e (AMY) showed that it is
only the ladder-type diagrams shown in Fig. 6 that contribute to leading order calculation;
the factors of g arising from additional vertices are canceled by near on-shell propagatorsand large statistical factors arising from the gluonic propagators. The near on-shellness ofthe quark lines makes the diagrams sensitive to thermal mass m21 ⇠ g 2 T 2 and the thermal
These
diagrams
contributetoLO
ifconsistently
small (g)angleradiation/
2 T of the quark
width ⇠
gFigurelines, Inwhich
to betheresummed.
5. Collinear diagrams.
the firstneedcase, called
bremsstrahlung diagram,the angle Furthermore
between the emitted photon and the outgoing emitting fermion is of order g. In the second case,
AMY showed
how Aurenche
these diagrams
can beresummedin terms of Zaraketa Schrödinger
equationannihilation
Gelis
Kobes
Petitgirard
called the pairannihilation diagram,
it is theangle between
the annihilating quark
and antiquark1998-2000
type di↵erential
andtheywhere
obtained
completeleading-orderresults
in [15]. In
that is equation,of order g. The
diagrams
the gluonthe
is attachedto the otherfermionic line arenotshow. In both cases the gluon is soft and is scattering on the hard constituents of the plasma, i.e.,
Sec. 3 we will
discuss in detailthis equationin thethecontext
of the treatmentof its NLO
it is an HTL gluon in theLandau cut.
In thenthese diagrams
gluon sameis scattering o↵light quarksof the soft
Photonformation
times
is
of
the
order
corrections. (the hard lines at the bottom). The corresponding case with gluons is not shown.
{fig_collinear}

scattering rate ⇒ interference: LPM effect• Requires resummationofinfinitenumberofladderdiagrams
In terms of the two-point function these processes correspond to diagrams with the
0

1⇤ 0

1

two nearly collinear fermion lines connectedB with arbitrary number of softCspacelike
gluons
B
C
B
C B
C
B
C B
C
B
B
C
C
with
same
kinematics
as
Q.
In
[14,
15]
Arnold,
Moore
and
Ya↵e
(AMY)
showed
that
it
is
d
B
C B
C
C B
C
=
= Re B3
C B calculation;Cd k
only the ladder-type diagrams shown in Fig.B
B 6 that contribute to leading order
C B
C
B
B
C
C
coll
@
@
A
A
the factors of g arising from additional vertices are canceled by near on-shell propagatorsand large statistical factors arising from the gluonic propagators. The near on-shellness ofthe quark lines makes the diagrams sensitive to thermal mass m21 ⇠ g 2 T 2 and the thermal
width ⇠ g 2 T of the quark lines, which need to be consistently resummed. Furthermore
Figure 6. The
uncrossed ladder diagrams that need to be resummed to account for the LPM e↵ect
AMY showed how these diagrams can be resummed in terms of a Schrödinger equation

AMY (Arnold Moore Yaffe) JHEP 0111, 0112, 0226 (2001-02)

in the collinear region. The cut shown here corresponds to the interference term on the right-handBeyond leading order• The soft scale gT introduces O(g) correctionsnB (p) ∼ T /p ∼ 1/g

3種類の寄与(correction from soft scale / collinear / semi-collinear)gg• In the collinear sector: account for 1-loop rungs (related to
NLO qhat). Euclidean (EQCD) evaluation
Caron-Huot PRD79, talks by Panero, Meyer• New semi-collinear processes: larger angle radiation, NLO
in collinear radiation approx. Requires a “modified qhat”,
relevance for jets too√gsoft plasmon,
timelike√g

soft Coulomb,
spacelike2

CLO+ δCsoft+sc• Add soft gluons to soft quarks: nasty all-HTL region
+
1
p
CLO
Analytic

0

P

1

2

3

4

2

CLO+NLO

4

5

6

7

8

0

9

10

• Analyticity allows us to take a detour in thek/T
complex plane
away from the nasty region ⇒Figurecompact
expression
19. Thefunctions C(k/T ) for Nc = 3, Nf

JG Hong Kurkela Lu
Moore Teaney JHEP0503

2(LO + coll)/LO

1.5(LO + NLO)/LO1

0.5(LO + soft+sc)/LO

αs=0.30
0
2

4

6

8
k/T

10

12

14

(LO+NLO) / LO

(LO+NLO) / LO

• Summing all contributions:
good convergence,
but with large
cancellations
between contributions:error estimate of LO

1.

0.