MeasurementsofTwo/Par1cle*Correla1ons...

Measurements of Two-‐Par1cle Correla1ons with respect to Higher-‐Order Event Planes

in √sNN=200 GeV Au+Au collisions at RHIC-‐PHENIX

Pre-‐Defense Session Nov 6th 2013

Takahito Todoroki High Energy Nuclear Physics Group

2013/11/06 pre-‐Defense 1

Outline •  Introduc)on –  Quark Gluon Plasma (QGP) –  Previous Measurements and Theore)cal Models –  Higher-‐Order Flow Contribu)ons in Two-‐Par)cle Correla)ons

•  Analysis –  Data Set & Experimental Set Up –  Flow and Two-‐Par)cle Correla)on Measurements –  Correla)ons with respect to Event Planes

•  Results & Discussion –  Inclusive Trigger Correla)ons –  Event Plane Dependent Correla)ons

•  Summary


INTRODUCTION


Quark Gluon Plasma (QGP) •  A fluid of quark and gluons deconfined from hadrons at high energy-‐density ε & temperature T

•  Predicted transi)on ε & T by LaRce-‐QCD

–  εc ~ 1.0 [GeV/fm3] –  Tc ~ 170 [MeV]

•  Rela)vis)c Heavy Ion Collisions at RHIC

–  ε ~5.0 -‐ 15.0 [GeV/fm3]


0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

1.0 1.5 2.0 2.5 3.0 3.5 4.0

T/Tc

�/T4 �SB/T4

3 flavour2+1 flavour

2 flavour

F. Karsch, Lect. Notes Phys. 583, 209 (2002)

Rela1vis1c Heavy Ion Collider

•  Accelerators at Brookhaven Na)onal Laboratory –  Tandem van de Graaff –  Linear Accelerator –  Booster Synchrotron –  Alterna)ng Gradient Synchrotron –  Rela)vis)c Heavy Ion Collider


Year Species !s [GeV ] "Ldt Ntot (sampled) Data SizeRun1 2000 Au - Au 130 1 !b-1 10 M 3 TB

Au - Au 200 24 !b-1 170 M 10 TBAu - Au 19 < 1 M

p - p 200 0.15 pb-1 3.7 B 20 TBd - Au 200 2.74 nb-1 5.5 B 46 TBp - p 200 0.35 pb-1 6.6 B 35 TB

Au - Au 200 241 !b-1 1.5 B 270 TBAu - Au 62.4 9 !b-1 58 M 10 TBCu - Cu 200 3 nb-1 8.6 B 173 TBCu - Cu 62.4 0.19 nb-1 0.4 B 48 TBCu - Cu 22.4 2.7 !b-1 9 M 1 TB

p - p 200 3.8 pb-1 85 B 262 TBp - p 200 10.7 pb-1 233 B 310 TBp - p 62.4 0.1 pb-1 28 B 25 TB

Run-7 2007 Au - Au 200 813 !b-1 5.1 B 650 TBd - Au 200 80 nb-1 160 B 437 TBp - p 200 5.2 pb-1 115 B 118 TB

Au - Au 9.2 few k

Run-6

Run-8

2002/03

2006

2007/08

2005

2001/02Run2

Run3

Run4 2003/04

Run5

•  p+p : 510 GeV •  d+Au, Cu+Cu, Cu+Au, Au+Au: 200GeV •  U+U : 193 GeV

PHENIX Run Summary

Space-‐Time Evolu1on


�µT �µ = 0�µjµ

B = 0

Hydrodynamic Expansion

Number & Species of Par1cles Fixed

(Kine1c Equilibrium)

Break of Kine1c Equilibrium

Collec1ve Expansion •  Pressure Gradient due to small λ/R<<1


Smooth Parton Density

Fluctua1ng Parton Density

Px

Py Pz

•  Expansion with respect to Ψn

Ed3N

dp3=

d2N

2�dpT d�

�1 +

�2vn cos n(��n)

�

vn =< cosn(��n) >

� : azimuthal angle of emitted particles� : azimuthal angle of event plane

Ed3N

dp3=

d2N

2�dpT d�

�1 +

�2vn cos n(��2)

�

vn =< cosn(��2) >

PRC81.054905 (2010)

Higher-‐Order Flow Harmonics

•  None-‐zero vn(n>2) •  Disentanglement of a degeneracy among models –  Ini)al Condi)on, Sheer Viscosity in Hydrodynamics

•  Backgrounds in correla)on studies


PRL107.252301 (2011)

Jet-‐Quenching

•  Suppression of par)cles compared to p+p collisions –  Nuclear modifica)on Factor RAA<1 –  Away-‐Side suppression of Correla)ons


p+p� Au+Au�

RAA =d2NAA/dpT d�

Ncolld2Npp/dpT d�

PRL91.072304 (2003)

SUPPRESSION OF AWAY-SIDE JET FRAGMENTS WITH . . . PHYSICAL REVIEW C 84, 024904 (2011)

FIG. 6. (Color online) Per-trigger azimuthal jet yields for the mostin-plane, !s = 0–15! (solid circles), and out-of-plane, !s = 75–90!

(open circles), trigger particle selections in midcentral (20%–60%)collisions for various partner momenta. Insets show away-sideregion on a zoomed scale. Bars indicate statistical uncertainties.Underlying event modulation systematic uncertainties are representedby bands through the points while the corresponding normalizationuncertainties are shown as dashed lines around zero. Near- andaway-side jet yield integration windows are indicated with arrows.

this source of systematic uncertainty has little correlationbetween the centrality and momentum selections.

For central events the near-side suppression is consistentwith a constant as a function of !s within the statisticaland !s-correlated systematic uncertainties. The values arealso consistent with no suppression when considering theglobal scale uncertainty that appears on the trigger particleorientation averaged IAA. On the away-side, there is significantsuppression in central events, as evidenced by the triggerparticle averaged IAA, but the statistical precision with whichto determine the !s variation is limited.

Midcentral (20%–60%) events, have greater eccentricityand could be expected to show correspondingly larger triggerparticle orientation dependence due to path-length variationthrough the collision zone. The same set of representativeper-trigger azimuthal yields is shown in Fig. 6 for themidcentral selection. Again, the near-side jets for the most

FIG. 7. (Color online) Nuclear jet suppression factor IAA byangle with respect to the reaction plane !s for near- and away-sideangular selections, circles and squares, respectively, in midcentral(20%–60%) collisions for various partner momenta. Bars indicatestatistical uncertainties. The shaded band shows the systematicuncertainty on the reaction-plane resolution unsmearing correction.Solid points show trigger particle angle averaged results and theglobal scale uncertainty.

in-plane and most out-of-plane trigger particle orientationsare consistent with each other, a direct indication of littlevariation with respect to the reaction plane. The mid-"! arealso in agreement with zero, as before, further demonstratingthat the underlying event flow correlations are well describedby Eqs. (6)–(9). In contrast to the near-side, the away-sidemeasurements (see insets in Fig. 6) change between thein-plane and out-of-plane trigger particle orientations withthe latter having consistently smaller yield for all partnermomenta.

The integrated near- and away-side per-trigger jet yieldsfor midcentral (20%–60%) collisions are shown in Fig. 7.The near-side jet is essentially flat, with negligible suppres-sion [IAA(!s) = 1]. The away-side jet yield is increasinglysuppressed with increasing !s . This falling trend results inonly small associated particle yield remaining for out-of-planetrigger particle orientations.

024904-9










024904-9










024904-9










024904-9

Au+Au 200GeV 20-‐60%

Path Length Dependence of High pT Correla1ons

•  v2 and v4{Ψ2} subtracted •  Monotonic suppression of away-‐side •  Parton Energy Loss depending on path

length 2013/11/06 pre-‐Defense 10

Short path length

Long path length










024904-9

I AA =

YAA/Y

pp










024904-9










024904-9

PRC.84.024904 (2011)

Double-‐Humps & Ridge of Interm. pT Correla1ons

•  Near-‐side long-‐range rapidity correla)ons (Ridge) •  Away-‐side double-‐humps of azimuthal correla)ons

–  v2 contribu)on subtracted •  Addi)onal Effect to Parton Energy-‐Loss

–  Lost Energy-‐Redistribu)on –  Boost of jet by medium expansion

2013/11/06 pre-‐Defense 11

B. I. ABELEV et al. PHYSICAL REVIEW C 80, 064912 (2009)

!"

-3-2

-10

12

3#"

-1.5-1

-0.50

0.51

1.5

) #" d!"

N/(d

2 d

4647484950515253

-310

Au+Au central3<pt

trig<4 GeV/c

!"

-3-2

-10

12

3#"

-1.5-1

-0.50

0.51

1.5

) #" d!"

N/(d

2 d 4850525456586062

-310

Au+Au central4<pt

trig<6 GeV/c

!"

-3-2

-10

12

3#"

-1.5-1

-0.50

0.51

1.5

)#" d!"

N/(d

2 d

02468

101214

-310

d+Au minimum bias3<pt

trig<4GeV/c

!"

-3-2

-10

12

3#"

-1.5-1

-0.50

0.51

1.5

)# " d!"

N/(d

2 d

0

2

4

6

8

10

12

-310

d+Au minimum bias4<pt

trig<6 GeV/c

FIG. 1. Charged-di-hadron distribution [Eq. (1)] for 2 GeV/c < passoct < passoc

t . Upper left: central Au + Au, 3 < ptrigt < 4 GeV/c; upper

right: central Au + Au, 4 < ptrigt < 6 GeV/c; lower left: minimum bias d + Au, 3 < p

trigt < 4 GeV/c; lower right: minimum bias d + Au,

4 < ptrigt < 6 GeV/c. Note the different vertical scales, as well as the suppressed zero in the upper panels.

by event mixing. Associated particles have 2 < passoct <

ptrigt GeV/c for consistency with previous results [5], except

for a new analysis, which directly compares correlations fordifferent p

trigt (Section VI A), where 2 < passoc

t < 4 GeV/cwas used.

Figure 1 shows distributions of the associated particle yielddefined in Eq. (1) for central Au + Au events with triggers3 < p

trigt < 4 and 4 < p

trigt < 6 GeV/c (upper panels) and for

d + Au events with the same ptrigt selections (lower panels). A

near-side peak centered on (!",!#) = (0, 0) is evident in allpanels and is consistent with jet fragmentation. In addition, asignificant enhancement of near-side correlated yield is seenat large !" for central Au + Au events but not for d + Auevents: the ridge.

In this analysis we examine the shape of the near-sideassociated yield distribution in detail via projections on the!" and !# axes. We characterize the shapes of both theridge and the jet-like peak and study the pt dependence ofthe ridge and jet-like yields.

IV. RIDGE SHAPE IN !"

To study the ridge quantitatively, the di-hadron distributionis projected onto the !" axis in intervals of !#:

dN

d!"

!!!!a,b

!" b

a

d!#d2N

d!#d!"; (2)

similarly for projection onto !#:

dN

d!#

!!!!a,b

!"

|!"|"[a,b]d!"

d2N

d!#d!". (3)

The contribution to the di-hadron distribution of ellipticflow (v2) in nuclear collisions [3] is estimated via

B!#[a, b] ! b!#

" b

a

d!##1 + 2

$v

trig2 vassoc

2

%cos 2!#

&, (4)

where the mean uncorrelated level b!# is fixed by theassumption of zero correlated yield at the minimum of theprojected distribution, in this case 1.0 < !# < 1.2 (zero

064912-4

PRC.80.064912 (2009) PRC.78.014901 (2008) DIHADRON AZIMUTHAL CORRELATIONS IN Au+Au . . . PHYSICAL REVIEW C 78, 014901 (2008)

(rad)!"0 2 4

(rad)!"0 2 4

!"/d

ab)d

Na

(1/N

0

0.01

0.02

0.03

0-5%

2.0-3.0 GeV/c#2.0-3.0 FIG. 9. (Color online) Per-trigger yield !" distribution

and corresponding fits for 2–3 ! 2–3 GeV/c in 0–5%Au+Au collisions. FIT1 (FIT2) is shown in the left panel(right panel). The total fit function and individual com-ponents are shown relative to the # level indicated by thehorizontal line.

jet fragmentation contribution and is parametrized to have thesame width as that for the p + p away-side jet. FIT1 has sixfree parameters: background level # , near-side peak integraland width, and shoulder peak location D, integral, and width.In addition to the parameters of FIT1, FIT2 has a parameterthat controls the integral of the fragmentation component.

The separate contributions of FIT1 and FIT2 are illustratedfor a typical pa

T ! pbT in Fig. 9.

The two fits treat the region around !" = $ differently.FIT2 tends to assign the yield around $ to the centerGaussian, while FIT1 tends to split that yield into the twoshoulder Gaussians. Note, however, that a single Gaussiancentered at $ can be treated as two shoulder Gaussianswith D = 0. Thus FIT1 does a good job at low pT andhigh pT , where the away-side is dominated by shoulder andhead components, respectively. It does not work as well forintermediate pT , where both components are important. Thecenter Gaussian and shoulder Gaussians used in FIT2 arestrongly anticorrelated. That is, a small shoulder yield implies alarge head yield and vice versa. In addition, the center Gaussiantends to “push” the shoulder Gaussians away from $ , and thisresults in larger D values than obtained with FIT1.

Figure 10(a) shows the D values obtained from the twofitting methods as a function of centrality for the pT selection2–3 ! 2–3 GeV/c. The systematic errors from v2 are shownas brackets (shaded bars) for FIT1 (FIT2). The values of Dfor FIT1 are consistent with zero in peripheral collisions, butgrow rapidly to "1 for Npart " 100, approaching "1.05 inthe most central collisions. The D values obtained from FIT2are slightly larger ("1.2 rad) in the most central collisions.They are also relatively stable to variations of v2 because mostof the yield variation is “absorbed” by the center Gaussian

[cf. Fig. 10(b)]. Thus, the associated systematic errors are alsosmaller than those for FIT1.

For Npart < 100, the centrality dependence of D is also quitedifferent for FIT1 and FIT2. As seen in Fig. 10, the D valuesfor FIT2 are above 1. However, the away-side yield in the SR,associated with these D values, are rather small, and the away-side distribution is essentially a single peak centered around$ . For such cases, the values of D are prone to fluctuationsand non-Gaussian tails. The deviation between the D valuesobtained with FIT1 and FIT2 for Npart < 100 simply reflectsthe weak constraint of the data on D in peripheral collisions.

Figure 11 shows the pT dependence of D in 0–20% centralAu+Au collisions. The values from FIT2 are basically flatwith pb

T . Those from FIT1 show a small increase with pbT ,

but with a larger systematic error. At low pT , the valuesfrom FIT1 are systematically lower than those from FIT2.However, they approach each other at large pa,b

T . From FIT1and FIT2, it appears that the values of D cover the range 1–1.2rad for pa

T , pbT

<" 4 GeV/c. This trend ruled out a Cherenkovgluon radiation model [34] (with only transition from scalarbound states), which predicts decreasing D with increasingmomentum.

2. Away-side jet per-trigger yield

Relative to p + p, the Au+Au yield is suppressed in theHR but is enhanced in the SR (cf. Fig. 6). A more detailedmapping of this modification pattern is obtained by comparingthe jet yields in the HR and SR as a function of partner pT .Such a comparison is given in Fig. 12 for central Au+Au andfor p + p collisions. The figure shows that relative to p + p,

partN

D (ra

d)

0

0.5

1

(a)1.5

2.0-3.0 GeV/c!2.0-3.0

FIT1FIT2

partN0 100 200 300 400

shou

lder

-pea

k fra

ctio

n

0

0.2

0.4

0.6

0.8

1

fraction of shoulder-peakyield from FIT2

0 100 200 300 400

(b)

FIG. 10. (Color online) (a) D vs Npart fromFIT1 (solid circles) and FIT2 (open circles) for2–3 ! 2–3 GeV/c bin. The error bars are thestatistical errors; shaded bars and brackets arethe systematic errors due to v2. (b) Fraction ofthe shoulder Gaussian yield relative to the totalaway-side yield as function of Npart determinedfrom FIT2.

014901-13

v2 subtracted

Conical Emission of Away-‐Side

2013/11/06 pre-‐Defense 12

-2 -1.5 -1 -0.5 0 0.5 1 1.5 20

0.05

0.1

0.15

0.2d+Au(a)

-2 -1.5 -1 -0.5 0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

1.2

1.4ZDC 12% Au+Au(b)

)/2 (circles and histograms)2q6-

1q6=(6 (squares) or /)/2-

2q6+

1q6=(Y

)6

or d

Y d

N/(d

Trig

1/N

Trigq-

1q=

1q6

Trig

q- 2q= 2q6

)2q

6d1

q6

N/(d

2 d

Trig1/N-1 0 1 2 3 4 5

0

1

2

3

4

5

00.020.040.060.080.10.120.14(a)

-1 0 1 2 3 4 5

0

1

2

3

4

5

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14(b)

-1 0 1 2 3 4 5

0

1

2

3

4

5

0

0.05

0.1

0.15

0.2

0.25(c)

-1 0 1 2 3 4 5

0

1

2

3

4

5

0

0.2

0.4

0.6

0.8

1(d)

-1 0 1 2 3 4 5

0

1

2

3

4

5

00.20.40.60.811.21.41.6(e)

-1 0 1 2 3 4 5

0

1

2

3

4

5

0

0.2

0.4

0.6

0.8

1

1.2(f)

Trigq-

1q=

1q6

Trig

q- 2q= 2q6

)2q

6d1

q6

N/(d

2 d

Trig1/N-1 0 1 2 3 4 5

0

1

2

3

4

5

00.020.040.060.080.10.120.14(a)

-1 0 1 2 3 4 5

0

1

2

3

4

5

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14(b)

-1 0 1 2 3 4 5

0

1

2

3

4

5

0

0.05

0.1

0.15

0.2

0.25(c)

-1 0 1 2 3 4 5

0

1

2

3

4

5

0

0.2

0.4

0.6

0.8

1(d)

-1 0 1 2 3 4 5

0

1

2

3

4

5

00.20.40.60.811.21.41.6(e)

-1 0 1 2 3 4 5

0

1

2

3

4

5

0

0.2

0.4

0.6

0.8

1

1.2(f)

Trigq-

1q=

1q6

Trig

q- 2q= 2q6

)2q

6d1

q6

N/(d

2 d

Trig1/N-1 0 1 2 3 4 5

0

1

2

3

4

5

00.020.040.060.080.10.120.14(a)

-1 0 1 2 3 4 5

0

1

2

3

4

5

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14(b)

-1 0 1 2 3 4 5

0

1

2

3

4

5

0

0.05

0.1

0.15

0.2

0.25(c)

-1 0 1 2 3 4 5

0

1

2

3

4

5

0

0.2

0.4

0.6

0.8

1(d)

-1 0 1 2 3 4 5

0

1

2

3

4

5

00.20.40.60.811.21.41.6(e)

-1 0 1 2 3 4 5

0

1

2

3

4

5

0

0.2

0.4

0.6

0.8

1

1.2(f)

Trigq-

1q=

1q6

Trig

q- 2q= 2q6

)2q

6d1

q6

N/(d

2 d

Trig1/N-1 0 1 2 3 4 5

0

1

2

3

4

5

00.020.040.060.080.10.120.14(a)

-1 0 1 2 3 4 5

0

1

2

3

4

5

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14(b)

-1 0 1 2 3 4 5

0

1

2

3

4

5

0

0.05

0.1

0.15

0.2

0.25(c)

-1 0 1 2 3 4 5

0

1

2

3

4

5

0

0.2

0.4

0.6

0.8

1(d)

-1 0 1 2 3 4 5

0

1

2

3

4

5

00.20.40.60.811.21.41.6(e)

-1 0 1 2 3 4 5

0

1

2

3

4

5

0

0.2

0.4

0.6

0.8

1

1.2(f)

Trig

q- 1q= 1q6

Trig q-2q=2q6

)2

q6d1

q6N/(d2 dTrig1/N

-10

12

34

5

012345

00.02

0.04

0.06

0.08

0.1

0.12

0.14

(a)

-10

12

34

5

012345

00.02

0.04

0.06

0.08

0.1

0.12

0.14

(b)

-10

12

34

5

012345

00.05

0.1

0.15

0.2

0.25

(c)

-10

12

34

5

012345

00.2

0.4

0.6

0.8

1(d

)

-10

12

34

5

012345

00.2

0.4

0.6

0.8

11.2

1.4

1.6

(e)

-10

12

34

5

012345

00.2

0.4

0.6

0.8

11.2

(f)

PRL102.052302 (2009)

2-particle correlation 3-particle correlation Experimental Data

Cherenkov Gluon Radia1on •  Gluon Radia)on from a superluminal parton

•  Momentum dependence of gluon opening angle

2013/11/06 pre-‐Defense 13

cos �c = c/n(p)vpart � 1/n(p)

n(p) = p/p0

Superluminal!parton!

Cherenkov Gluon�

θc�

vpart~ c at GeV/c scale

: Index of Reflec1on

PRL96.172302 (2006)

Mach Cone Shock Wave •  Shock Wave from a supersonic parton

•  pT independence of double-‐hump posi)on

–  vpart~ constant at GeV scale –  cs ~ constant at Au+Au 200 GeV

2013/11/06 pre-‐Defense 14

θMach�Supersonic!parton!

Mach-Cone!Shock Wave�

cos �Mach = cs/vpart

cs : speed of sound

PRC73.011901(R) (2006)

Jet Deflec1on •  Deflec)on from ini)al direc)on –  Boost by medium expansion –  Energy-‐momentum loss

•  Hydro + Energy-‐Momentum Loss

2013/11/06 pre-‐Defense 15

Jet Deflection�

Medium Expansion�

Parton� Initial Direction��µTµ� = S�

S�(t, �x) =1

(�

2��)3exp� [�x� �xjet(t)]2

2�2

��

dE

dt,dM

dt, 0, 0

� �T (t, �x)Tmax

�3

PRL105.222301 (2010)

Hot-‐Spot Model

•  Hot-‐Spot : domain of high parton density •  Hot-‐Spot + Hydrodynamic Expansion •  Double-‐humps without hard-‐scanered partons

2013/11/06 pre-‐Defense 16

PLB712.226 (2012)

Contribu1ons of vn (n>2) in correla1ons

•  Double-‐hump & ridge of long-‐rapidity correla)on explained •  Short-‐rapidity correla)on with vn subtrac)on to discuss parton

behavior 2013/11/06 pre-‐Defense 17

Track at |η|<2.5 with EP from full FCAL 3.3<|η|<4.8

vn with EP Method

2Par. Correlation

PRC86.014907 (2012)

ATLAS

Mo1va1on of this Disserta1on •  Focus on azimuthal two-‐par)cle correla)ons •  Provide robust experimental results aoer vn subtrac)on –  Centrality & pT dependence, double-‐humps etc. –  Revisit of previous models

•  Diagnose correla)on phenomena at intermediate-‐pT with control of parton path length with respect to event-‐planes (Ψ2,Ψ3)

–  Parton-‐Energy Loss –  Re-‐distribu)on of lost energy from partons –  Possible boost of Jet by medium expansion

2013/11/06 pre-‐Defense 18

My Contribu1ons

2013/11/06 pre-‐Defense 19

M1,2 : AY 2008~2009

DNP-‐JPS Joint Mee1ng

D1 (RIKEN JRA) : AY 2010

Heavy Ion Pub PHENIX Run9 PHENIX Run10

PHENIX Run12

JPS Spring



JPS Fall WPCF2011 Hard Probes2012

Quark Mamer2012 Nagoya-‐Mini Workhop2012

HIC•HIP

preliminary request Au+Au ridge analysis

preliminary request Au+Au vn-‐correla1on

preliminary request Au+Au PID vn

preliminary request Au+Au correla1ons w.r.t. EP

vn EP calibra1on

*Oral (intern.) *Oral (Domes1c) *Experimental *Analysis *Service work Ac1vity Categories

D4 : AY 2013

PHENIX Run13

Detector Maintenance



ANALYSYS

2013/11/06 pre-‐Defense 20

Data Set & Par1cle Selec1on •  PHENIX year 2007 Experiment •  Au+Au collisions at √sNN=200 GeV – Minimum Bias Trigger –  4.4 billion events

•  Charged Hadron Selec)on –  2σ Matching Cut –  Electron Veto –  Energy/Momentum cut for High pT par)cles

•  Background rejec)on –  Pair cut of miss-‐reconstructed hadron pairs

2013/11/06 pre-‐Defense 21

PHENIX Detector -‐ 2007 Experiment •  Trigger, collision vertex, centrality –  Beam-‐Beam-‐Counter (BBC) –  Zero-‐Degree-‐Calorimeter(ZDC)

•  Event Plane –  BBC –  Reac)on-‐Plane-‐Detector(RXN)

•  Central Arm, Δφ=π |η|<0.35 – Momentum, Tracking, Electron Veto

•  Drio Chamber (DC) •  Pad Chamber(PC) •  Electromagne)c Calorimeter(EMC) •  Ring Image Cherenkov Detector(RICH)

2013/11/06 pre-‐Defense 22

West

South Side� View

Beam� View

PHENIX� Detector2007

North

East

MuTr

MuID MuIDHBDRxNP

MPC HBDRxNP

PbSc PbSc

PbSc PbSc

PbSc PbGl

PbSc PbGl

TOF

PC1 PC1

PC3

PC2

Central� Magnet

CentralMagnet

North� Muon� M

agnetSouth� Muon� Magnet

TECPC3

BBMPC

BB

RICH RICH

DC DC

ZDC� NorthZDC� South

aerogel

TOF

RXN

BBC

ZDC

DC

RICH

PC3

EMC

Charged Track

Centrality

•  BBC charge sum divided in percen)le

–  Same number of events in each bins

2013/11/06 pre-‐Defense 23

BBC

Num

ber o

f eve

nts

*2 [rad]2Ψ *3 [rad]3Ψ *4 [rad]4Ψ-3 -2 -1 0 1 2 3-3 -2 -1 0 1 2 3-3 -2 -1 0 1 2 3

40455055606570758085

610×

obsnΨ Re-centnΨ FouriernΨ

=200GeVNNsAu+Au Reaction Plane Detetor

|<2.8η1.0<|

Event Plane Calibra1on

2013/11/06 pre-‐Defense 24

Raw distribu1on

Re-‐centering

n⇥Fouriern = n⇥Rec

n + n�⇥n

n�⇥n =�

k

�Ak cos (kn⇥Rec

n ) + Bk sin (kn⇥Recn )

�

Ak = �2k

�cos (kn⇥Rec

n )�, Bk =

2k

�sin (kn⇥Rec

n )�

Fourier correc1on

�i :wi :

Azimuthal angle

Weight (Charge etc.)

Qx =�

i wi cos(n�i)�i wi

, Qy =�

i wi sin(n�i)�i wi

�n =1n

tan�1

�Qy

Qx

�

QRecx =

Qx � �Qx��x

, QRecy =

Qy � �Qy��y

�Recn =

1n

tan�1�QRec

y /QRecx

�

i�

Event Plane Resolu1on & vn Measurements

•  Resolu)on +/-‐η

2013/11/06 pre-‐Defense 25

vn =vobs

n

�EPn

=�cos n(⇥ � �EP

n )�

�cos n(�EPn � �n)�

EP Resolu1on PRC58.1671

⇥EPn =

�cos kn(�EP±�

n ��n)�

=��

cos kn(�EP (+�)n ��EP (��)

n )�

=�

8⇤2

n

�I(k�1)/2

�⇤2

n

4

�+ I(k+1)/2

�⇤2

n

4

��2

�EPn =

�

82�2

n

�I(k�1)/2

�2�2

n

4

�+ I(k+1)/2

�2�2

n

4

��2

•  Resolu)on +&-‐η –  χ->√2χ

•  vn measurements

Centrality %0 20 40 60 80 100

)]> 2Ψ-

obs

2Ψ

<cos

[2*(

0

0.2

0.4

0.6

0.8

1

Centrality %0 20 40 60 80 100

)]> 3Ψ-

obs

3Ψ

<cos

[3*(

00.1

0.20.30.4

0.50.6

η RXN:In+Out,+&-

η BBC:+&-

Centrality %0 20 40 60 80 100

)]> 4Ψ-

obs

4Ψ

<cos

[4*(

0

0.05

0.1

0.15

0.2

Centrality %0 20 40 60 80 100

)]> 2Ψ-

obs

2Ψ

<cos

[4*(

0

0.2

0.4

0.6

0.8

1

vn Results •  Consistent results with previous measurements –  Used for background subtrac)on

2013/11/06 pre-‐Defense 26

2V3V

4V} 2

Ψ{ 4V

[GeV/c]T

p

=200GeV, EP MethodNNsAu+Au

0 1 2 3 4 5 6 7 8-0.05

00.05

0.10.150.2

0.250.3 40-50, (e)

0 1 2 3 4 5 6 7 8-0.05

00.05

0.10.150.2

0.250.3 30-40, (d)

0 1 2 3 4 5 6 7 8-0.05

00.05

0.10.150.2

0.250.3 20-30, (c)

0 1 2 3 4 5 6 7 8-0.05

00.05

0.10.150.2

0.250.3 10-20, (b)

0 1 2 3 4 5 6 7 8-0.05

00.05

0.10.150.2

0.250.3 0-10, (a)

0 1 2 3 4 5 6 7 80

0.05

0.1

0.15

0.2(j)

0 1 2 3 4 5 6 7 80

0.05

0.1

0.15

0.2(i)

0 1 2 3 4 5 6 7 80

0.05

0.1

0.15

0.2(h)

0 1 2 3 4 5 6 7 80

0.05

0.1

0.15

0.2(g)

0 1 2 3 4 5 6 7 80

0.05

0.1

0.15

0.2(f)

0 1 2 3 4 5 6 7 80

0.05

0.1

0.15

0.2 (o)

0 1 2 3 4 5 6 7 80

0.05

0.1

0.15

0.2 (n)

0 1 2 3 4 5 6 7 80

0.05

0.1

0.15

0.2 (m)

0 1 2 3 4 5 6 7 80

0.05

0.1

0.15

0.2 (l)

0 1 2 3 4 5 6 7 80

0.05

0.1

0.15

0.2 This Ana. integratedT This Ana. P

PRL107.052301

(k)

0 1 2 3 4 5 6 7 8-0.020

0.020.040.060.08

0.1 (t)

0 1 2 3 4 5 6 7 8-0.020

0.020.040.060.08

0.1 (s)

0 1 2 3 4 5 6 7 8-0.020

0.020.040.060.08

0.1 (r)

0 1 2 3 4 5 6 7 8-0.020

0.020.040.060.08

0.1 (q)

0 1 2 3 4 5 6 7 8-0.020

0.020.040.060.08

0.1 (p)

φΔ

-3 -2 -1 0 1 2 3 ηΔ-0.6-0.4-0.2 0 0.2 0.4 0.6

# of

Ent

ries

0123456789

310×

φΔ

-3 -2 -1 0 1 2 3 ηΔ-0.6-0.4-0.2 0 0.2 0.4 0.6

# of

Ent

ries

02468

1012

310×

Real Pair

Mixed Pair

Two Par1cle Correla1ons

2013/11/06 pre-‐Defense 27

•  Pair distribu)ons in real and mixed events �� = �a � �t,�� = �a � �t

C(��,��) =N ta

mix

N tareal

d2N tareal/d��d��

d2N tamix/d��d��

φΔ

-3 -2 -1 0 1 2 3 ηΔ-0.6-0.4-0.2 0 0.2 0.4 0.6

)ηΔ,φ

ΔC(

0.81

1.21.41.61.8

•  Two-‐Par)cle Correla)ons

Near-‐Side : Δφ=0

Away-‐Side : Δφ=±π

φΔ-1 0 1 2 3 4

2C

0.920.940.960.98

11.021.041.061.08

Expr.2: C

2: Fit to Expr. C

: Pure Flow (ZYAM)

=200 GeV, 20-30%NNsAu+Au 1-2 GeV/c⊗=2-4a

Tp⊗t

Tp

Flow Subtrac1on & Pair Yield per a Trigger (PTY) •  Analy)cal Formula of Pure Flow

2013/11/06 pre-‐Defense 28

j(��) = C(��)� b0

�1 +

�

n=1

2vtnva

n cos (n��)

�

F (��) = 1 +�

2V�n cos (n��)

= 1 +�

2vtnva

n cos (n��)

•  Flow subtrac)ons –  Zero Yield At Minimum Assump)on

1N t

dN ta

d�⇥=

12�⇤

N ta

N tj(�⇥)

•  Pair yield per a trigger

� : Tracking efficiency of associate par1cles

Event-‐Plane Dependence

•  Selec)ng trigger par)cle w.r.t. Ψ2 & Ψ3

•  Control of parton path length inside medium •  Sensi)vity to each harmonic plane

2013/11/06 pre-‐Defense 29

!Trig.

!Asso.

!s

"2

#!

!Trig.

!Asso.

!s

"3

#!

Flow Contribu1ons with respect to EP •  No analy)cal formula of pure flow w.r.t EP •  Run a Monte Carlo simula)on •  Azimuthal distribu)on –  Using Measured vn

•  Observed Event Plane Resolu)on •  Observed correla)on between EP –  <4(Ψ2-Ψ4)>=v4{Ψ2}/v4{Ψ4} –  <6(Ψ2-Ψ3)>=0

2013/11/06 pre-‐Defense 30

Ed3N

dp3=

d2N

2�dpT d�

�1 +

�

n=2,3,4

2vn cos n(��n)

�

Flow Contribu1ons with respect to EP

•  pTT : 2-‐4, pTa:1-‐2 GeV/c •  Good reconstruc)on of correla)on shape by MC simula)on for both Ψ2, Ψ3 dependence

•  Except around Δφ=0, π where affected by jet

2013/11/06 pre-‐Defense 31

)>4Ψ-2Ψ(n=2,3,4) + <cos4(n=200GeV, Pure Flow : vNNsAu+Au

[rad]tφ-aφ = φΔ

1-2

GeV

/c⊗

), 2-

4φ

Δ d

epen

dent

Cf(

2,3

Ψ

-1 0 1 2 3 40.70.80.9

11.11.21.3

<02Ψ-tφ<8

π-:In-plane 2Ψ

(b)

-1 0 1 2 3 40.70.80.9

11.11.21.3 Correlations

Pure Flow

8π-3<2Ψ-

tφ<8

π-4:Out-of-plane 2Ψ

20-30% (a)

-1 0 1 2 3 40.85

0.9

0.951

1.051.1

<03Ψ-tφ<12

π-:In-plane 3Ψ

(d)

-1 0 1 2 3 40.85

0.9

0.951

1.051.1

12π-3<3Ψ-

tφ<12

π-4:Out-of-plane 3Ψ

(c)

Resolu1on Correc1on for Trigger Selec1on •  FiRng Method –  Azimuthal anisotropy of correla)ons yield

–  Resolu)on correc)on in analogous to vn measurements

•  Itera)on Method –  Trigger smearing effect by measured resolu)on S

–  Correla)on Yield A –  Smeared Correla)ons B –  Effec)ve correc)on coefficient C –  Itera)on un)l convergence 2013/11/06 pre-‐Defense 32

2Ψ-tφ=sφ

-1.5 -1 -0.5 0 0.5 1 1.5

)φΔ, sφ(

cor

) & 1

+Yφ

Δ, sφ(ra

w1+

Y

1

1.05

1.1

1.15

1.2

Corected curveFit to raw dataCorrected dataRaw data

)φΔ+sφcos4(raw4

)+2vφΔ+sφcos2(raw2=1+2vraw)sφF(

)φΔ+sφcos4(42σ/raw4

)+2vφΔ+sφcos2(2σ/raw2=1+2vcor)sφF(

/24.π=-φΔAu+Au 20-30%,

B(n) = SA(n)

C(n) = A(n)/B(n)

CA(n) = A(n+1)

Systema1c Uncertain1es •  Flow vn Measurements –  Fluctua)on within RXN EP –  Rapidity dependence of EP : RXN-‐BBC difference – Matching cut of CNT Par)cles

•  Two-‐Par)cle Correla)ons –  Systema)cs from vn – Matching cut of CNT Par)cles

•  Event Plane Dependent Correla)ons –  Unfolding Method : Fit & Itera)on –  Parameter in itera)on method

2013/11/06 pre-‐Defense 33

Results & Discussion

2013/11/06 pre-‐Defense 34

Two-‐Par1cle Correla1ons •  Suppression of Away-‐Side in most central collisions

•  Away-‐side shape in peripheral collisions

–  Single peak at high pT –  Double hump at intm. pT

•  pT independence of double hump posi)on below pT<4 GeV/c

2013/11/06 pre-‐Defense 35

(n=2,3,4) subtractedn=200 GeV, vNNsAu+Au

[rad]tφ-aφ = φΔ

φΔ

/dta

dN

tPT

Y=1/

N

-1 0 1 2 3 40

0.0050.01

0.0150.02

30-40%(b)

-1 0 1 2 3 40

0.0050.01

0.0150.02 4-10x4-10 GeV/c

0-10%(a)

-1 0 1 2 3 40

0.020.040.060.080.1 (d)

-1 0 1 2 3 40

0.020.040.060.080.1 4-10x2-4 GeV/c (c)

-1 0 1 2 3 40

0.0050.01

0.0150.020.0250.030.035 (f)

-1 0 1 2 3 40

0.0050.01

0.0150.020.0250.030.035 2-4x2-4 GeV/c (e)

-1 0 1 2 3 40

0.020.040.060.080.1

0.120.14 (h)

-1 0 1 2 3 40

0.020.040.060.080.1

0.120.14 2-4x1-2 GeV/c (g)

Hardness of Correla1on Yields

•  Hardness increase with trigger and associate pT –  Different Physics depending on pT

2013/11/06 pre-‐Defense 36

1pa

T

dY

d�pT=

1pa

T

1(pa,max

T � pa,minT )

�d��

1Ntrig

dN

d��

[GeV/c]T

Associate p0 1 2 3 4 5

φΔd Tp

Δdpa

irN2 d

asso

cTp1

trig

N1

-1210

-1110

-1010

-910

-810

-710

-610

-510

-410

-310

-210

-1101

10210

310

410

0-10%-210-20% x 10-420-30% x 10-630-40% x 10-840-50% x 10

subtracted}4Ψ{4 v3 v2v

Au+Au 200GeV/4|π|<|φΔNear Side:|

[GeV/c]T

Associate p0 1 2 3 4 5

φΔd Tp

Δdpa

irN2 d

asso

cTp1

trig

N1

-1210

-1110

-1010

-910

-810

-710

-610

-510

-410

-310

-210

-1101

10210

310

410

:4-10 GeV/ctrigT

p

:2-4 GeV/ctrigT

p

:1-2 GeV/ctrigT

p

subtracted}4Ψ{4 v3 v2v/4|π|<|π-φΔAway Side:|

•  pT spectra of correla)on yield

Comp. w/ Model : Cherenkov Gluon Radia1on

•  Strong momentum dependence •  Disfavored by pT independence of experimental data

2013/11/06 pre-‐Defense 37

to the parton energy loss. Adopting the results obtained forphoton Cherenkov radiation [27] we can estimate thisenergy loss by

dEdx! 4!"s

Zn"p0#>1

p0

!1$ 1

n2"p0#

"dp0; (4)

where n"p0# ! j ~pj=p0 is the index of reflection. Using thedispersion relation in our simple model, the typical energyscale for the soft mode where Cherenkov radiation canhappen is p0 % T. The Cherenkov energy loss is aboutdE=dx% 0:1 GeV=fm for T % 300 MeV. This is muchsmaller than the normal radiative energy loss induced bymultiple scattering of the energetic partons [9]. As dis-cussed in Ref. [16], bremsstrahlung, induced by multiplescattering, of soft gluons with a spacelike dispersion rela-tion can still lead to Cherenkov-like angular distributionsdue to Landau-Pomeranchuck-Migdal interference. SuchCherenkov-like gluon bremsstrahlung will lead to a similaremission pattern of soft hadrons as pure Cherenkov radia-tion. Thus, a distinctive experimental signature of theCherenkov-like gluon radiation is the strong momentumdependence of the emission angle of soft hadrons leadingto the disappearance of a conelike structure for large pTasssociated hadrons.

In conclusion, we have shown how bound states in theQGP or more generally additional mass scales give rise toradiation of Cherenkov gluons off a fast jet traversing themedium. These Cherenkov gluons lead to a conelike emis-sion pattern of soft hadrons. The cone angle with respect tothe jet direction exhibits a strong momentum dependencein contrast to a Mach cone. Pure Cherenkov radiation leadsto energy loss which, however, is too small to account forthe jet suppression observed in RHIC experiments.Collision-induced Cherenkov-like bremsstrahlung [16]can explain both the observed energy loss and the emissionpattern of soft hadrons in the direction of quenched jets.

We thank F. Karsch and E. Shuryak for helpful discus-sions. Research supported by the Director, Office ofEnergy Research, Office of High Energy and NuclearPhysics, Division of Nuclear Physics, U.S. Department ofEnergy under Contract No. DE-AC02-05CH11231.

*Current address: Department of Physics, Duke University,Durham, NC 27708, USA.

[1] F. Karsch and E. Laermann, hep-lat/0305025.[2] J. P. Blaizot, E. Iancu, and A. Rebhan, Phys. Rev. Lett. 83,

2906 (1999); J. O. Andersen, E. Braaten, and M. Strick-land, Phys. Rev. D 61, 074016 (2000).

[3] E. Braaten and R. D. Pisarski, Nucl. Phys. B337, 569(1990); J. Frenkel and J. C. Taylor, Nucl. Phys. B334,199 (1990).

[4] S. Datta, F. Karsch, P. Petreczky, and I. Wetzorke, Phys.Rev. D 69, 094507 (2004); M. Asakawa and T. Hatsuda,Phys. Rev. Lett. 92, 012001 (2004).

[5] M. Asakawa, T. Hatsuda, and Y. Nakahara, Nucl. Phys.A715, 863 (2003); Nucl. Phys. B, Proc. Suppl. 119, 481(2003).

[6] E. V. Shuryak and I. Zahed, Phys. Rev. D 70, 054507(2004); Phys. Rev. C 70, 021901 (2004).

[7] V. Koch, A. Majumder, and J. Randrup, Phys. Rev. Lett.95, 182301 (2005); S. Ejiri, F. Karsch, and K. Redlich,Phys. Lett. B 633, 275 (2006).

[8] K. H. Ackermann et al., Phys. Rev. Lett. 86, 402 (2001);S. S. Adler et al., Phys. Rev. Lett. 91, 182301 (2003).

[9] M. Gyulassy, I. Vitev, X. N. Wang, and B. W. Zhang, nucl-th/0302077; X. N. Wang, Nucl. Phys. A750, 98 (2005).

[10] S. S. Adler et al., Phys. Rev. Lett. 91, 072301 (2003).[11] C. Adler et al., Phys. Rev. Lett. 90, 082302 (2003).[12] A. Majumder and X. N. Wang, Phys. Rev. D 70, 014007

(2004); 72, 034007 (2005).[13] J. Adams et al., Phys. Rev. Lett. 95, 152301 (2005);

F. Wang, J. Phys. G 30, S1299 (2004).[14] S. S. Adler et al., nucl-ex/0507004.[15] I. Vitev, hep-ph/0501255.[16] A. Majumder and X.-N. Wang, nucl-th/0507062 [Phys.

Rev. C (to be published)].[17] J. Casalderrey-Solana, E. V. Shuryak, and D. Teaney,

J. Phys.: Conf. Ser. 27, 22 (2005).[18] L. M. Satarov, H. Stoecker, and I. N. Mishustin, hep-ph/

0505245.[19] J. Ruppert and B. Muller, Phys. Lett. B 618, 123 (2005).[20] I. M. Dremin, JETP Lett. 30, 140 (1979) [Pis’ma Zh. Eksp.

Teor. Fiz. 30, 152 (1979)]; Nucl. Phys. A767, 233 (2006).[21] P. Petreczky, F. Karsch, E. Laermann, S. Stickan, and

I. Wetzorke, Nucl. Phys. B, Proc. Suppl. 106, 513 (2002).[22] G. F. Bertsch, B. A. Li, G. E. Brown, and V. Koch, Nucl.

Phys. A490, 745 (1988).[23] H. A. Weldon, Phys. Rev. D 28, 2007 (1983).[24] S. M. H. Wong, Phys. Rev. D 64, 025007 (2001); A. Ma-

jumder and C. Gale, Phys. Rev. C 65, 055203 (2002).[25] E. V. Shuryak and I. Zahed, hep-ph/0406100.[26] S. J. Sin and I. Zahed, Phys. Lett. B 608, 265 (2005).[27] J. D. Jackson, Classical Eletrodynamics (John Wiley &

Son, New York, 1975), 2nd ed.

0 0.5 1 1.5p

0

20

40

60

80

100

! c

m1=1T,m2=3Tm1=0.5T,m2=3Tm1=0.5T,m2=1T

FIG. 5 (color online). Dependence of the Cherenkov angle onmomentum of the emitted particle.

PRL 96, 172302 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending5 MAY 2006

172302-4

Cherenkov Gluon Radia1on Experimental Results ) subtracted4Ψ(4 & v3

, v2

Au+Au 200GeV, v

[rad]trigφ- assoφ = φΔ

φΔ

/dta

dN

t1/

N00.010.020.03

-1 0 1 2 3 4

40-50%(e)

0

0.05

0.1

-1 0 1 2 3 4

(j)

00.050.10.15

-1 0 1 2 3 4

(o)

00.020.040.06

-1 0 1 2 3 4

(t)

0

0.05

0.1

-1 0 1 2 3 4

(y)

00.010.020.03

-1 0 1 2 3 4

30-40%(d)

0

0.05

0.1

-1 0 1 2 3 4

(i)

00.050.10.15

-1 0 1 2 3 4

(n)

00.020.040.06

-1 0 1 2 3 4

(s)

0

0.05

0.1

-1 0 1 2 3 4

(x)

00.010.020.03

-1 0 1 2 3 4

20-30%(c)

0

0.05

0.1

-1 0 1 2 3 4

(h)

00.050.10.15

-1 0 1 2 3 4

(m)

00.020.040.06

-1 0 1 2 3 4

(r)

0

0.05

0.1

-1 0 1 2 3 4

(w)

00.010.020.03

-1 0 1 2 3 4

10-20%(b)

0

0.05

0.1

-1 0 1 2 3 4

(g)

00.050.10.15

-1 0 1 2 3 4

(l)

00.020.040.06

-1 0 1 2 3 4

(q)

0

0.05

0.1

-1 0 1 2 3 4

(v)

00.010.020.03

-1 0 1 2 3 4

0-10%(a)2-4×:2-4t,a

Tp

0

0.05

0.1

-1 0 1 2 3 4

(f)1-2×:2-4t,a

Tp

00.050.10.15

-1 0 1 2 3 4

(k)0.5-1×:2-4t,a

Tp

00.020.040.06

-1 0 1 2 3 4

(p)1-2×:1-2t,a

Tp

0

0.05

0.1

-1 0 1 2 3 4

(u)0.5-1×:1-2t,a

Tp

) subtracted4Ψ(4 & v3

, v2

Au+Au 200GeV, v


φΔ

/dta

dN

t1/

N

00.010.020.03

-1 0 1 2 3 4

40-50%(e)

0

0.05

0.1

-1 0 1 2 3 4

(j)

00.050.10.15

-1 0 1 2 3 4

(o)

00.020.040.06

-1 0 1 2 3 4

(t)

0

0.05

0.1

-1 0 1 2 3 4

(y)

00.010.020.03

-1 0 1 2 3 4

30-40%(d)

0

0.05

0.1

-1 0 1 2 3 4

(i)

00.050.10.15

-1 0 1 2 3 4

(n)

00.020.040.06

-1 0 1 2 3 4

(s)

0

0.05

0.1

-1 0 1 2 3 4

(x)

00.010.020.03

-1 0 1 2 3 4

20-30%(c)

0

0.05

0.1

-1 0 1 2 3 4

(h)

00.050.10.15

-1 0 1 2 3 4

(m)

00.020.040.06

-1 0 1 2 3 4

(r)

0

0.05

0.1

-1 0 1 2 3 4

(w)

00.010.020.03

-1 0 1 2 3 4

10-20%(b)

0

0.05

0.1

-1 0 1 2 3 4

(g)

00.050.10.15

-1 0 1 2 3 4

(l)

00.020.040.06

-1 0 1 2 3 4

(q)

0

0.05

0.1

-1 0 1 2 3 4

(v)

00.010.020.03

-1 0 1 2 3 4

0-10%(a)2-4×:2-4t,a

Tp

0

0.05

0.1

-1 0 1 2 3 4

(f)1-2×:2-4t,a

Tp

00.050.10.15

-1 0 1 2 3 4

(k)0.5-1×:2-4t,a

Tp

00.020.040.06

-1 0 1 2 3 4

(p)1-2×:1-2t,a

Tp

0

0.05

0.1

-1 0 1 2 3 4

(u)0.5-1×:1-2t,a

Tp


, v2

Au+Au 200GeV, v


φΔ

/dta

dN

t1/

N

00.010.020.03

-1 0 1 2 3 4

40-50%(e)

0

0.05

0.1

-1 0 1 2 3 4

(j)

00.050.10.15

-1 0 1 2 3 4

(o)

00.020.040.06

-1 0 1 2 3 4

(t)

0

0.05

0.1

-1 0 1 2 3 4

(y)

00.010.020.03

-1 0 1 2 3 4

30-40%(d)

0

0.05

0.1

-1 0 1 2 3 4

(i)

00.050.10.15

-1 0 1 2 3 4

(n)

00.020.040.06

-1 0 1 2 3 4

(s)

0

0.05

0.1

-1 0 1 2 3 4

(x)

00.010.020.03

-1 0 1 2 3 4

20-30%(c)

0

0.05

0.1

-1 0 1 2 3 4

(h)

00.050.10.15

-1 0 1 2 3 4

(m)

00.020.040.06

-1 0 1 2 3 4

(r)

0

0.05

0.1

-1 0 1 2 3 4

(w)

00.010.020.03

-1 0 1 2 3 4

10-20%(b)

0

0.05

0.1

-1 0 1 2 3 4

(g)

00.050.10.15

-1 0 1 2 3 4

(l)

00.020.040.06

-1 0 1 2 3 4

(q)

0

0.05

0.1

-1 0 1 2 3 4

(v)

00.010.020.03

-1 0 1 2 3 4

0-10%(a)2-4×:2-4t,a

Tp

0

0.05

0.1

-1 0 1 2 3 4

(f)1-2×:2-4t,a

Tp

00.050.10.15

-1 0 1 2 3 4

(k)0.5-1×:2-4t,a

Tp

00.020.040.06

-1 0 1 2 3 4

(p)1-2×:1-2t,a

Tp

0

0.05

0.1

-1 0 1 2 3 4

(u)0.5-1×:1-2t,a

Tp


[rad]tφ-aφ = φΔ

φΔ

/dta

dN

tPT

Y=1/

N

-1 0 1 2 3 40

0.0050.01

0.0150.02

30-40%(b)

-1 0 1 2 3 40

0.0050.01

0.0150.02 4-10x4-10 GeV/c

0-10%(a)

-1 0 1 2 3 40

0.020.040.060.080.1 (d)

-1 0 1 2 3 40

0.020.040.060.080.1 4-10x2-4 GeV/c (c)

-1 0 1 2 3 40

0.0050.01

0.0150.020.0250.030.035 (f)

-1 0 1 2 3 40

0.0050.01

0.0150.020.0250.030.035 2-4x2-4 GeV/c (e)

-1 0 1 2 3 40

0.020.040.060.080.1

0.120.14 (h)

-1 0 1 2 3 40

0.020.040.060.080.1

0.120.14 2-4x1-2 GeV/c (g)


, v2

Au+Au 200GeV, v


φΔ

/dta

dN

t1/

N

00.010.020.03

-1 0 1 2 3 4

40-50%(e)

0

0.05

0.1

-1 0 1 2 3 4

(j)

00.050.10.15

-1 0 1 2 3 4

(o)

00.020.040.06

-1 0 1 2 3 4

(t)

0

0.05

0.1

-1 0 1 2 3 4

(y)

00.010.020.03

-1 0 1 2 3 4

30-40%(d)

0

0.05

0.1

-1 0 1 2 3 4

(i)

00.050.10.15

-1 0 1 2 3 4

(n)

00.020.040.06

-1 0 1 2 3 4

(s)

0

0.05

0.1

-1 0 1 2 3 4

(x)

00.010.020.03

-1 0 1 2 3 4

20-30%(c)

0

0.05

0.1

-1 0 1 2 3 4

(h)

00.050.10.15

-1 0 1 2 3 4

(m)

00.020.040.06

-1 0 1 2 3 4

(r)

0

0.05

0.1

-1 0 1 2 3 4

(w)

00.010.020.03

-1 0 1 2 3 4

10-20%(b)

0

0.05

0.1

-1 0 1 2 3 4

(g)

00.050.10.15

-1 0 1 2 3 4

(l)

00.020.040.06

-1 0 1 2 3 4

(q)

0

0.05

0.1

-1 0 1 2 3 4

(v)

00.010.020.03

-1 0 1 2 3 4

0-10%(a)2-4×:2-4t,a

Tp

0

0.05

0.1

-1 0 1 2 3 4

(f)1-2×:2-4t,a

Tp

00.050.10.15

-1 0 1 2 3 4

(k)0.5-1×:2-4t,a

Tp

00.020.040.06

-1 0 1 2 3 4

(p)1-2×:1-2t,a

Tp

0

0.05

0.1

-1 0 1 2 3 4

(u)0.5-1×:1-2t,a

Tp


, v2

Au+Au 200GeV, v


φΔ

/dta

dN

t1/

N

00.010.020.03

-1 0 1 2 3 4

40-50%(e)

0

0.05

0.1

-1 0 1 2 3 4

(j)

00.050.10.15

-1 0 1 2 3 4

(o)

00.020.040.06

-1 0 1 2 3 4

(t)

0

0.05

0.1

-1 0 1 2 3 4

(y)

00.010.020.03

-1 0 1 2 3 4

30-40%(d)

0

0.05

0.1

-1 0 1 2 3 4

(i)

00.050.10.15

-1 0 1 2 3 4

(n)

00.020.040.06

-1 0 1 2 3 4

(s)

0

0.05

0.1

-1 0 1 2 3 4

(x)

00.010.020.03

-1 0 1 2 3 4

20-30%(c)

0

0.05

0.1

-1 0 1 2 3 4

(h)

00.050.10.15

-1 0 1 2 3 4

(m)

00.020.040.06

-1 0 1 2 3 4

(r)

0

0.05

0.1

-1 0 1 2 3 4

(w)

00.010.020.03

-1 0 1 2 3 4

10-20%(b)

0

0.05

0.1

-1 0 1 2 3 4

(g)

00.050.10.15

-1 0 1 2 3 4

(l)

00.020.040.06

-1 0 1 2 3 4

(q)

0

0.05

0.1

-1 0 1 2 3 4

(v)

00.010.020.03

-1 0 1 2 3 4

0-10%(a)2-4×:2-4t,a

Tp

0

0.05

0.1

-1 0 1 2 3 4

(f)1-2×:2-4t,a

Tp

00.050.10.15

-1 0 1 2 3 4

(k)0.5-1×:2-4t,a

Tp

00.020.040.06

-1 0 1 2 3 4

(p)1-2×:1-2t,a

Tp

0

0.05

0.1

-1 0 1 2 3 4

(u)0.5-1×:1-2t,a

Tp

Comp. w/ Model : Jet-‐Deflec1on & Mach-‐Cone

•  Momentum Loss to obtain pT independent Double-‐hump –  Energy + Momentum Loss is most realis)c

•  Mach-‐Cone also shows pT independence

2013/11/06 pre-‐Defense 38

pTa=2GeV/c pTa=3GeV/c

pTt=3.5 GeV/c pTt=3.5 GeV/c

Mach-‐Cone Mach-‐Cone

dE/dt = 1GeV/fmdM/dt = (1/v)(dE/dt)

(v = 0.999)

Energy-‐Momentum Loss Rate

PRL105.222301 (2010)

Comp. w/ Model : Jet-‐Deflec1on & Hot-‐Spot

•  Intermediate pT : Both models consistent with data •  Hot-‐Spot disfavored by the double-‐hump at high-‐pT •  Consistent with the behavior of pT spectra

2013/11/06 pre-‐Defense 39

Hot and Cold Baryonic Matter – HCBM 2010

0

0.005

0.01

0.015

0.02

0.025

0.03

-1 0 1 2 3 4

1/N

dN

/d(Δφ)

φ [rad]

Hot SpotJets

0

0.005

0.01

0.015

0.02

0.025

-1 0 1 2 3 41/

N d

N/d

(Δφ)

φ [rad]

Hot SpotJets

Fig. 3. Two-particle correlation function from a hot spot event (dashed blue lines) and averaged jet events (blacksolid lines), assuming a passocT = 2.0 GeV and ptrigT = 3.5 GeV (left panel) as well as p

trigT = 8.0 GeV (right panel).

case and it is also not necessary to average over many events since there is no trigger jet axis and thusall events can be converted into each other due to rotational symmetry.

Fig. 3 shows the two-particle correlation function for such a hot spot event (blue dashed lines)assuming a passocT = 2.0 GeV and a ptrigT = 3.5 GeV (left panel) as well as a ptrigT = 8.0 GeV (rightpanel), obtained according to

1NdNd!"

=1N

!

dNd"

dNd(!" ! ")

d" (8)

and compared with the averaged jet events from Fig. 1 (black solid line). Here we chose !e/e0 = 6,other ratios give similar results.

As can be seen, the double-peak structure is more pronounced in case of a hot spot and gets evenstronger for larger ptrigT , in contrast to the averaged jet events where the two peak structure starts tocoalesce into one peak for larger ptrigT like seen in the data.

However, it seems rather unlikely that a hot spot creates particles with very large pT . But for smallptrigT [16,17] a superposition of fluctuating events (hot spots) and jets might probably lead to a ratherclean double-peak structure. This should also be seen at the LHC.

It is important to note in this context that the e!ect of triangular flow and hot spots are very closelylinked to each other and might actually not be disentangled. Each hot spot (and thus fluctuating initialconditions) will lead to a nonzero triangular flow.

In conclusion, we have shown that a double-peak structure on the away side of soft-hard corre-lations obtained via averaging over di!erent jet events in which the particles are emitted from thedeflected wakes created by jets [37] coalesces into one peak for larger ptrigT as seen in experimentaldata [16,17], in contrast to the the two-peak structure obtained from hot spots. Since such a distinctionis not possible experimentally, it is necessary to study soft-hard correlations induced by heavy-flavortagged jets [42] with those induced by light-flavor jets at RHIC and LHC in order to disentangle themedium e!ects (hot spots) from jets and to test if a conical correlation occurs even for subsonic “jets”[37].

B.B. thanks J. Noronha, G. Torrieri, M. Gyulassy, and D. Rischke for all the discussions andacknowledges support from the Alexander von Humboldt foundation via a Feodor Lynen fellowshipand DOE under Grant No. DE-FG02-93ER40764.

References1. I. Arsene et al. [BRAHMS Collaboration], Nucl. Phys. A 757, 1 (2005).2. K. Adcox et al. [PHENIX Collaboration], Nucl. Phys. A 757, 184 (2005).3. B. B. Back et al., Nucl. Phys. A 757, 28 (2005).

pTt=3.5 GeV/c pTa=2.0GeV/c pTt=8.0 GeV/c

pTa=2.0GeV/c


[rad]tφ-aφ = φΔ

φΔ

/dta

dN

tPT

Y=1/

N -1 0 1 2 3 40

0.0050.01

0.0150.02

40-50%(e)

-1 0 1 2 3 40

0.020.040.060.080.1

0.120.14 (j)-1 0 1 2 3 4

00.0050.01

0.0150.02

30-40%(d)

-1 0 1 2 3 40

0.020.040.060.080.1

0.120.14 (i)-1 0 1 2 3 4

00.0050.01

0.0150.02

20-30%(c)

-1 0 1 2 3 40

0.020.040.060.080.1

0.120.14 (h)-1 0 1 2 3 4

00.0050.01

0.0150.02

10-20%(b)

-1 0 1 2 3 40

0.020.040.060.080.1

0.120.14 (g)-1 0 1 2 3 4

00.0050.01

0.0150.02 4-10x4-10 GeV/c

0-10%(a)

-1 0 1 2 3 40

0.020.040.060.080.1

0.120.14 2-4x1-2 GeV/c (f)


[rad]tφ-aφ = φΔφ

Δ/d

ta d

Nt

PTY=

1/N -1 0 1 2 3 4

00.0050.01

0.0150.02

40-50%(e)

-1 0 1 2 3 40

0.020.040.060.080.1

0.120.14 (j)-1 0 1 2 3 4

00.0050.01

0.0150.02

30-40%(d)

-1 0 1 2 3 40

0.020.040.060.080.1

0.120.14 (i)-1 0 1 2 3 4

00.0050.01

0.0150.02

20-30%(c)

-1 0 1 2 3 40

0.020.040.060.080.1

0.120.14 (h)-1 0 1 2 3 4

00.0050.01

0.0150.02

10-20%(b)

-1 0 1 2 3 40

0.020.040.060.080.1

0.120.14 (g)-1 0 1 2 3 4

00.0050.01

0.0150.02 4-10x4-10 GeV/c

0-10%(a)

-1 0 1 2 3 40

0.020.040.060.080.1

0.120.14 2-4x1-2 GeV/c (f)

Experimental Results Hot-‐Spot : PLB712.226 (2012) Jet : PRL105.222301 (2010)

)> by ZYAM4Ψ-2Ψ(n=2,3,4) + <cos4(n=200GeV, Pure Flow: vNNsAu+Au

[rad]tφ-aφ = φΔ

1-2

GeV

⊗),

2-4

φΔ

dep

ende

nt P

TY(

2Ψ

-1 0 1 2 3 4

-0.1

0

0.1

0.2

0.3

0.4

0.5 40-50%

/8π<-32Ψ-tφ/8<π-4

<02Ψ-tφ/8<π-

-1 0 1 2 3 4

-0.1

0

0.1

0.2

0.3

0.4

0.5 0-10%

/8π<-32Ψ-tφ/8<π-4

<02Ψ-tφ/8<π-

Ψ2 dependence of PTY •  Mach-‐Cone disfavored –  Double-‐hump must always appear in Mach-‐Cone

•  In-‐plane trigger –  Enhance in peripheral collisions: with thin medium

–  Parton Energy Loss •  Out-‐of-‐plane trigger –  Enhance in central collisions: thick medium

–  Energy re-‐distribu)on & boost by collec)ve expansion

2013/11/06 pre-‐Defense 40


[rad]tφ-aφ = φΔ

1-2

GeV

⊗),

2-4

φΔ

dep

ende

nt P

TY(

3Ψ

-1 0 1 2 3 4

-0.1

0

0.1

0.2

0.3

0.4

0.5 40-50%

/12π<-33Ψ-tφ/12<π-4

<03Ψ-tφ/12<π-

-1 0 1 2 3 4

-0.1

0

0.1

0.2

0.3

0.4

0.5 0-10%

/12π<-33Ψ-tφ/12<π-4

<03Ψ-tφ/12<π-

Ψ3 dependence of PTY

•  Similar but weaker trends as Ψ2 dependence

•  In-‐plane trigger –  Enhance in peripheral collisions with thin medium

•  Out-‐of-‐plane trigger –  Possible enhance in central collisions with thick medium

•  Weaker Ψ3 dependence than Ψ2

2013/11/06 pre-‐Defense 41

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

2Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

0-10%

<02Ψ-tφ/8<π-

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

2Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

40-50%

<02Ψ-tφ/8<π-

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

2Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

0-10%

/8π<-32Ψ-tφ/8<π-4

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

2Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

40-50%

/8π<-32Ψ-tφ/8<π-4

Ψ2 dependence of PTY (Polar Coordinate)

•  Yield correlates with geometry

•  Enhance of In-‐plane yield with increase of centrality

–  Shortest average path length •  Enhance of Out-‐of-‐plane yield with decrease of centrality

–  Longest average path length

2013/11/06 pre-‐Defense 42

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

3Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

0-10%

<03Ψ-tφ/12<π-

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

3Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

40-50%

<03Ψ-tφ/12<π-

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

3Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

0-10%

/12π<-33Ψ-tφ/12<π-4

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

3Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

40-50%

/12π<-33Ψ-tφ/12<π-4

Ψ3 dependence of PTY (Polar Coordinate)

•  Enhance of In-‐plane yield with increase of centrality

–  Shortest average path length •  Possible enhance of Out-‐of-‐plane yield with decrease of centrality

2013/11/06 pre-‐Defense 43

Azimuthal anisotropy of PTY : vnPTY

•  Extrac)on of vnPTY by fiRng

2013/11/06 pre-‐Defense 44

Au+Au 200GeV1-2GeV/c⊗=2-4asso

Tp⊗trig

Tp

/4|π<|φΔNear-Side,

/4|π<|π-φΔAway-Side,

[rad]2Ψ-associateφ

-1.4 -1.2 -1 -0.8 -0.6-0.4 -0.2 0

Inte

grat

ed Y

ield

00.20.4

0.60.8

10-10%


-1.4 -1.2 -1 -0.8 -0.6-0.4 -0.2 0

Inte

grat

ed Y

ield

00.20.4

0.60.8

110-20%


-1.4 -1.2 -1 -0.8 -0.6-0.4 -0.2 0In

tegr

ated

Yie

ld0

0.20.4

0.60.8

120-30%


-1.4 -1.2 -1 -0.8 -0.6-0.4 -0.2 0

Inte

grat

ed Y

ield

00.20.4

0.60.8

130-40%


-1.4 -1.2 -1 -0.8 -0.6-0.4 -0.2 0

Inte

grat

ed Y

ield

00.20.4

0.60.8

140-50%


Tp⊗trig

Tp




-1.4 -1.2 -1 -0.8 -0.6-0.4 -0.2 0

Inte

grat

ed Y

ield

-0.10

0.10.20.30.40.50.6 0-10%


-1.4 -1.2 -1 -0.8 -0.6-0.4 -0.2 0

Inte

grat

ed Y

ield

-0.10

0.10.20.30.40.50.6 10-20%


-1.4 -1.2 -1 -0.8 -0.6-0.4 -0.2 0

Inte

grat

ed Y

ield

-0.10

0.10.20.30.40.50.6 20-30%


-1.4 -1.2 -1 -0.8 -0.6-0.4 -0.2 0

Inte

grat

ed Y

ield

-0.10

0.10.20.30.40.50.6 30-40%


-1.4 -1.2 -1 -0.8 -0.6-0.4 -0.2 0

Inte

grat

ed Y

ield

-0.10

0.10.20.30.40.50.6 40-50%

104 CHAPTER 5. DISCUSSIONS

which might indicate the correlated yield per a trigger is boosted into out-of-plane direction bythe v4{ 4}. While the v2 is 2.5 times larger than v4{ 4} in peripheral collisions, so that jet ismore-boosted in in-plane direction.

For 3 dependent correlated yield per a trigger, we find the similar trends as 2 dependentcorrelations. In in-plane trigger case, the associate yield in in-plane direction increases with in-crease of centrality, where the average thickness of medium decreases. In out-of-plan trigger case,the associate yield at out-of-plane shows a hint of possible enhance, which is almost independentof centrality. The increase of away-side yield from out-of-plane to in-plane suggests the existenceof energy-momentum loss correlated with 3. In addition, the hint of enhance in associate yieldlocated in out-of-plane direction may suggest the re-distribution of lost energy also correlateswith 3. We can again mention the boost of jet by expanding medium. The third-order flowharmonics v3 may play main role for the enhance at in-plane direction, and possible sixth-orderflow with respect to 3:v6{ 3}, which has not been measured yet, may works for the hint ofenhance of out-of-plane yiled, in analogous to the boosted jet scenario suggested in 2 dependentcorrelations.

The parton energy-loss, possible energy-redistribution, and the boost of jet by medium ex-pansion seem to be more strongly ruled by second-order harmonics of a QGP medium geometrythan third-order harmonics of it. This observed trends may be due to di↵erent strength of partic-ipant eccentricity between second and third-order as shown in Fig.5.14 calculated by a GlauberMonte Carlo Simulation.

5.2.2 Path-length Dependence of Per Trigger Yield

For more quantitative discussion on this observation, integrated correlated yield at near-side(�� <

|⇡|) and away-side(�� ⇡ < |⇡|) as a function of associate angle from 2 and 3 are plotted inFig.5.15 and 5.16 for 5 di↵erent centrality selections.

The azimuthal anisotropy of correlated associate yield vPTYn is obtained by Fourier fitting to

the yield as a function of associate angle with respect to event-plane for 2 dependent correlationsas

F (�a � 2) = a{1 + 2vPTY2 cos 2(�a � 2) + 2vPTY

4 cos 4(�a � 2)}, (5.4)

and for 3 dependent correlations as

F (�a � 3) = a{1 + 2vPTY3 cos 3(�a � 3)}, (5.5)

where a is the average of the yields. The results of vPTYn as a function of Npart, converted

from centrality, is shown in Fig.5.17. One can see the negative vPTY2 at Npart > 200 and the

consistently positive vPTY4 in both near and away-side in 2 dependent correlations, and the

negative vPTY3 of away-side at Npart > 200 in 2 dependent correlations.

The ⇡0 v2 as a function of Npart at pT = 6-9 GeV/c, where dominated by particles originatingfrom jets, is compared with model calculations that employs various models with (left) quadraticand (right) cubic path-length dependence of parton energy loss in Fig.5.18.

We find the parton energy-momentum loss forms the negative vn, and other physics e↵ectis required to obtain the negative vn. This comparison complements the interpretation given inthe last section; there exists at least an additional e↵ect in addition to parton energy loss.

104 CHAPTER 5. DISCUSSIONS

which might indicate the correlated yield per a trigger is boosted into out-of-plane direction bythe v4{ 4}. While the v2 is 2.5 times larger than v4{ 4} in peripheral collisions, so that jet ismore-boosted in in-plane direction.

For 3 dependent correlated yield per a trigger, we find the similar trends as 2 dependentcorrelations. In in-plane trigger case, the associate yield in in-plane direction increases with in-crease of centrality, where the average thickness of medium decreases. In out-of-plan trigger case,the associate yield at out-of-plane shows a hint of possible enhance, which is almost independentof centrality. The increase of away-side yield from out-of-plane to in-plane suggests the existenceof energy-momentum loss correlated with 3. In addition, the hint of enhance in associate yieldlocated in out-of-plane direction may suggest the re-distribution of lost energy also correlateswith 3. We can again mention the boost of jet by expanding medium. The third-order flowharmonics v3 may play main role for the enhance at in-plane direction, and possible sixth-orderflow with respect to 3:v6{ 3}, which has not been measured yet, may works for the hint ofenhance of out-of-plane yiled, in analogous to the boosted jet scenario suggested in 2 dependentcorrelations.

The parton energy-loss, possible energy-redistribution, and the boost of jet by medium ex-pansion seem to be more strongly ruled by second-order harmonics of a QGP medium geometrythan third-order harmonics of it. This observed trends may be due to di↵erent strength of partic-ipant eccentricity between second and third-order as shown in Fig.5.14 calculated by a GlauberMonte Carlo Simulation.

5.2.2 Path-length Dependence of Per Trigger Yield

For more quantitative discussion on this observation, integrated correlated yield at near-side(�� <

|⇡|) and away-side(�� ⇡ < |⇡|) as a function of associate angle from 2 and 3 are plotted inFig.5.15 and 5.16 for 5 di↵erent centrality selections.

The azimuthal anisotropy of correlated associate yield vPTYn is obtained by Fourier fitting to

the yield as a function of associate angle with respect to event-plane for 2 dependent correlationsas

F (�a � 2) = a{1 + 2vPTY2 cos 2(�a � 2) + 2vPTY

4 cos 4(�a � 2)}, (5.4)

and for 3 dependent correlations as

F (�a � 3) = a{1 + 2vPTY3 cos 3(�a � 3)}, (5.5)

where a is the average of the yields. The results of vPTYn as a function of Npart, converted

from centrality, is shown in Fig.5.17. One can see the negative vPTY2 at Npart > 200 and the

consistently positive vPTY4 in both near and away-side in 2 dependent correlations, and the

negative vPTY3 of away-side at Npart > 200 in 2 dependent correlations.

The ⇡0 v2 as a function of Npart at pT = 6-9 GeV/c, where dominated by particles originatingfrom jets, is compared with model calculations that employs various models with (left) quadraticand (right) cubic path-length dependence of parton energy loss in Fig.5.18.

We find the parton energy-momentum loss forms the negative vn, and other physics e↵ectis required to obtain the negative vn. This comparison complements the interpretation given inthe last section; there exists at least an additional e↵ect in addition to parton energy loss.

Ψ2 dependence

Ψ3 dependence


Tp⊗trig

Tp




-1.4 -1.2 -1 -0.8 -0.6-0.4 -0.2 0In

tegr

ated

Yie

ld

00.20.4

0.60.8

10-10%


-1.4 -1.2 -1 -0.8 -0.6-0.4 -0.2 0

Inte

grat

ed Y

ield

00.20.4

0.60.8

110-20%


-1.4 -1.2 -1 -0.8 -0.6-0.4 -0.2 0

Inte

grat

ed Y

ield

00.20.4

0.60.8

120-30%


-1.4 -1.2 -1 -0.8 -0.6-0.4 -0.2 0

Inte

grat

ed Y

ield

00.20.4

0.60.8

130-40%


-1.4 -1.2 -1 -0.8 -0.6-0.4 -0.2 0

Inte

grat

ed Y

ield

00.20.4

0.60.8

140-50%

vnPTY & vnEP

•  vnPTY is a part of vnEP •  vnPTY amplitude is one order larger than vnEP

2013/11/06 pre-‐Defense 45

partN0 50 100 150 200 250 300 350 400

/4π|<φ

Δ N

ear-S

ide:

|PT

Ynv

-1.5

-1

-0.5

0

0.5

1

1.5

}2Ψ{4PTYv

}2Ψ{4EPv

=200 GeVNNsAu+Au 1-2 GeV/c⊗=2-4

Tap⊗

Ttp

partN0 50 100 150 200 250 300 350 400

/4π|<π-φ

Δ A

way

-Sid

e:|

PTY

nv-1.5

-1

-0.5

0

0.5

1

1.5

}2Ψ{4PTYv

}2Ψ{4EPv


Tap⊗

Ttp

partN0 50 100 150 200 250 300 350 400

/4π|<φ

Δ N

ear-S

ide:

|PT

Ynv

-1.5

-1

-0.5

0

0.5

1

1.5 }3Ψ{3PTYv

}3Ψ{3EPv


Tap⊗

Ttp

partN0 50 100 150 200 250 300 350 400

/4π|<π-φ

Δ A

way

-Sid

e:|

PTY

nv

-1.5

-1

-0.5

0

0.5

1

1.5 }3Ψ{3PTYv

}3Ψ{3EPv


Tap⊗

Ttp

partN0 50 100 150 200 250 300 350 400

/4π|<φ

Δ N

ear-S

ide:

|PT

Ynv

-1.5

-1

-0.5

0

0.5

1

1.5


Tap⊗

Ttp

}2Ψ{2PTYv

}2Ψ{2EPv

partN0 50 100 150 200 250 300 350 400

/4π|<π-φ

Δ A

way

-Sid

e:|

PTY

nv

-1.5

-1

-0.5

0

0.5

1

1.5


Tap⊗

Ttp

}2Ψ{2PTYv

}2Ψ{2EPv

v2PTY & High-‐pT π0 v2

•  Models with parton energy-‐loss provide posi)ve π0 v2 •  Addi)onal effects required to explain nega)ve v2

2013/11/06 pre-‐Defense 46

for a quadratic dependence (!ldl) of energy loss in alongitudinally expanding medium (!1=l), and ! is tunedto reproduce the central RAA data. The medium density " isgiven by two leading candidates of the initial geometry:MC Glauber geometry "GL"x; y# $ 0:43"part"x; y# %0:14"coll"x; y#, i.e., a mixture of participant density profileand binary collision profile from PHOBOS [26]; and MCCGC geometry "CGC"x; y# of Drescher and Nara [14]. Theeffect of fluctuations for both profiles were included via thestandard rotation procedure [13]. The short-dashed curvesin Fig. 3(a) show that the result for Glauber geometrywithout rotation ("GL) compares reasonably well withthose from WHDG [21] and a version of ASW modelfrom [27]. Consequently, we use the JW model to estimatethe shape distortions due to fluctuations and CGC effects.The results for Glauber geometry with rotation ("Rot

GL ) andCGC geometry with rotation ("Rot

CGC) each lead to a!15%–20% increase of v2 in midcentral collisions.However, these calculated results still fall below the data.

Figure 3(b) compares the same data with three JWmodels for the same matter profiles, but calculated for aline integral motivated by AdS/CFT correspondence I $Rdll". The stronger l dependence for "GL significantly

increases (by >50%) the calculated v2, and brings it closeto the data for midcentral collisions. However, a sizablefractional difference in the central bin seems to require anadditional increase from fluctuations and CGC geometry.Figure 3(b) also shows a MR model from [27], whichimplements the AdS/CFT l dependence within the ASWframework [28]; it compares reasonably well with the JW

model for "GL (short-dashed curves). Note that the MR andJW models in Fig. 3 have been tuned independently toreproduce the 0–5% #0 RAA data, and they all describe thecentrality dependence of RAA very well [see Figs. 3(c) and3(d)]. On the other hand, these models predict a strongersuppression for dihadrons than for single hadrons, oppositeto experimental findings [29]; thus a global confrontationof any model with all experimental observables iswarranted.In summary, we presented results on #0 azimuthal an-

isotropy (v2) in 1<pT < 18 GeV=c in Au% Au colli-sions at

!!!!!!!!sNN

p $ 200 GeV. The measurements indicatesizable v2"pT# that decreases gradually for 3 & pT &7–10 GeV=c, but remains positive for pT > 10 GeV=c.This large v2 exceeds expectations of PQCD energy-lossmodels even at pT ! 10 GeV=c. Estimates of the v2 in-crease due to modifications of initial geometry from gluonsaturation effects and fluctuations indicate that they areinsufficient to reconcile data and theory. Incorporating anAdS/CFT-like path-length dependence for jet quenching ina PQCD-based framework [27] and a schematic model [25]both compare well with the data. However, more detailedstudy beyond these simplified models are required toquantify the nature of the path-length dependence. Ourprecision data provide key constraints on the initial ge-ometry, medium space-time evolution, and the jet-quenching mechanisms.We thank the staff of the Collider-Accelerator and

Physics Departments at BNL for their vital contributions.We acknowledge support from the Office of Nuclear

0 100 200 300

v 2

0

0.05

0.1

0.15

0.2

6 - 9 GeV/c

GL!dl "JW: I ~

RotGL

!dl "JW: I ~

RotCGC

!dl "JW: I ~

WHDG MR: ASW(a)

0 100 200 300

6 - 9 GeV/c

MR: AdS/CFT

GL!dl l"JW: I ~

RotGL

!dl l"JW: I ~

RotCGC

!dl l"JW: I ~

(b)

Npart Npart

0 100 200 300

RA

A

(c)0.20.30.40.60.81.0

0 100 200 300

(d)

FIG. 3 (color online). v2 vs Npart in 6–9 GeV=c compared with various models: (a) WHDG [21] (shaded bands), ASW [27] (solidtriangle), and three JW calculations [25] with quadratic l dependence with longitudinal expansion for Glauber geometry (dashed lines),rotated Glauber geometry (long dashed lines), and rotated CGC geometry (solid lines); (b) Same as (a) except that AdS/CFT modifiedcalculation in ASW framework (triangle) from [27] is shown and the JW calculations were done for cubic l dependence withlongitudinal expansion; (c)–(d) the comparison of calculated RAAs from these models with data.

PRL 105, 142301 (2010) P HY S I CA L R EV I EW LE T T E R Sweek ending

1 OCTOBER 2010

142301-6

partN0 50 100 150 200 250 300 350 400

/4π|<φ

Δ N

ear-S

ide:

|PT

Ynv

-1.5

-1

-0.5

0

0.5

1

1.5


Tap⊗

Ttp

}2Ψ{2PTYv

}2Ψ{2EPv

partN0 50 100 150 200 250 300 350 400

/4π|<π-φ

Δ A

way

-Sid

e:|

PTY

nv

-1.5

-1

-0.5

0

0.5

1

1.5


Tap⊗

Ttp

}2Ψ{2PTYv

}2Ψ{2EPv

Path length dependence of PTY

•  Angle from EP converted to Path-‐Length by Glauber Model •  Non-‐monotonic behavior •  Yields does not scale on a universal curve

2013/11/06 pre-‐Defense 47

) fm2

Ψ-φPath Length L(2 3 4 5 6 7

/4π|<φ

ΔN

ear S

ide

Yiel

d : |

-0.2

0

0.2

0.4

0.6

0.8

1

1.2=200 GeVNNsAu+Au

:2-4x1-2 GeV/cT

p

) fm2


/4π|<π-φ

ΔAw

ay S

ide

Yiel

d : |

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0-10%10-20%20-30%30-40%40-50%

) fm3


/4π|<φ

ΔN

ear S

ide

Yiel

d : |

-0.2

0

0.2

0.4

0.6

0.8

) fm3


/4π|<π-φ

ΔAw

ay S

ide

Yiel

d : |

-0.2

0

0.2

0.4

0.6

0.8

) fm2


/4π|<φ

ΔN

ear S

ide

Yiel

d : |

-0.2

0

0.2

0.4

0.6

0.8

1

1.2=200 GeVNNsAu+Au

:2-4x1-2 GeV/cT

p

) fm2


/4π|<π-φ

ΔAw

ay S

ide

Yiel

d : |

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0-10%10-20%20-30%30-40%40-50%

) fm3


/4π|<φ

ΔN

ear S

ide

Yiel

d : |

-0.2

0

0.2

0.4

0.6

0.8

) fm3


/4π|<π-φ

ΔAw

ay S

ide

Yiel

d : |

-0.2

0

0.2

0.4

0.6

0.8

) fm2


/4π|<φ

Δ :

|co

llNe

ar S

ide

Yiel

d/N

-2-101234567

-310×

=200 GeVNNsAu+Au :2-4x1-2 GeV/c

Tp

) fm2


/4π|<π-φ

Δ :

|co

llAw

ay S

ide

Yiel

d/N

-2-101234567

-310×

0-10%10-20%20-30%30-40%40-50%

) fm3


/4π|<φ

Δ :

|co

llNe

ar S

ide

Yiel

d/N

0

1

2

3

4

-310×

) fm3


/4π|<π-φ

Δ :

|co

llAw

ay S

ide

Yiel

d/N

0

1

2

3

4

-310×

Path length dependence of PTY/Npart

•  Approximately scaled on a curve •  Associate yields from QGP medium

2013/11/06 pre-‐Defense 48

) fm2


/4π|<φ

Δ :

|pa

rtN

ear S

ide

Yiel

d/N

-2

0

2

4

6

8

10

-310×


Tp

) fm2


/4π|<π-φ

Δ :

|pa

rtAw

ay S

ide

Yiel

d/N

-2

0

2

4

6

8

10

-310×

0-10%10-20%20-30%30-40%40-50%

) fm3


/4π|<φ

Δ :

|pa

rtN

ear S

ide

Yiel

d/N

-101

234567

-310×

) fm3


/4π|<π-φ

Δ :

|pa

rtAw

ay S

ide

Yiel

d/N

-101

234567

-310×

) fm2


/4π|<φ

Δ :

|pa

rtN

ear S

ide

Yiel

d/N

-2

0

2

4

6

8

10

-310×


Tp

) fm2


/4π|<π-φ

Δ :

|pa

rtAw

ay S

ide

Yiel

d/N

-2

0

2

4

6

8

10

-310×

0-10%10-20%20-30%30-40%40-50%

) fm3


/4π|<φ

Δ :

|pa

rtN

ear S

ide

Yiel

d/N

-101

234567

-310×

) fm3


/4π|<π-φ

Δ :

|pa

rtAw

ay S

ide

Yiel

d/N

-101

234567

-310×

) fm2


/4π|<φ

Δ :

|co

llNe

ar S

ide

Yiel

d/N

-2-101234567

-310×


Tp

) fm2


/4π|<π-φ

Δ :

|co

llAw

ay S

ide

Yiel

d/N

-2-101234567

-310×

0-10%10-20%20-30%30-40%40-50%

) fm3


/4π|<φ

Δ :

|co

llNe

ar S

ide

Yiel

d/N

0

1

2

3

4

-310×

) fm3


/4π|<π-φ

Δ :

|co

llAw

ay S

ide

Yiel

d/N

0

1

2

3

4

-310×

Path length dependence of PTY/Ncoll

•  Also approximately scaled on a curve •  Associate yields from hard-‐scanering at ini)al collisions •  Coupling of jet with medium

2013/11/06 pre-‐Defense 49

) fm2


/4π|<φ

Δ :

|co

llN

ear S

ide

Yiel

d/N

-2-101234567

-310×


Tp

) fm2


/4π|<π-φ

Δ :

|co

llAw

ay S

ide

Yiel

d/N

-2-101234567

-310×

0-10%10-20%20-30%30-40%40-50%

) fm3


/4π|<φ

Δ :

|co

llN

ear S

ide

Yiel

d/N

0

1

2

3

4

-310×

) fm3


/4π|<π-φ

Δ :

|co

llAw

ay S

ide

Yiel

d/N

0

1

2

3

4

-310×

) fm2


/4π|<φ

Δ :

|co

llN

ear S

ide

Yiel

d/N

-2-101234567

-310×


Tp

) fm2


/4π|<π-φ

Δ :

|co

llAw

ay S

ide

Yiel

d/N

-2-101234567

-310×

0-10%10-20%20-30%30-40%40-50%

) fm3


/4π|<φ

Δ :

|co

llN

ear S

ide

Yiel

d/N

0

1

2

3

4

-310×

) fm3


/4π|<π-φ

Δ :

|co

llAw

ay S

ide

Yiel

d/N

0

1

2

3

4

-310×

) fm2


/4π|<φ

Δ :

|co

llNe

ar S

ide

Yiel

d/N

-2-101234567

-310×


Tp

) fm2


/4π|<π-φ

Δ :

|co

llAw

ay S

ide

Yiel

d/N

-2-101234567

-310×

0-10%10-20%20-30%30-40%40-50%

) fm3


/4π|<φ

Δ :

|co

llNe

ar S

ide

Yiel

d/N

0

1

2

3

4

-310×

) fm3


/4π|<π-φ

Δ :

|co

llAw

ay S

ide

Yiel

d/N

0

1

2

3

4

-310×

Summary -‐ I •  Two-‐Par)cle correla)ons were measured with subtrac)on of backgrounds from vn(n=2,3,4)

•  New experimental data disfavored theore)cal models –  Cherenkov Gluon Radia)on – Mach-‐Cone Shock Wave –  Hot-‐Spot Models

•  Jet-‐Deflec)on model is qualita)vely consistent with data

2013/11/06 pre-‐Defense 50

Summary -‐ II •  Event-‐Plane dependent correla)ons shows two compe)ng effects

–  Increase / decrease of correla)on yield with increase of path-‐length

•  Anisotropy of correla)on yield vnPTY –  Addi)onal Effect in addi)on to parton-‐energy loss

•  Scale of Correla)on Yield by Npart & Ncoll –  Jet-‐Medium Coupling

•  Energy-‐Loss, Energy Re-‐distribu)on, and boost of jet by medium need to be considered in future theore)cal models

2013/11/06 pre-‐Defense 51

BACK UP

2013/11/06 pre-‐Defense 52

•  Two-‐Par)cle Correla)ons at CNT – Without rapidity gap, where Jet contribu)on survives

•  Flow Measurements –  CNT Par)cle & Forward Event Plane at RXN, BBC –  Jet contribu)on suppressed

Rapidity Selec1on in the Measurements

2013/11/06 pre-‐Defense 53

vn =< cos n(��n) >

0 5 -5 η

dN/dη"

CNT : |η|<0.35

BBC : 3.0<|η|<3.9

RXN : 1.0<η<2.8

Tracking Efficiency

2013/11/06 pre-‐Defense 54

� =�uncor

�cor

GeV/cT

p0 1 2 3 4 5]

-2[(G

eV/c

)ηd T

/dp

2)d

Nev

tN Tpπ

1/(2

-1510-1310-1110-910-710-510-310-110

10310510710910

11101210

0-10% -210-20%x10-420-30%x10-630-40%x10-840-50%x10

Solid: PRC69.034910σBlack Open: Uncorrected:2.5σColord Open: Uncorrected :2

Fit Func)on

F (pT ) = p0 ��

p1

p1 + pT

�p2

•  Efficiency correc)on by ra)o of uncorrected invariant yield over corrected ones

EP Resolu1on in Monte Carlo

•  Convert resolu)on to χ

2013/11/06 pre-‐Defense 55

[rad]realΨ-obsΨ)=obsΨ-φ)-(realΨ-φ(-1.5 -1 -0.5 0 0.5 1 1.5

]2 z e{1

+Erf(

z)}

π[1

+z/22

χ- eπ1

0

0.2

0.4

0.6

0.8

1

1.2

)realΨ-obsΨ cos2(χz = =1.1χ=1.0χ=0.9χ=0.8χ=0.7χ=0.6χ=0.5χ=0.4χ=0.3χ=0.2χ=0.1χ=0.0χ

Centrality0 5 10 15 20 25 30 35 40 45 50

/4)]

2 nχ( 1/4

)+I

2 nχ( 0[I/42 nχ- e nχ 2

2π

of

nχ

0

0.5

1

1.5

2

]2Ψ for Res[2χ

]3Ψ for Res[3χ

]4Ψ for Res[4χ

dNeve

d[kn(�obsn ��real

n )]=

1�

e��2n/2

�1 + z

��[1 + erf(z)]ez2

�

�cos [kn(�obs

n ��realn )]

�=�

�

2�

2�ne��2

n/4

�I(k�1)/2

��2

n

4

�+ I(k+1)/2

��2

n

4

��.

•  Distribu)on between real and observed EP using χ

Ψ2-Ψ4 correla1on in Monte Carlo

•  Ψ2-Ψ4 correla)on :

2013/11/06 pre-‐Defense 56

Centrality %0 5 10 15 20 25 30 35 40 45 50

/4)]

2 42χ( 1/4

)+I

2 42χ( 0[I/4

2 42χ- e42χ 2

2π

of

42χ 0

0.2

0.4

0.6

0.8

1

1.2=1-2&2-4GeV/c

Taverage p

=2-4GeV/cT

p

=1-2GeV/cT

p

Centrality %0 5 10 15 20 25 30 35 40 45 50

} 4Ψ{ 4

/v} 2Ψ{ 4

)>=v

2Ψ- 4

Ψ<c

os4(

0

0.2

0.4

0.6

0.8

1

1.2=1-2&2-4GeV/c

Taverage p

=2-4GeV/cT

p

=1-2GeV/cT

p

�cos [4(�2 ��4)]� =�

�

2�

2�42e

��242/4

�I0

��2

42

4

�+ I1

��2

42

4

��•  Obtain χ & reconstruct distribu)on

dNeve

d[kn(�obsn ��real

n )]=

1�

e��2n/2

�1 + z

��[1 + erf(z)]ez2

�

[rad]2Ψ-4Ψ-0.6 -0.4 -0.2 0 0.2 0.4 0.6

]2 z e{1

+Erf(

z)}

π[1

+z/22

χ- eπ1

0

0.2

0.4

0.6

0.8

1

1.2

_2)Ψ_4-Ψ cosr4(χz = =1.1χ=1.0χ=0.9χ=0.8χ=0.7χ=0.6χ=0.5χ=0.4χ=0.3χ=0.2χ=0.1χ=0.0χ

�cos [4(�2 � �4)]� = v4 {�2} /v4 {�4}

2Ψ-tφ=sφ

-1.5 -1 -0.5 0 0.5 1 1.5

)φΔ, sφ(

cor

) & 1

+Yφ

Δ, sφ(ra

w1+

Y1

1.05

1.1

1.15

1.2

Corected curveFit to raw dataCorrected dataRaw data

)φΔ+sφcos4(raw4

)+2vφΔ+sφcos2(raw2=1+2vraw)sφF(

)φΔ+sφcos4(42σ/raw4

)+2vφΔ+sφcos2(2σ/raw2=1+2vcor)sφF(

/24.π=-φΔAu+Au 20-30%,

Unfolding : Fisng Method

•  Offset λ=1.0 to avoid possible division by zero

•  Assuming correla)on yield has anisotropy w.r.t. EP

•  Correc)on by EP resolu)on

2013/11/06 pre-‐Defense 57

� + Y cor(⇤s,�⇤) =� + b0

�1 + 2vY

2 /⇥ cos 2(⇤s + �⇤) + 2vY4 /⇥42 cos 4(⇤s + �⇤)

�

� + b0

�1 + 2vY

2 cos 2(⇤s + �⇤) + 2vY4 cos 4(⇤s + �⇤)

� (� + Y (⇤s,�⇤))

� + Y cor(⇤s,�⇤) =� + b0

�1 + 2vY

3 /⇥3 cos 3(⇤s + �⇤)�

� + b0

�1 + 2vY

3 cos 3(⇤s + �⇤)� (� + Y (⇤s,�⇤))

Ψ2 dependent case

Ψ3 dependent case Fisng

Fisng

PRC.84.024904 (2011)

Unfolding : Itera1on

2013/11/06 pre-‐Defense 58


]2 z e{1

+Erf(

z)}

π[1

+z/22

χ- eπ1

0

0.2

0.4

0.6

0.8

1

1.2

)realΨ-obsΨ cos2(χz = =1.1χ=1.0χ=0.9χ=0.8χ=0.7χ=0.6χ=0.5χ=0.4χ=0.3χ=0.2χ=0.1χ=0.0χS =

�

��

s0 s1 s2 s3 s4 s3 s2 s1

s1 s0 s1 s2 s3 s4 s3 s2

s2 s1 s0 s1 s2 s3 s4 s3

s3 s2 s1 s0 s1 s2 s3 s4

s4 s3 s2 s1 s0 s1 s2 s3

s3 s4 s3 s2 s1 s0 s1 s2

s2 s3 s4 s3 s2 s1 s0 s1

s1 s2 s3 s4 s3 s2 s1 s0

�

��

,A(k) =

�

��

1 + Y (0, k)1 + Y (1, k)1 + Y (2, k)1 + Y (3, k)1 + Y (4, k)1 + Y (5, k)1 + Y (6, k)1 + Y (7, k)

�

��

,

cii = A(i, k)/B(i, k) Acor(k) = C(k)A(k)

•  Smearing of measured correla)ons

•  Correc)on factor B(k) = SA(k)

cij(i �=j) = 0

Correla)on + Offset Smearing Effect

•  Corrected yield

Unfolding : Itera1on

•  Itera)on un)l conversion 2013/11/06 pre-‐Defense 59

c(n)ii (k) = (1� r)c(n)

ii (k) + (r/2) c(n)ii (k � 1) + (r/2) c(n)

ii (k + 1)

3.6. TWO PARTICLE CORRELATIONS 63

A(1)=Offset(1) + PTY A(n)=A(n-1)C(n)�

Smeared PTY B(n)=SA(n)�

Correction Matrix C(n)=A(n)/B(n)�

Smoothing Correction Matrix C(n)=(1-r)C(n)+rC(n)(k-1)

+rC(n)(k+1)�A(300)-Offset(1)�

A(1)=Offset(1) + PTY, Smearing Matrix : S�

300 Loops�

Figure 3.13: Flow chart of the Iteration Method of Unfolding.


]2 z e{1

+Erf(

z)}

π[1

+z/22

χ- eπ1

0

0.2

0.4

0.6

0.8

1

1.2

)realΨ-obsΨ cos2(χz = =1.1χ=1.0χ=0.9χ=0.8χ=0.7χ=0.6χ=0.5χ=0.4χ=0.3χ=0.2χ=0.1χ=0.0χ

Figure 3.14: ��-�z correlations in (Left) PC1 and (Right) PC3 after pair selection in PC1.

A� A(n)

B� B(n)

C� C(n)

Acor � A(n+1)

Smoothing

Nota1on in itera1on

Zero Yield at Near-‐Side

•  Correla)on and Pure Flow is fined at Δφ=0

•  Double-‐hump is not so sensi)ve to flow subtrac)on

2013/11/06 pre-‐Defense 60

φΔ-1 0 1 2 3 4

φΔ

/dpair

dN tr1/N

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

PTY pTt x pTa = 2-‐4 x 1-‐2 GeV/c

20-‐30%

High pT correla1ons

2013/11/06 pre-‐Defense 61


, v2

Au+Au 200GeV, v


φΔ

/dta

dN

t1/

N

00.0050.010.0150.02

-1 0 1 2 3 4

40-50%(e)

0

0.05

0.1

-1 0 1 2 3 4

(j)

0

0.1

0.2

-1 0 1 2 3 4

(o)

0

0.1

0.2

-1 0 1 2 3 4

(t)

00.0050.010.0150.02

-1 0 1 2 3 4

30-40%(d)

0

0.05

0.1

-1 0 1 2 3 4

(i)

0

0.1

0.2

-1 0 1 2 3 4

(n)

0

0.1

0.2

-1 0 1 2 3 4

(s)

00.0050.010.0150.02

-1 0 1 2 3 4

20-30%(c)

0

0.05

0.1

-1 0 1 2 3 4

(h)

0

0.1

0.2

-1 0 1 2 3 4

(m)

0

0.1

0.2

-1 0 1 2 3 4

(r)

00.0050.010.0150.02

-1 0 1 2 3 4

10-20%(b)

0

0.05

0.1

-1 0 1 2 3 4

(g)

0

0.1

0.2

-1 0 1 2 3 4

(l)

0

0.1

0.2

-1 0 1 2 3 4

(q)

00.0050.010.0150.02

-1 0 1 2 3 4

0-10%(a)4-10×:4-10t,a

Tp

0

0.05

0.1

-1 0 1 2 3 4

(f)2-4×:4-10t,a

Tp

0

0.1

0.2

-1 0 1 2 3 4

(k)1-2×:4-10t,a

Tp

0

0.1

0.2

-1 0 1 2 3 4

(p)0.5-1×:4-10t,a

Tp

Intermediate pT correla1ons

2013/11/06 pre-‐Defense 62


, v2

Au+Au 200GeV, v


φΔ

/dta

dN

t1/

N

00.010.020.03

-1 0 1 2 3 4

40-50%(e)

0

0.05

0.1

-1 0 1 2 3 4

(j)

00.050.10.15

-1 0 1 2 3 4

(o)

00.020.040.06

-1 0 1 2 3 4

(t)

0

0.05

0.1

-1 0 1 2 3 4

(y)

00.010.020.03

-1 0 1 2 3 4

30-40%(d)

0

0.05

0.1

-1 0 1 2 3 4

(i)

00.050.10.15

-1 0 1 2 3 4

(n)

00.020.040.06

-1 0 1 2 3 4

(s)

0

0.05

0.1

-1 0 1 2 3 4

(x)

00.010.020.03

-1 0 1 2 3 4

20-30%(c)

0

0.05

0.1

-1 0 1 2 3 4

(h)

00.050.10.15

-1 0 1 2 3 4

(m)

00.020.040.06

-1 0 1 2 3 4

(r)

0

0.05

0.1

-1 0 1 2 3 4

(w)

00.010.020.03

-1 0 1 2 3 4

10-20%(b)

0

0.05

0.1

-1 0 1 2 3 4

(g)

00.050.10.15

-1 0 1 2 3 4

(l)

00.020.040.06

-1 0 1 2 3 4

(q)

0

0.05

0.1

-1 0 1 2 3 4

(v)

00.010.020.03

-1 0 1 2 3 4

0-10%(a)2-4×:2-4t,a

Tp

0

0.05

0.1

-1 0 1 2 3 4

(f)1-2×:2-4t,a

Tp

00.050.10.15

-1 0 1 2 3 4

(k)0.5-1×:2-4t,a

Tp

00.020.040.06

-1 0 1 2 3 4

(p)1-2×:1-2t,a

Tp

0

0.05

0.1

-1 0 1 2 3 4

(u)0.5-1×:1-2t,a

Tp


2013/11/06 pre-‐Defense 63


[rad]tφ-aφ = φΔ

1-2

GeV

⊗),

2-4

φΔ

dep

ende

nt P

TY(

2Ψ

-1 0 1 2 3 4

0

0.2

0.4

0.6

0.8

1

1.240-50%(e)

-1 0 1 2 3 4

0

0.2

0.4

0.6

0.8

1

1.230-40%(d)

-1 0 1 2 3 4

0

0.2

0.4

0.6

0.8

1

1.220-30%(c)

-1 0 1 2 3 4

0

0.2

0.4

0.6

0.8

1

1.210-20%(b)

-1 0 1 2 3 4

0

0.2

0.4

0.6

0.8

1

1.20-10%

/8π<-32Ψ-tφ/8<π-4

(a)

/8π<-22Ψ-tφ/8<π-3

/8π<-2Ψ-tφ/8<π-2

<02Ψ-tφ/8<π-

Ψ2 dependence of PTY (Polar)

2013/11/06 pre-‐Defense 64

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

2Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

0-10%

<02Ψ-tφ/8<π-

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

2Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

10-20%

<02Ψ-tφ/8<π-

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

2Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

20-30%

<02Ψ-tφ/8<π-

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

2Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

30-40%

<02Ψ-tφ/8<π-

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

2Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

40-50%

<02Ψ-tφ/8<π-

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

2Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.160-10%

/8π<-2Ψ-tφ/8<π-2

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

2Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.1610-20%

/8π<-2Ψ-tφ/8<π-2

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

2Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.1620-30%

/8π<-2Ψ-tφ/8<π-2

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

2Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.1630-40%

/8π<-2Ψ-tφ/8<π-2

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

2Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.1640-50%

/8π<-2Ψ-tφ/8<π-2

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

2Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

0-10%

/8π<-22Ψ-tφ/8<π-3

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

2Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

10-20%

/8π<-22Ψ-tφ/8<π-3

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

2Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

20-30%

/8π<-22Ψ-tφ/8<π-3

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

2Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

30-40%

/8π<-22Ψ-tφ/8<π-3

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

2Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

40-50%

/8π<-22Ψ-tφ/8<π-3

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

2Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.160-10%

/8π<-32Ψ-tφ/8<π-4

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

2Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.1610-20%

/8π<-32Ψ-tφ/8<π-4

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

2Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.1620-30%

/8π<-32Ψ-tφ/8<π-4

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

2Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.1630-40%

/8π<-32Ψ-tφ/8<π-4

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

2Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.1640-50%

/8π<-32Ψ-tφ/8<π-4


2013/11/06 pre-‐Defense 65


[rad]tφ-aφ = φΔ

1-2

GeV

⊗),

2-4

φΔ

dep

ende

nt P

TY(

3Ψ

-1 0 1 2 3 4

0

0.2

0.4

0.6

0.8

1

1.240-50%(e)

-1 0 1 2 3 4

0

0.2

0.4

0.6

0.8

1

1.230-40%(d)

-1 0 1 2 3 4

0

0.2

0.4

0.6

0.8

1

1.220-30%(c)

-1 0 1 2 3 4

0

0.2

0.4

0.6

0.8

1

1.210-20%(b)

-1 0 1 2 3 4

0

0.2

0.4

0.6

0.8

1

1.20-10%

/12π<-33Ψ-tφ/12<π-4

(a)

/12π<-23Ψ-tφ/12<π-3

/12π<-3Ψ-tφ/12<π-2

<03Ψ-tφ/12<π-

Ψ3 dependence of PTY (Polar)

2013/11/06 pre-‐Defense 66

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

3Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

0-10%

<03Ψ-tφ/12<π-

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

3Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

10-20%

<03Ψ-tφ/12<π-

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

3Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

20-30%

<03Ψ-tφ/12<π-

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

3Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

30-40%

<03Ψ-tφ/12<π-

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

3Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

40-50%

<03Ψ-tφ/12<π-

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

3Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.160-10%

/12π<-3Ψ-tφ/12<π-2

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

3Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.1610-20%

/12π<-3Ψ-tφ/12<π-2

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

3Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.1620-30%

/12π<-3Ψ-tφ/12<π-2

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

3Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.1630-40%

/12π<-3Ψ-tφ/12<π-2

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

3Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.1640-50%

/12π<-3Ψ-tφ/12<π-2

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

3Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

0-10%

/12π<-23Ψ-tφ/12<π-3

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

3Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

10-20%

/12π<-23Ψ-tφ/12<π-3

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

3Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

20-30%

/12π<-23Ψ-tφ/12<π-3

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

3Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

30-40%

/12π<-23Ψ-tφ/12<π-3

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

3Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.16

40-50%

/12π<-23Ψ-tφ/12<π-3

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

3Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.160-10%

/12π<-33Ψ-tφ/12<π-4

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

3Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.1610-20%

/12π<-33Ψ-tφ/12<π-4

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

3Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.1620-30%

/12π<-33Ψ-tφ/12<π-4

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

3Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.1630-40%

/12π<-33Ψ-tφ/12<π-4

Arbitrary unit-0.3 -0.2 -0.1 0 0.1 0.2 0.3

in P

olar

Coo

rdin

ate

3Ψ

PTY

w.r.t

.

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Offset: 0.1640-50%

/12π<-33Ψ-tφ/12<π-4

Glauber Model •  Woods-‐Saxon Distribu)on –  Nucleon density distribu)on

•  Collision range •  Number of nucleons par)cipated in a collision

•  Number of binary nucleons collisions in a collision

2013/11/06 pre-‐Defense 67

1.2. RELATIVISTIC HEAVY ION COLLISIONS 5

Figure 1.3: A schematic idea of the space-time evolution of relativistic heavy-ion collisions.

• Nucleons keeps flying straight on initial orbit,

• Nucleus collisions are built up from inelastic nucleon interactions,

• Cross-section of inelastic nucleon interaction is independent of number of collisions Ncoll.

The analytical formulation of Grauber Model is given by the calculations based on Wood-Saxon Potential of nucleons in a nucleus at A = 197 as

⇢A(r) =⇢A0

1 + e(r�RA

)/aA

. (1.4)

where RA=6.38 fm is a radius and aA=0.54 fm is a di↵usion parameter of Au nuclei, and ⇢A

satisfiesR

dr⇢A(r) = A. �0 = 42 mb atp

sNN =200 GeV [5]. The nucleon density function iscalculated by the integral of ⇢A(x, y, z) in z direction as

TA(x, y) =Z 1

�1dz⇢A(x, y, z). (1.5)

The desisty function of number of participantNpart of a nucleus collision of mass number A andB with a impact parameter b is given as

npartA(x, y; b) = TA(x + b/2, y)

(

1�✓

1� �0TB(x� b/2, y)B

◆B)

(1.6)

+ TB(x + b/2, y)

(

1�✓

1� �0TA(x + b/2, y)A

◆A)

, (1.7)

and Npart can be given by the integral of npart in x-y direction as

Npart(b) =Z

dxdynpart(x, y; b). (1.8)

Path-‐Length based on Glauber MC •  Path-‐Length : distance from center to surface as a func)on of angle form the event-‐planes

2013/11/06 pre-‐Defense 68

x [fm]-15 -10 -5 0 5 10 15

y [fm

]

-15

-10

-5

0

5

10

15

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016=200-240part rotation, N2Ψ

)part2

Ψ-φL(

part2Ψ

φ

x [fm]-15 -10 -5 0 5 10 15

y [fm

]-15

-10

-5

0

5

10

15

0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

0.0014

0.0016 rotation3Ψ

)part3

Ψ-φL(

part3Ψ

φ

Eccentricity by Glauber Model

2013/11/06 pre-‐Defense 69

Npart0 50 100 150 200 250 300 350 400

>2/<

r2 > pφ

sinn

2+<

r2 > pφ

cosn

2<r

=

nε

0

0.2

0.4

0.6

0.8

1

2ε

3ε

4ε

Path length dependence of PTY

•  Near & Away-‐Side of both Ψ2, Ψ3 dependent correla)ons do not form a universal curve

2013/11/06 pre-‐Defense 70

) fm2


/4π|<φ

Δ :

|co

llN

ear S

ide

Yiel

d/N

-2-101234567

-310×


Tp

) fm2


/4π|<π-φ

Δ :

|co

llAw

ay S

ide

Yiel

d/N

-2-101234567

-310×

0-10%10-20%20-30%30-40%40-50%

) fm3


/4π|<φ

Δ :

|co

llN

ear S

ide

Yiel

d/N

0

1

2

3

4

-310×

) fm3


/4π|<π-φ

Δ :

|co

llAw

ay S

ide

Yiel

d/N

0

1

2

3

4

-310×

Boost by v4

•  Boost by v4 to out-‐of-‐plane direc)on in central collisions •  Boost by v2 to in-‐plane direc)on in peripheral collisions 2013/11/06 pre-‐Defense 71

v2

v4

Central Collisions v2 = v4

Peripheral Collisions v2 > v4

v2

v4

MeasurementsofTwo/Par1cle*Correla1ons...

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