Azimuthal sensitive HBTpin Pb+Pb sN N = 2.76T eV collisionsat LHC-ALICE experiment
A School for young Asian scientists
2014.Sep.24
Naoto Tanakafor the ALICE collaboration
University of Tsukuba
1Space - Time Evolution■ To quantify the properties of QGP, a precise understanding of spatial andtemporal evolution is required■ HBT correlation is a unique tool to measure3 the source size at the kinetic

章 序論

1

freeze-out

衝突の描像及び粒子生成の描像

対論的なエネルギーでの原子核衝突実験における衝突からの QGP 生成とその後の時空発展の描像について説行なう (図 1.3)。

Kinetic freeze-out↑
Hadron phasesource size
Chemical freeze-out↑
Mixed Phase (?)

emitting time(?) order phase transition↑
Partonic phase

Freeze out time
pre-equilibrium

Pre-collision

図 1.3 原子核衝突における系の時空発展

2

HBT interferometry■ Measure the source size with correlation of two identical particles
 Robert Hanbury Brown & Richard Q.Twiss- A test of new stellar interferometer on Sirius(1950s)

Robert Hanbury Brown(1916–2002)

 G. Goldhaber, S. Goldhaber, Lee, Paris- Influence of Bose-Einstein Statistics on the Anti-proton proton annihilation process(1960s)⌘1 ⇣ ip1 (x1 r1 ) ip2 (x2 r2 )ee± eip1 (x1 r2 ) eip2 (x2 r1 )2 (p1, p2) = p2

sourceP1

r1

x1

C2C(q)(q)2

Correlation Function

22

Gerson. Goldhaber(1924–2010)

7fm

1.85fm
3fm

1.6

1.5

R

C2 (q) = 1 + exp( R 2 q2 )

1.4

r2

P2

x2

1/R

1.2

110

D

0

0.02

0.04

P2 (p1 , p2 )C2 (p1 , p2 ) ⌘⇡ 1 ± |⇢(q)|2
P (p1 )P (p2 )

0.06

0.08

0.1

0.1

0.12

0.14

0.16

0.18

0.2q
0.2
q(GeV/c)Gaussian distribution
particle emitting source3

3D HBT analysis■ For more detailed spatial information, correlation function is expanded to 3-dimension
LCMS ( Longitudinally Co-Moving System ) pz1 + pz2 = 0
2C2 (qout , qside , qlong ) = 1 + ( Rout
q2out

2Rsideq2sidekT =pT 1 + pT 2
22Rlongq2long )Rlong：source size along the longitudinal direction (beam direction)
Rout ：source along the pair transverse momentum + emission duration
Rside：source size along the perpendicular to Rout：chaoticity＝ (in coherence) – (resonance) – (Background)der
tocte

Rside

Transverse Plane

Rout
Beam axis

Rlong
Rout

Beam axis

Rside4

Azimuthal anisotropy
particleemitting

peripheralcollision■ In non-central collision,
initial overlap region is almond shapeBeamaxis z■ Local thermal equilibrium is established Results & Discussion
nd→ meanfree pathof particles
is muchshorterthan
Azimuthal HBT
w.r.t
2
order
event
plane
the system sizex★ Pressure gradient is steeper at shot axis than long one planereaction

Event plane– Measuring emitting particle anisotropy,Initial spatial
we can measure
the 2ndeccentricity
event plane✓P◆
1wi sin(n i )1
P=tannnwi cos(n i )pypz Azimuthally sensitive HBT– Dividing pair angle w.r.t. Ψ2 in azimuthal plane-> measure the freeze-out source size indetailed at azimuthal plane
6 5
74
Momentum anisotropy v2
Whatisthe83
final
9 eccentricity2?
112Δφ 938
4reaction planepx
5 6 7v2 Plane
5Ev
Pl enan tTAC seminar, Dec.20, 2012
Takafumi Niida,e★Spatial eccentricity

PressuregradientHBT with respect to 2nd oder event plane
Radii vs. Azimuthal Angle

Rside : width52● φpair - ΨEP, 2 is the angle between pair and ΨEP, 2● Rout, Rside oscillate
2Rµ,0('222 ) = Rµ,0 + 2Rµ,2 cos(2('Rout : depth+emission duration2 ))out-of-plane( µ = side, out, long )222 ) = Ros,0 + 2Ros,2 cos(2('2 ))in-planeewvi

4:
24

2Ros,0('in,0po20

14til,2nd order
Event planeprAnd22ysdaue

7.5Azimuthal plane◆ in-plane ：small Rout , large Rside◆ out-plane：large Rout, small Rside→ Initial ellipticity still remains at freeze
out despite there is strong elliptic flow !

Fig. 48: kT dependence of radii vs. pair emission angle at centrality 20-30%

6Eccentricity at

Final eccentricity at LHC

Model Comparisons

1 Comparison of final eccentricity to MC-Glauber & MC-KLN

compare our results of the relative oscillations to systematic hydrodynamic studies of pion azimuthal
sotropy to study the final shape of the source at freeze-out. We compare the following models: hydrodels with Monte Carlo Glauber (MC-Glauber) initial conditions and with Monte Carlo Kharzeevin-Nardi (MC-KLN) initial conditions by Ulrich Heinz and Chun Shen [23] , and Ultra Relativistic
antum Molecular Dynamics (urQMD) by Mike Lisa et al. [28]. The data is compared to results fromfollowing collaborations E895, CERES, and STAR. The data ranges in energies from 2.7 GeV to 2.76
V, whereas the models extend to 5.5 TeV. STAR data ranging from 7.7 GeV to 200 GeV are STARliminary by Christopher Anson. The models show predictions for the final spatial eccentricity, ✏f ,final
2
2
ch is related to the relative oscillations in all data in the following manner, ✏f = 2Rside,0/Rout,0.
e hydro with MC-Glauber and MC-KLN initial conditions shows a monotonic decrease in ✏f as the222
ision energyside,0increases. At higher
has a longer lifetime to transform
2 collision energies
2side,0 the fireballside,2
m its original deformed shape to become more isotropic [23]. When comparing these models with2
ALICE data, they both underestimate
the data. The UrQMD model seems to follow the data points
side,2m the STAR energies to ALICE. We cannot make a definite reason at this stage without a more direct
f2 and average radii from the models. We observe that the ALICE data
mparison of radii oscillations
side,0nt is lower than most of the pervious experiments.

pionRs2

Rs,02

cos(2('))

kaon

67:

p,014
Pb-Pb sNN = 2.76 TeV

Apr

ALICE 0.3 < kT < 0.4 GeV/ c 10-30%d102s (GeV)

22n10" This Indicates that source exp" PHENIX and STAR results are! εfinal ≈ εinitial for kaonil,CERES (-1 < y < -0.5) 10-25%

y0! εfinal ≈ εinitial/2 for pion

E895 (-0.6 < y < 0.6) 7.4-29.7%

f2side,2dTu ε , 2R /Resda
y22nA2side,0AzHYDRO, MC-Glauber, η/s = 0.08

0.2in-plane

20

prAzHYDRO, MC-KLN, η/s = 0.2

STAR prelim. QM’12 Au-Au 10-30%
0.15 < kT < 0.6 GeV/ c

PRC70, 044907 (2004)

2Rs,2
ε final = 2 2
Rs,0UrQMD

0.4π/2 π
φpair- Ψ2

22Rs,n= Rs,n(Δφ )cos(nΔφ )4,RR:24+ 2R01" =2)=R04('il,2R0

in-plane

4:24◆ Final eccentricity is determined by initial eccentricity,pressure gradient and expand time etc.

εRs,22

" Kaon may freeze-out sooner th★ ALICEhas
εf of m be"dataDue tothelowest
differenceT- longer Freeze out time?
- effect of elliptic flow

103

s-dependence of the final spatial eccentricity ✏f of the isothermal kinetic freeze-out surface at Tdec =7

✓ O

9:C
D;
S?:I 8:D20>
BJ8DG;
TI=6G:A6A
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A:6 I>DCIG><< 9>C<E L G I:G
-20

6GI =><EE>8A: =p >120GeV/c
8A
<p > (GeV/c)

20> 8.0 GeV/c

What is already known about Jet
0Tped
sub estal atrac nd flowted-20:6C9■ Quenched
Jet energy
where?
-40
9>
 -40 JH goes?:T,1

YasuoM■ Jet quenching

IAKE, A

sianWintepT,2 > 50GeV/cJ Δφ > 5>πB|η>A | < 1.6
1,2 6 1,26GrS0.4IA> (d):H GDCOut-of-Cone@:D7
B: J<< I=
CMS 0-30%
ΔR<0.8 9>
8=6 :HI :ΔR≥0.8

40 Pb+Pb s =2.76 TeV
40 H6>C< dijet asymmetry, inC>HE

for both centrality ranges
andevenforevents
withlargeE;;::6G observed
B-1
7J  is not related tob8momentum:I∫ L dt = 6.7 µThis
9data and simulation.
shows that the7Jdijet
imbalance
>HCI7I> in the calorimet
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20 in the event due to instrumental;>Cgaps
C 20 C(e.g.
tected activity
inefficiencies
6AH >C>C:G<>I>C9IN
physics (e.g. neutrino production) effects.
:CH ADHH 6<: >6A
8
G:6 0 :B D;0I:9
6II E6GI> 0.5 GeV/c

DC>
(a)
CG
In-ConeOut-of-C
J :(b)0.5H-1.0 GeV/c-20-20 ΔR<0.8
Δ R≥0.8
1.0 - 2.0 GeV/c
J40 PYTHIA+HYDJET 0-30%40(c)In-ConeINN

T<p > (GeV/c)- Azimuthal correlation w.r.t.chool, 2012.1.11high pT leading particle (trigger)

I

ID
Phys.Rev.C 84,024906(2011)
H6BJEE:>
B>0.2
H>93.3 Overall momentumof0.1 balance
0.20.3dijet events
0.4 ?:
0.1
0.3
A6

2.0 - 4.0 GeV/c-40> 8.0 GeV/c

20
020
0.1

0.2

AJ

0.3

0.4

0.1

00.2

AJ

0.3

0.4

T

<p > (GeV/c)-40464.0 - 8.0 GeV/c

X||k<p>=piT cos(Figure 15: Average missing transversemomentum,
h6 pT ii, for-20
trackswith jetpT )> 0.5 GeV/c, proleadingT-20

PRL91.072304 (2003)

assocptrig=4-6 GeV/c, pT > 2 GeV/cTpp: clean di-jetdAu: similar to pp

Au+Au : similar on the same sideback-to-back disappeared

kpT,1 > 120GeV/ci
jected onto the leading jet axis (solid leadcircles).
Theh6 p i values are shown
as a function of dijet
sub Tlead
pppT,2 >or
50GeV/casymmetry A J -40
for 0–30% centrality,(DR <subleading jet cones-40 leadingTT 0.8) one of theAj = insidesublead5lead(left) and outside (DR > 0.8) the leading
jet cones (right).
theΔ φ1,2> πFor|η1,2| < solid
1.6 circles,
pT and+ subleading
pT6
vertical bars and brackets represent the statistical and systematic uncertainties, respectively.
For the individual pT(c)ranges,
uncertainties
as verticalbars.
0.1the statistical
0.2
0.3
0.4 are shown
0.1
0.2
0.3(d)

0.4★ Missingenergy of Jet is redistributed
CMS 0-30%
Δ R<0.8
Δ R≥0.8
40 Pb+Pb s =2.76 TeV
40k
The figure also showscontributions
to h6 pT i for five transversemomentum
ranges from
0.5–
astheLlow
pT hadrons
towardlargeangle= 6.7verticalµb1 GeV/c to pT > 8 GeV/c.
bars for each range denote statistical uncertainties. For∫ dt The
In-ConeOut-of-CNN-1k

20 a large negative contribution to h6 p i (i.e.,20
data and simulation,in the direction of the leading jet)
TeV/c)

Direct evidence of Jet quenching8

Azimuthal sensitive HBT w.r.t. Jet axis
Jet reconstruction Parameters

peripheral
Collisioncollision
Beamaxis z- input track : ITS + TPCHow is the effect to source size??

 planereaction

QGPJet- algorithm : anti kT- R size ( =p⌘2 +2) : 0.3- pT cut of single particle : 0.15 (GeV/c)- Leading Jet pT threshold : 20 (GeV/c)xspace time evolutionview

p o in tewvi
point
nt

Freeze outview poi

Hadronaffectphase★ If Jet modification
thegeometry of source,
HBT radii oscillate w.r.t. Jet axis

1 2 345★Jet energy
is re-distributed
Kinetic
freeze-out
into low pT particles↑ReconstructedLeading Jet

9out of plane

R = 0.2 anti-k T, |η |<0.7jet

syst error (Correlated)T■ Background flow of underlying event(dN in plane/(dp dη))/(dNch,jetJet v2p

1.5T, track> 0.15 GeV/c , p

T, leadV0 event plane> 3 GeV/ cpT dependence of v2ch,jetch, jet

1＊Evenif v2 background is estimated,
・Event plane : VZERO
There is non-zero v2 signal(2.8 < η < 5.1, -3.7 < η < -1.7)
30
40
50
60
70
80
90100
★ path-lengthdependence
・Background : E by E fourier fitting
p ch (GeV/ c )obs2,EP ]) + v3 cos (3 ['T, jet

ALI−PREL−752283,EP ])}v2ch,jet =< cos(2('ch,jetjetv ch,{EP, |∆η|>0.9 }2⇢(') = ⇢0 ⇥ 1 + {v2obs cos (2 ['2,V 0 )) >

0.4

0.3

0-5%, stat errors

ALICE Preliminary

syst error (Shape)

Pb-Pb sNN = 2.76 TeV
R = 0.2 anti-k T, |η |<0.7
jetsyst error (Correlated)p

0.2

T, track> 0.15 GeV/c , pT, lead> 3 GeV/ c0.10p (v =0, 40 < p ch230★ Cannot perfectly separate Jet and flow
ALI−PREL−75239

4050

T, jet60< 80 GeV/ c ) = 0.44708090p ch

T, jet100(GeV/ c )Fig. 49: R = 0.2 charged jets, 0-5 %. The shape uncertainty (uncorrelated uncertainty) is represented bboxes, the correlated uncertainty by shaded boxes. Top panel: in-plane jet yield divided by out-of-plane
10 jejetOutlook to understand Jet-flow correlation★ Estimate v2 background to measure the correct Jet pT★ cannot perfectly separate Jet and flow-> It seems Jet modification effect is buried in flow effectin geometrical space...
★ Subtract Ψ2 effect- if there is Jet modification (re-distribution of Jet) to geometrical size
jet and flow effects are superposition

11

Summary
Azimuthally sensitive HBT with respect to Ψ2• Rout, Rside have azimuthal dependence• Rout, Rside oscillate out-of-phase• Initial ellipticity still remains at freeze out despite there is strong elliptic flow
• Final eccentricity at LHC is lowest because of expansion time and v2

Azimuthally sensitive HBT with respect to Jet axis
• Azimuthally sensitive HBT w.r.t. Jet axis has similar oscillation to Ψ2 HBT• It’s necessary to estimate v2 background• To see clearly jet modification in geometrical space, we should understandjet - flow correlation and subtract v2 effect to HBT radii

12

Back up13

HBT measurement in experiment
How to calculate correlation function C2 in experimentC2 =P (p1 , p2 )QReal
=P (p1 )P (p2 )QM ix

QReal : pair in same event (HBT effect)
QMix : pair in different event (no HBT effect)
C2 : Correlation function• Event Mixing- Selecting Real event and Mix event in similar event (centrality, z-vertex),
we can exclude correlation from acceptance and efficiency→ C2 includes HBT effect and any other physics correlations- Pair cut- Coulomb interaction

14

ALICE Detectors & performance• ITS+TPC ( |η| < 0.9 )◊ charged particle tracking◊ PID dE/dx ( p = 0.15 - 0.5 (GeV/c))✓ ◆2ct- ハドロンの質量の違いから飛行時間を測定m2 = p 21Lすることで粒子識別- PID momentum range (p = 0.5 - 3.0 (GeV/c))• VZERO (2.8 < η < 5.1, -3.7 < η < -1.7)- centrality determination, Event trigger- measure the event plane
R2• TOF ( |η| < 0.9 ) !

RA2 {B,C}

ALICE Performance Pb-Pb s NN = 2.76 TeV
2014/04/29

0.80.6ABTPC

V0-A V0-C

CV0-A

TPC V0-C

V0-C

TPC V0-A

FMD-A TPC FMD-C

0.4

FMD-C TPC FMD-A

0.20102030

40506070

T0-A

TPC V0-C

T0-C

TPC V0-A80

centrality %ALI−PERF−72756

15

JetJetreconstruction
andcorrections
corrections
reconstruction &andbackgroundsubtraction
Jet
reconstruction
Informationfrom
fromallallsub-detectors
sub-detectorscombined
combinedinto
intoparticle
particlecandidates
candidates
Information
Parameters■“Particle
Jet reconstruction
flow”
event
reconstruction
method[1-2]“Particle flow” event reconstruction method[1-2] - R size ( = p ⌘ + ) : 0.3
2● Information from charged track by TPC+ITS$p =1
ΔR &dij = min(k ti2 p ,k tj2 p ) 2 % p = 0R &' p = −1
2

arXiv:1107.0179- pT cut of single particle: 0.15 (GeV/c)[1][1]
arXiv:1107.0179[2]
CMS-PAS-PFT-09-001[2] CMS-PAS-PFT-09-001- Jet pT threshold: 20 (GeV/c)kT algorithm
Cambridge/Aachen algorithm
anti-kT algorithm

diB = 1/pT i
kti = pT i

 Azimuthally sensitive HBT

pTpT

S-PAS-PFT-09-001
PAS-PFT-09-001

ηη
φ or η
Jetenergy
energyJet
Correct
Correction
Jet pTCorrection

removeunderlying
PYTHIA
MCsimulation"
simulation"
Calculatebackground
Remove MCunderlying
removeunderlying
PYTHIAdensityρeventData
contribution
eventscontribution
contribution
driveneventsData driven
EPJC(2007)
117
EPJC
5050
(2007)
117

Leading jet
Correction
Correctionηη
Correctjetjet
Correct
energyenergy1 2 3
4
5

anti-kT clusteringti-kclustering-kT Tclustering
algorithm
algorithm
algorithm

ηφ orηη
Background
Background
Backgroundsubtraction
calculation
subtraction– Dividing pair angle w.r.t. Leading Jet
in azimuthal plane (8 division)-> measure the freeze-out source size indetailed at azimuthal planeET (GeV/c)
ET (GeV/c)

ET (GeV/c)
ET (GeV/c)

ET (GeV/c)
ET (GeV/c)

recJetenergy
energycorrected
correctedfor
forbackgroundbackgroundinfluence
Jetpjet⇢ch · Areajet
TT = pinfluence

Rawjetjet JetRaw
Raw
energypT
energy216