28 May 2012

Hard Probes 2012

1

TWO PARTICLE CORRELATIONMEASUREMENTS AT PHENIX	
Takahito Todoroki For the PHENIX Collaboration
University of Tsukuba & RIKEN Nishina Center
Hard Probes 2012 at Cagliari, Italy	28 May 2012

Hard Probes 20122

Contents	
• Higher harmonic event plane and flow(vn)• Correlations with vn subtractions• Correlations relative to event plane- At high and intermediate pT• Summary	28 May 2012

Hard Probes 20123

Motivations	• Dissect possible interplay of hard-

scattered partons & hot dense medium• To have definitive answer what remains

in correlations after vn subtractions• To test path length dependence ofparton energy loss via correlations
relative to event plane28 May 2012

4

Hard Probes 2012

Initial state of collisions	
Smooth picture	

Fluctuating picture	
!3
!2

Φ2	

!4

• Initial collision geometry- Smooth to Fluctuating picture• Azimuthal particle distribution- vn(even){Φ2} only ⟶ vn(even){Φn} + vn(odd) {Φn} 	

dN/dφ = 1 +�

2vn cos n(φ − Φn )

28 May 2012

5

Hard Probes 2012

Charged Hadron vn at PHENIX	

PRL.107.252301	

• v3 is comparable to v2 at 0~10%"

Charged particle vn : |η|<0.35
Event plane Φn: |η|=1.0~2.8• v2 evolution as centrality increment, no evolution in v3 "• v4{Φ4} ~ 2 x v4{Φ2}"28 May 2012

6

Hard Probes 2012

Identified Particle vn	
200 GeV Au+Au 0-50%
v2{!2}

0.2"+"K+K
pp

0.15

Vn

0.2

PHENIX Preliminaryv3{!3}x1.5

0.2

v4{!4}x1.5

0.2

 

-

0.15

0.15

0.15

0.1

0.1

0.1

0.1

0.05

0.05

0.05

0.05

0

0

0

0
:pT

0

v4{!2}x5.0

correlated sys. of "±

1

2

3

40

1

2

3

40

1

2

3

40

1

2

3

4

pT [GeV/c]• Mass dependence at low pT : Hydrodynamics• Baryon/Meson diff. at mid pT: Quark Coalescence	Jet(∆φ) = C2 (∆φ) − b0 F low(∆φ)

28 May 20127

Hard Probes 2012vn contributions in correlations	Jet(∆φ) = CF (∆φ) − b0 F low(∆φ)
Phys. Rev. C 80, 064912 (2009)	

2< pTasso < pTtrig GeV/C	

Phys. Rev. C 78, 014901 (2008)	○:p+p●: Au+Au	

trig
asso
Jet(∆φ)=cos
C2 (∆φ)−bFlow(∆φ)0b0 2vRidge	
v
3∆φv
subtracted	
2
3
3
n=3	

b0n=3	
2v3trig v3asso cos 3∆φtrig asso∼ b0 2vn vn cos n∆φ• Contributions from vn :"∼ b0 2vn vn
あああああああああああああ

trig asso

Shoulder	cos n∆φ• Ridge & Shoulder positions : Agree with v3 peaks"
あああああああああああああああああああ• vn subtractions needed to get real jet correlations	28 May 20128

Hard Probes 2012

Correlations with Δη gap	 QM’11 J. Jia ATLAS Flow Plenary	No	
  Flow	
  Subtrac:on	￮ measured correlations 	
vn with EP Method 	
Track at |η|<2.5	
  
with	
  EP	
  from	  full	
  FCAL	
  3.3<|η|<4.8	

Pb+Pb	
  2.76TeV	

vn with 2Par. Cor Method 	Charged	  par:cle	
  pair	  with	  large	
  rapidity	
  gap	
  e.g.	
  	
  |Δη|>2	

• vn reproduce Ridge & Shoulder at 0-5%	

28 May 20129

Hard Probes 2012

Correlations without Δη gap	PHENIX PRELIMINARY	

Au+Au 200GeV 0-20%	

Incl.γ - hadron
2-3x1-2 GeV/c	

|Δη|<0.7	

• Away side shoulders are almost gone in

most-central collisions 0-20%"

28 May 2012

Hard Probes 201210

Correlations up to centrality 50%	
V2,	
  V3	
  &	
  V4(Φ4)	
  modula0on	
  by	
  ZYAM	  method	• Away side shoulders- Canceled in most-central collisions : 0-10%- Remain in mid-central collisions : 20-50%• To Do : Include v1 term to vn modulation for

definitive answer

28 May 201211

Hard Probes 2012

Correlations relative to event plane	Mid rapidity	φs	Forward rapidity	

φt	
Δφ	

Φn	
φa	

• Control parton path length- By selecting trigger relative to forward

event plane- Reduce autocorrelations of jet itself	28 May 201212

Hard Probes 2012

High pT range	

SUPPRESSION OF AWAY-SIDE JET FRAGMENTS WITH . . .

ESSION OF AWAY-SIDE JET FRAGMENTS WITH . . .

v2 & v4{Φ2} modulated	

PRC.84.024904	

IAA = YAA/Ypp	

Au+Au 200GeV 20-60%	

PHYSICAL REVIEW

Short path
Long pathne) Per-trigger azimuthal jet yields for the mostlength	length	7. (Color online) Nuclear jet suppression factor IAA byG.
6. (Color
online)Per-trigger azimuthal
jet◦yields forFIG.
the most
solid
circles),and out-of-plane,
φs = 75–90◦
7. (Color
online)suppressnear- andjetaway-side
with respect
to FIG.
the reactionplane
φs forNuclear
0–15◦ (solid
circles), andout-of-plane, φanglee, φs = selectionss = 75–90
particlein midcentral(20%–60%)withto thereaction planeφs for n
selections,angle
circles
andrespectsquares,
respectively,in midcentral
circles),particleselections
in midcentral angular(20%–60%)
partner trigger
momenta.
Insetsshow away-side
angularcirclesand squares,
respecti
for selections,various partner
momenta.
Bars indicate
ons
various
partner
momenta.
Insets show(20%–60%)
away-sidecollisions
scale.forBars
indicate
statisticaluncertainties.
(20%–60%)
collisions
for showsvariousthe
partnermomstatistical uncertainties.
The shadedband
systematicon a systematic
zoomed scale.
Bars indicate
statistical uncertainties.
lationuncertainties
are represented
uncertainties.
shaded correction.
band shoreaction-plane
resolution The
unsmearing
ying event
systematic
uncertainties areuncertainty
representedon thestatisticalpointswhilemodulation
the corresponding
normalizationon theangle
reaction-plane
resolution
Solid points showuncertainty
trigger particle
averaged results
and unsm
theds as
throughthelines
pointswhilezero.
the correspondingwn
dashedaroundNear- and normalization
Solid points show trigger particle angle averag
gration arewindows
aintiesshownareasindicateddashed withlinesarrows.
around zero.global
Near-scale
anduncertainty.
global scale uncertainty.

• Near side yield : No suppression• Away side yield : Monotonic decrease	28 May 201213

Hard Probes 2012

Intermediate pT range	out-­‐of-­‐plane	  	
  trigger	
  case	  Trig.	  in-­‐plane	  	
  trigger	
  case	  PHENIX preliminary

Au+Au 200GeV 20-50%
h-h :2-4x1-2GeV/cv2 & v4{Φ2} modulated	Trig.	  
Φ2 R.P.

Flow	
  subtracted	
  yield	  is	
  shown	
  radially	
  with	  base	  line.	  

Φ2 R.P.

Trig.	  surface dominance

Trig.	  penetration dominance• Constant suppression of back-to-back jet• Two competitive effects seen

28 May 2012

Hard Probes 201214

Summary	• Higher harmonic flow vn has been measured• By vn modulation to correlations,- Shoulders almost gone in most-central collisions- Shoulders remain in mid-central collisions• Correlations relative to event plane- Monotonic away side suppression at high pT- Constant suppression of di-jet & Twocompetitive effects at intermediate pT• Fully vn modulated analyses are in progress

28 May 2012

Hard Probes 2012

Backup Slides	

15

< cos j (Φn- Φm)momentum reconstruction with azimuthal angle coverage-5-5Hard Probes 201216
’ ¼ " rad in the central region (j!0 j " 0:35).
To estimate the event plane !n in each detector, we(c)(d) 2.5
6(Φ A3 - ΦB2) (x20)
2(ΦA2 - Φ B1)
2.5
generalize to all orders n our earlier procedure for eventCA
B
D
3(Φ 3 - Φ1 ) (x20)
2(Φ2 - Φ1 )2
2
Cplane determination (see [9] and especially definitions in4(ΦA4 - Φ B2)
3(Φ 3 - Φ D1) (x20)
1.51.5[24]). For Peach event-plane
detector we evaluateP11tanðn"n Þ ¼ wi sinðn#i Þ= wi cosðn#iweek
Þ for the!n subending
0.5
0.5
V I E W Levent
E T Testimator
E R S "n , where the #i 16
areDECEMBER
the azimuths2011of00elements in that detector and the weights wi reflect the
-0.5
-0.5
energyor multiplicity(a)in that element.
Acceptance correc(b) 253(Φ A3 - ΦB3) (x10)2(ΦA2 - Φ B2)
25
100
80
60
40
20
0 100
80
60
40
20
0
tionsC [24]forimperfect
detector
efficiency
were
employedC
D
D
PRL.107.252301
	
3(
Φ
Φ
)
(x10)
2(
Φ
Φ
)
20
3
3
centrality [%]22
to ensurea flat (azimuthally independent)
event-plane20
A
B
A
B
1(
Φ
Φ
)
4(
Φ
Φ
)
(x10)
1
1
4
4 considerations. In
distribution,
as required by symmetry
15
15
FIG. 1 (color online). Raw correlation strengths hcosðj½"An &general,thehit
distributions
samplevirtuallyallmomenta.
10
10"Bm 'Þi and hcosðj½"Cn & "Dm 'Þi of the event planes for various
Tomeasurev,
theazimuth#ofeachparticleiscorren55detector combinations as a function of the collision centrality,
lated with the !n via Eq. (1). The measured vn f!n g ¼
binned in percentages of the total cross section, where 0%00avghcosðn½# & "avgn 'Þi=Resð!n Þ, where "n is the average ofcorresponds to impact parameter ¼ 0. Panels (a) and (b) show
-5
the "n for north and south subevents and where the de--5 the two subevent correlations for m ¼ n; (c) and (d) show thetwo subevent correlations for m ! n. The detectors in which thenominator Res(!n ) represents a resolution factor
event plane is measured are: A: RXN North, B: BBC South, C:
described
in [24]. Thisfactor corrects
vn for the (d)event(c)6(Φ A3 - ΦB2) (x20)
2(ΦA2 - Φ B1)
2.5
2.5
MPC North, and D: MPC South. Data in (b) and (d) have been
by-event
dispersion of the "n . Its magnitude
can be estiC
A
B
D
3(
Φ
Φ
)
(x20)
)
2(
Φ
Φ
3
1
2 via
1 the two and three subevents
2
matedmethod[9] in which 2 scaled by factors of 10 and 20, respectively.
C
A
B
D
4(
Φ
Φ
)
3(
Φ
Φ
)
(x20)
2
1
the 4correlation
between "n from 3different
subevents is1.5
1.5
measured. The strength of this correlation is generally 1
The subevent correlations hcosðj½"An & "Bm 'Þi for n ! m
1ABquantified as hcosðn½"n & "n 'Þi for subevents A, B, which
are also of interest. Figure 1(c) confirms the expected
0.5
0.5
measures the cosine of the dispersion of the "n estimator
correlation between !1 and !2 (due to sidewards flow),00with respect to the true !n .
as well as that between !2 and !4 [24]. By contrast,
-0.5
-0.5
Figure 1 shows the centrality dependence of this correFig. 1(d) shows that there is no significant correlation
lation strength hcosðj½"An & "Bm 'Þi for subevent combinaobserved
between !2 and !3 , a result which is indepen100
80
60
40
20
0 100
80
60
40
20
0
tions (A, B) involving different event-plane detectors withdent of the detectors used. The order j ¼ 6 is chosen to[%]#!0 ( 5 and #!0 centrality( 7. The raw
correlations are presented
account for the n multiplet of directions (2"=n) of !2 andas measured; however, the magnitudes are specific to Athe
!3 . The absence of this correlation suggests that the flucFIG. 1 (color
online).
Rawcorrelation
strengths hcosðj½"
n &PHENIX
detectors
involved.
The
systematic
uncertainties
tuations for !3 about !2 are substantial. This is well
C & "D 'Þi of the event planes for varioushcosðj½""Bm 'Þi and(notnmshown) for these correlations are of similar relative
reproduced by Glauber modeling [25,26] and therefore
detector combinations
ofthecollision
centrality,
size to those forasvnaf!functiong
discussed
below.
The
uncertainties
supports an initial state fluctuation origin of !3 and v3 .
nbinned inarepercentagesof thetotal crosssection,where
0% A small correlation between !3 and !1 is indicated incorrelated acrosscentrality
and n suchthat therelative
28 May 2012

< cos j (Φn- Φm) > [%]Φi - Φj correlations 	 28 May 201217

Hard Probes 2012

vn via event plane method	RXN	

vn =< cos n(φ − Φn ) >RXN in: 1.5<|η|<2.8& out: 1.0<|η|<1.5

CNT: |η|<0.35
dN/dη	

MPC: 3.1<|η|<3.7
BBC: 3.0<|η|<3.9
2cm Pb converter in front

ZDC/SMD
-5

0

5

η

• Mid rapidity particle anisotropy relative toforward event planes	w contributions that may influ28 May 2012
n f!n g, such as jet correlations,h less than all other uncertainties

initialHard"2Probesvalues
The two
2012associated with each model.
18
models have similar "3 , and thus the larger viscosity
needed with MC-KLN calculations to match v2 , leads toa much lower v3 than obtained with Glauber MC calculations. Consequently, our measurement of v3 f!3 g helps toDegeneracy among models
wn in Fig. 2 increase with p forby v3	e, anddisentangled
decrease for more centralTcalculations"centrality
dependence of v2 f!2 g
additional calculations, demontraints the data provide and also
namics to the details of different
dium evolution. Alver et al. [27]v3v2

reases as expected from central(Event	  Plane	  Method)	
ns,
followingthe
expectedin• v3 seems to prefer low 0.3 (a) pT = 0.75-1.0 GeV/c
act parameter [19,27,28]. The
PHENIX
viscosity"
KLN+ 4πη/s = 2
ess statistical significance, also
0.2
Glauber + 4πη/s = 1 (1)much less centrality dependent,- Glauber+4πη/s =1
0.1
e to v2 f!2 g in the most central
works
better"onsistentwith Glaubercalcula0
0
100
200
300
ations of the generalized ‘‘trian(c)p=0.75-1.0
GeV/c
0.1
CGC-KLN+4πη/sT26]. -The
Fig. 2 panels (b) and (d) =2
UrQMD + 4πη/s = 0
Glauber + 4πη/s = 1 (2)!2 g andv3 f!3 g to results fromfailed"0.05
s. The pT and centrality trends
Moretog •arein goodconstraints
agreement with thehown,especially at pT belowhydrodynamics
0
0

100

200

Npart

300

(b) pT = 1.75-2.0 GeV/c

V2	

0

100

200

300

100

200

300

(d) pT = 1.75-2.0 GeV/c

V3	

0

Npart

PRL.107.252301	
  FIG. 3 (color online). Comparisonof [(a)(ppg132)	
and (b)] v2 f!2 g vsB. Alver et. al., PRC82, 034913(2010).!
Npartet. al.,measurements
Npart and [(c) and (d)] v3 f!3 g B.vs
Schenke
PRL106, 042301(2011).!andPetersen et. al., PRC82, 041901(2010).!
theoretical predictions (see text):H. ‘‘MC-KLN
þ 4!"=s ¼ 2’’
and ‘‘Glauber þ 4!"=s ¼ 1 (1)’’ [27]; ‘‘Glauber þ 4!"=s ¼ 1

28 May 201219

Hard Probes 201234!"#$%&'()*+,(+,'(-.'/+(01%/'(#'+,"2$#+'()*!"#!$ ,'-*./.)#'+ %#$'()*³

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QM’11 J. Jia ATLAS Flow Plenary	28 May 201220

Hard Probes 2012

Scaling property of v2	
0.12

v2/nq

0.10

(a)

10-20%

(b)

0.12

0.10

0.10

0.08

0.08

0.06

0.06

0.04

0.04

0.04

0.02

0.02

0.02

! +!
K++Kp+p

0.06

0.0

-

+

0.08

0.12

v2/nq

0.12

0-10%

14

0.5

1.0

20-40%

1.5

2.0

2.5

3.0
0.12

(c)

0.5

1.0

40-60%

1.5

2.0

2.5

3.0

(d)

0.12

0.10

0.10

0.10

0.08

0.08

0.08

0.06

0.06

0.06

0.04

0.04

0.04

0.02

0.02

0.0 0.5 1.0 1.5 2.0 2.5 3.0
KET /nq (GeV)

Au+Au sNN = 200 GeV

0.02

0.5 1.0 1.5 2.0 2.5 3.0
KET /nq (GeV)

FIG. 9: (color online) The quark-number-scaled v2 (v2 /nq ) of identified hadrons are shown as a function of the kinetic energy
per quark, KET /nq in 0–10% centrality (panel (a)), 10–20% (panel (b)), 20–40% (panel (c)), and 40–60% centrality (panel (d))

28 May 2012

21

Hard Probes 2012

Scaling property of vn	
200 GeV Au+Au 0-50%

0.1 v {! }/n2/222q

0.1 v {! }/n4/2x4.0
44q

0.1 v {! }/n4/2x15
42q0.08  

0.08

0.08

0.06

0.06

0.06

0.04

0.04

0.04

0.04

0.02

0.02

0.02

0.02

0

0

0

0

"+"-

n/2

0.08

V n/nqPHENIX Preliminary

0.1 v {! }/n3/2x2.5
3
3
q

K+K
pp

0.06

-



:KET correlated sys. of "±

-0.02

0

0.5

1

1.5

-0.02
2 0

0.5

1

1.5

-0.02
2 0

0.5

1

1.5

-0.02
2 0

0.5

1

1.5

2

KET/nq [GeV]• vn(KET/nq)/nq failed on v3, v4 & v4{Φ2}• vn(KET/nq)/nqn/2 : need correction power

28 May 2012

Hard Probes 2012

Fourier decomposition of flow
subtracted correlations	

22

28 May 2012

Hard Probes 201223

Correlations relative to Φ3