HBT measurement with respect to event planein Pb-Pb at 2.76TeV collisions from ALICE2016.Sep.23
Naoto Tanaka for the ALICE collaboration
University of Tsukuba
JPS meeting @ University of Miyazaki

Space time evolution
and azimuthal anisotropy
Heavy Ions: Results from the LHC
Initialgeometry
peripheral

Azimuthal anisotropy

Source shape@ freezeout

Pb-Pb 2.76TeV

collisionTime

Beam axis z	reactionplanex

Initial state

Energy Stopping
Hard Collisions

Hydrodynamic"
Evolution

Momentum anisotropy at final state
Hadron Freezeout

Figure 1. The time evolution of a high energy heavy ion collision.

✦A powerful probe of hydrodynamic evolution

Ψ3

= hcos [n (✦ Azimuthal anisotropy vninterferometry,n )]icorrelations
and fluctuations, resonance production, particle ra
✓P
◆

Ψ

✦ Event plane2
1provide
wi sin(ni)
etc.
information
about
the
thermodynamics
ofthesystem.
1 crucial
P
tan
n =
n
wi cos(n i )Ψ4dilep• Electromagnetic probes: The electromagnetic probes, i.e. photons andbeam
are produced at different phases of evolution. They are not distorted by final
Source shape @ freeze
outinteractions
and once
produced
can escape
the interaction
region,unaffected,anic! Initial
sourceeccentricity
with fluctuations
leads
to momentum
thefinalstate,sourceshape✓ A lot of parameters contributes
at final
known
ashighering to thetodetectors
informationabout
the harmonicconditionsflow
andvpropertiesof the mednevolution
timeTheandviscosity of direct thermal radiation‣ Initial eccentricity, collective
PHENIX'PRL.1
at the timeflow,
ofSensitive
their
production.
measurementca"to η/s (PRL107.252301)
used as a direct fingerprint of the hot and dense medium.

✦ To quantify the properties ofdN
QGP, a precise understanding of spatial and temporal

1+2⌃v• Quarkonia and/heavy
flavour:
Quarkonia (J/n cos[n(n )] ,
evolution is requiredd, c and ⌥ family) produ
is considered to provide an unique signature of QGP [1]. It is a sensitive prob
2
0

HBT
■ Method to measure the source size with two identical particles
 Quantum interference between two identical particles
 Unique tool to measure source size at kinetic freeze out Geometrical source size ≠ HBT radii = “Length of homogeneity”
C2 (p1 , p2 ) ⌘detectorC2(q)sourceP2 (p1 , p2 )⇡ 1 ± |⇢(q)|2
P (p1 )P (p2 )1/R
C2 (q) = 1 + exp( R 2 q2 )detectorvy■
ion3D
collision.
HBT analysis! + p!)! (pT1
T2
kT experimental=
HBT: A (mostly)
overview
22

1.5
Hadron Freezeout★ kT dependence

1
0

0.1

q = p1 - p2 (GeV/c)
nucl-th/0305084

Bertsch Pratt parametrization

2
2
C
(q
,
q
,
q
)
=
1
+
(
R
q
2
out
side
long
out out
nce production, particle ratios,2Rside
q2side2Rlong
q2long )Beam axis

Routsidemostly to collective expansion [2].
source areRdue
flow pushes higher pT particles more at the surf
picture, analytical expressions R
haveout been derived! t
and emission duration from the mT (mT =p2Tradii. This is discussed further in section 3. (b) HB
plane in non-central
collisions allow the possibility t
Rlong
Beam axis
transverse eccentricity at freeze-out to its initial ec
model calculation (Figure 1(b)). This is discussed fu

r
to

Rside

c
te

Rlong
：sourcethe longitudinal direction (beam direction)
bes,
i.e.
photonssize
andalong
dileptons
aredistortedby finalstatetransverse momentum + emission duration
Routnot：sourcealong
the pairction
region, unaffected, carryRside：source size along the perpendicular to Routs and properties of the medium(in coherence)– (resonance) – (Background)direct：chaoticity＝
thermal radiation
can bedenamics of the system.

Figure 1. (a) Contours representing
transverse plane for kT = 0.0 GeV/c (topemission direction is to the right, illustr
nearer to the surface. (b) Contours of cotimes in the evolution of a noncentral cocalculations taken from Ref. [19].

:22

WSPC/Trim Size: 9in x 6in for Review Volume

qgp3

tions for pions with transverse momentum K
Azimuthally sensitive HBT withtooverallΨ2 source deformation, b
do respect
not probe theHydrodynamic description of ultrarelativistic heavy-ion collisions
69
outer edge as a function of the azimuthal emi
 explicit
Dividing
thearisespairrelativendicatedΦ-dependence
fromangle
the rotation
between the to the Ψ2 in azimuthal plane
These pictures suggest that, if one wants t
rd direction x ∥K and the x-axis. In addition, the components S
spatialtensor, being
defined as expectation
valueswith ameasurements explores spatial deformation of the source
Differential
azimuthalangle
HBTcorrelation
deformation of the source at freeze-out, one
endent emission function S(x, K) = S(x, Y, K , Φ), contribute an imΦ-dependence which is not shown here. Both types of Φ-dependenceswith smalltransverse pairmomenta
KT . Th
model shows oscillation in azimuthal
angle dependenceof HBTradii
 Hydrodynamical
analyzed
together, exploiting the symmetries of the emission funcith respect(out-of-planeto the reaction plane andextended
to projectile-target
interchange.shape)sourcein Fig. 32 which show the azimuthal oscillatio
190
ndsthat in general R , R and R are superpositions of cosines ofmultiples of Φ while R is a superposition of sines of even multiples
HBT radius parameters for several values o
In lowest
order R , R , and R thus
oscillate with cos(2Φ) aroundHydrodynamic
model
o

T

µν

T

2
l

2
l

2

5

20

2

1
0

200

⊥

0.5 GeV
−5

Φ=π/4
0

5
x (fm)K =⊥0.5 GeV
−5

0

Φ=π/2
0

5
x (fm)

1
0

100

−1
−5 K =

02

out-plane

0

10

0

2

0

2

5

Φ=0

K (GeV)
⊥
0.00
0.15
0.30
0.45

Rlong (fm )y (fm)

⊥

2

K =0

2

K =
⊥
0.5 GeV

Ros (fm )

−5

20

2

ΨRP

0

2

40

2

10

2

in-plane5

Ros (fm )RHIC 1

Rside (fm )y (fm)

Au+Au 130GeV

Rside (fm )Azimuthal angle dependence of HBT radii

2
constant average while Ros
oscillates with sin(2Φ) around zero.

22oRout (fm )

2
s

2
os
2
o

2
s

π/2

φ

π 0

π/2

φ

π

0

−1
0

nucl-th/0305084

Fig. 32. Oscillations of the HBT radii for diﬀerent t
collisions (left) and the source elongated into the recircled lines in the right panel show the geometricparameters.
Azimuthally sensitive HBT gives us moredetailed information of space-time

Rsidedensity: widthContours of constant emission
for the source created in 130 A GeV
74 The top left panel shows
collisions at b = 7 fm as predictedbyhydrodynamics.
Rout : depth + time
tours for KT = 0, the three other panels show contours for KT = 0.5 GeV pointing
ﬀerent directions. The thick solid oval lines indicate the maximum extension ofrce.

Sec 3.2 we saw for non-central collisions that, as time evolves, the init-of-plane deformation of the nuclear reaction zone decreases, crosses

evolution4

R 2side (fm2)

R 2out (fm2)

50

50

Pb-Pb sNN = 2.76 TeV

Azimuthal angle dependence of HBT w.r.t. Ψ2
‣
‣

40
30

40
30

✓ Fit function

Rout has explicit oscillation and Rside has weak oscillation
20
20
Rout and Rside oscillate
out-of-phase

Eccentricity
at f
R: Average HBT radii✓

R 2μ, 0 + 2R 2μ, n cos( n( φpair − Ψn) )✓10 shape still remains at freeze out
10➡ Initial elliptic
0
π/4
π/2
3π/4
(out-of-plane extended
source)
ϕ -Ψ
1

40
30

2

50
40

Pair

50

3

0

π

0

EP,2 (rad)Pb-Pb sNN = 2.76 TeV

λR 2side (fm2)50

R 2long (fm2)

R 2out (fm2)

0

✓

π/4

30

π/2

2

ϕ

Pair

0.3 < k T < 0.4 GeV/ c40

0-5% centrality

0.6

0

0

π/4

1

π/2

2

20-30% centrality
30-40% centrality

kaon

3

0

π

0

ϕ 10- ΨEP,2 (rad)

π/4

1

π/2

Pair

2

ϕ

Pair

3π/4

3

R 2μ, n : nth order Oscillation

Rs,22

Source@ freeze out

in-planeparticipant

π/2 πflow
φpair- Ψ2
PRC70, 044907 (2004)

✦ Rside : width2
R = Rs,n(Δφ )cos(nΔφ )✦ Rout : depth + time

0.4

10

3π/4

Rs,02
0

40-50% centrality

10

EP,2

5-10% centrality

0.5

μ, 0

3

10-20% centrality

20

20

π
2
pion

R
s 
-Ψ
(rad)

3π/4

0.7

30

20

1

2

2
s,n

π

- ΨEP,20.3(rad)in-plane01

λR 2long (fm2)

2
R
0
π/4
3π/4
π
0
π
/4
π
/2
3
π
/4
s,2
0.3 < k < 0.4 GeV/ ceccentricity
isobtainedbyrelative
amplitude
from
Blast
Wave
model
‣ Final source
ε
=
2
ϕ -Ψ
(rad)
ϕ
Ψ
(rad)
EP,2
EP,2
final
0-5% centrality
2
Pair
Pair
ALI−PREL−60322
40
0.6
Rs,0(Phys. Rev. C 70, 044907)
5-10% centrality
10-20% centrality
20-30%
centrality‣ 30The magnitude of Rout Rside0.5relative
amplitude
decreases from central to peripheral collisions
50

0.7
π/2

2

3

0

π

1

3

T

30-40% centrality

10

0.4
0.3

0.1
0

0

π/4

1

π/2

ALI−PREL−60322

2

ϕ

Pair

3π/4

3

π

- ΨEP,2 (rad)0

R 2side,2 / R 2side,040-50% centrality

R 2side,2/ R 2side,0R 2out,2 / R 2side,020

R 2out,2/ R 2side,02

Pb-Pb sNN = 2.76 TeV

0.1

0

1

0

2

π/4

π/2

ϕ

3

3π/4
Pair

π

- ΨEP,2 (rad)00.2 < k T < 0.3 GeV/ c
0.3 < k T < 0.4 GeV/ c-0.1
00.4 < k T < 0.5 GeV/ c

-0.1
10

20

30

40
50
centrality (%)

00.5 < k T < 0.7 GeV/ c

10

20

30

40
50
centrality (%)! εfinal ≈ εinitial/2 for pionsourceeccentricity✓ Final" ThisIndicatesthat source expand
2side,2
PHENIXSTAR
εfinal= 2 Rand/ R 2results•"side,0 are co! εfinal ≈ εinitial for kaon
★ Contributing factors to εfinal" Kaon may freeze-out sooner thanDue geometry
to the difference of mT betwe‣"initial‣ collective flow
‣ freeze out time

2R2µ,n/R2i ,0✦ AMPT and Blast wave model (S.Voloshin, J. Phys. G38, 124097)

Initial + vs oscillati

Same oscillation sign of Rout and Rside → Relative amplitude negative value
0
PHYSICAL REVIEW LETTERS
222301 (2014)✓

Au+Au 200GeV @ PHENIXµ=s

Au+Au- 200GeV+ +π π +π πµ=oµ=lin-planeΨ 2, Ψ 320

R2µ [fm2]

15
10 (a)

25
20

out-plane

(b)

0-10%

(c)

20-30%

10 (e)

(f)

-2

0

2

φ - Ψn

(g)

-2

0

2

(h)

-2

φ - Ψn [rad]

0

0.2

STAR

0

R2os=0

Ψ2

15

n=3

(d)

Ψ2

sys. error

week ending
6 JUNE 2014

2
2
¡n=2
=
|2R
/R
n µ=os µ,n i ,0|202nd-order

(a)

0.2

0

=s,ii=o
=s
µµ=o,

A

0

0.4

/

0.2

(a)
(c)

2
2
¡
=
|2R
/R
|
n
-2
0
2
µ,n i ,0central-2R2µ,n/R2i ,0

n=2

Rout

-2R
2R2µ,n/R2i ,0

Rside

n=3

/

STAR
0.2
0.2
HBT w.r.t. Ψ3 shows finite oscillation in expanding source, but almost
no oscillation in static source✦ HBT w.r.t. Ψ3 measured @ PHENIX Au+Au 200GeV (Phys.Rev.Lett. 112 222301)

25

A

2
2
-2Rµ,n/Ri ,0✓µ=s, i =s

n=2
n=3

2
2
2Rµ,n/Ri ,0Triangular deformation via HBT

0
00

¡n
µ=o, i =operiphe! pions in 0.2 <0.222
22
HBTThew.r.t.
Ψdependence
3 in LHCr✦
online).
azimuthalof Renergy
for charged
kT < 2.0 GeV=c with respect tos , Ro , Rl , and Ros p
ﬃﬃﬃﬃﬃﬃﬃﬃd) and✓third-order(e)–(h)event plane
Au þLHC
Au collisions at sNN ¼ 200
GeV.2The
R22os~isfinal
plottedrelative eccentricity
to dotted lines under th
Difference
between
RHICinand"
2R/R
sources,2s,0Source@freeze out
R2os ¼ 0. The• filled
symbolsshow
the &extracted
HBTduration
radii and the open
symbolsarereflectedbysymmetryaroundLargerradialflow
evolutionSTAR result
Bands of two• thinlines show the systematic uncertainties and dashed lines show the fit lines by Eq. participant(3).
viscosity"εfinal ≈ εinital/2, source eccentricity is reduced, bflow✓ Hydrodynamic model (P. Bozek, J. Phys. G38, 124097)
out-of-plane0•
Relative
amplitude
Rside
is negativeand decreases withincreasing centrality; however, the (c)llation amplitudes
wereextractedofby
fitting
therd-order!
3•
Triangulardeformation is washed-out or even reversed
2
6

ALICE detector
FMD
ITS

In this analysis

VZERO✓ Trigger & centrality✓ V0A : 2.8 < η < 5.1✓ V0C : -3.7 < η < -1.7

VZERO

VZERO
TPC

TPC & ITS

✓ Tracking & PID✓ Vertex✓ |ηtrack| < 0.8

TOF
✓ PID
✓ |ηtrack| < 0.8

TOFη Acceptance
TPC-0.8 to 0.8

FMD✓ Event plane✓ FMDA : 1.7 < η < 5.0✓ FMDC : -3.4 < η < -1.7

HBT
Event plane7

Event plane via FMD
The FMD Detector••

Event plane resolution are extracted with 3 sub event method

What is the FMD?
FMD1

FMD2
FMD3

Res {

1

Res{Ψ3}•

Event plane resolution

Silicon strip detector
3 sub detector : FMD1, FMD2, FMD3
2 types of rings : inner and outer• inner : 20 sectors (0 < φ < 2π)• outer : 40 sectors (0 < φ < 2π)

Res{Ψ2}

•

n} =

s

< cos(n(AnB )) >< cos(n( AnnC )) >< cos(n( Bnn13 sub-detector: FMD1, 2, &ALICE
3
work in progress
0.8
0.8 outer2 typesof rings: inner and
0.6

0TPC(TPC, FMDA, FMDC)FMDAC(FMD , FMDA, TPC)

Made of0.4
silicon sensors
0.2

0.2

E.P. Resolution|η| < 1.0

0.6

0.4

C )) >
nC-3.4 < η < -1.7, 1.7 < η < 5.0

V0AC(V0 , V0A, TPC)
C

0-3.7 < η < -1.7, 2.8 < η < 5.1
0

10 20 30 40 50 60 70

0

10 20 30 40 50 60 70

centrality(%)

centrality(%)

Inners: 20 azimuthal sectors, 512 radial strips
Outers:40 azimuthal
sectors,
radial strips
FMD eventplane and
HBT256
measurememt
Total of 51,200 channels• 3rd order harmonics, FMD resolution is approximately 15% better than V0

Christian Holm Christensen

18This excellent resolution allows us precise measurement of higher order event plane• Rapidity gap between HBT measurement and E.P. is |Δη| > 0.9→ Mid-rapidity (-0.8 < η < 0.8)

•

HBT

•

Event Plane → Forward rapidity (-3.4 < η < -1.7, 1.7 < η < 5.0)

8Analysis method for HBT✦ 2.76 TeV Pb-Pb collisions✦ Particle Identification‣ Charged pions are identified with TPC and TOF combined PID✦ Correlation function
R(q)
C2 =
M (q)

‣ R(q) : real pairs‣ M(q) : mixed pairs (made by event mixing)‣ q : relative momentum✦ Event mixing class‣ Event with similar centrality, Z-vertex and Ψ3 angle are used
✦ Fit function

C2 = N [(1
G=

2
2
Rout
qout

) + Kc (1 + exp (G))]
2
2
Rside
qside

2
2
Rlong
qlong

2
Ros
qout qside

2
Rol
qout qlong

2
Rsl
qside qlong✓ KC is Coulomb correction factor✦ Event plane‣ Ψ3 is determined via FMD (1.7 < η < 5.0, -3.4 < η < -1.7)✦ Event plane resolution correction (U.Heinz, Phys.Rev.C66, 044903(2002))✦ Momentum resolution correction‣ Estimated with HIJING and GEANT9R 2side (fm2)

R 2out (fm2)

Azimuthal angle dependence of HBT w.r.t. Ψ3
30

20

ALICE
work in progress30

Pb-Pb 2.76TeV in ALICE
Charged pion pair(-0.8 < η < 0.8)
Event plane is determined with FMD

20

•

10
0.5

1
ϕ

pair

1.5
2
- ΨEP, 3 (rad)

0

0.5

1
ϕ

pair

1.5
2
- ΨEP, 3 (rad)0.7

λR 2long (fm2)

•

10
0

40

0.2 < kT < 2.0GeV/c
Centrality
10-20%
20-30%
30-40%
40-50%

0.6

30

0.5

20

0.4
0.3

10
0

0.5

1
ϕ

pair

1.5
2
- ΨEP, 3 (rad)0.2

Fit function

0

0.5

1
ϕ

pair

1.5
2
- ΨEP, 3 (rad)R2μ,0 + 2 R2μ,3 cos(3(φpair - Ψ3))‣

R2μ,0 : Average HBT radii‣

R2μ,3 : Oscillation amplitude

Average HBT radii✓ centrality dependence✦ Azimuthal angle dependence✓ Rout has explicit oscillation✓ Rside has small oscillation✦ Rout and Rside oscillate in-phase➡ unlike HBT w.r.t. Ψ2✓ Rlong and λ have no oscillation✓ Small centrality dependence➡ similar to v3
✦

10

0.05
0
−0.05
−0.1

0.1

ALICE
work in progress

0.05
0
−0.05

0.1

0.15

0.2

0.25

−0.1

0.3

0.1

0.15

0.2

0.05

✦ R 2out,3 / R 2out,0−0.05

0.2 < kT < 2.0
0.05
0

0.3

−0.1

0.1

0.15

0.2

0.25

0.3

εinitial

0.1
0.05

0 is positive✓ Relative amplitude of R 2out

✓ -2R 2out,3 / R 2out,0 increase with increasing initial ε3−0.05✦ R 2side,3 / R 2side,0

−0.1

0.25

εinitial

2R 2os,3/ R 2side,0-2R 2out,3/ R 2side,0

0.1

0.1

−0.05

εinitial

0-2R 2long,3/ R 2long,00.1

2R 2side,3/ R 2side,0-2R 2out,3/ R 2out,0Initial ε3 vs Relative amplitude−0.1✓0.1Relative
0.15
0.2amplitude
0.25
0.3 of R 2side is0.1negative
0.15
0.2 (εinitial
0.25 <
0.30.25)εinitial✓ No centrality dependence
can be seenεinitial✦ R 2long,3 / R 2long,0✓ Relative amplitude of R 2long has almost no amplitude

11

Hydrodynamic model comparison
100
200
0.05

ALICE
work in progress

0.2 < kT < 2.0

400

Npart

3+1D Hydrodynamic model

0

−0.05

0.05
0.05

R 2long,3/ R 2long,0R 2s,3/R 2s,0R 2side,3/ R 2side,0

ALICE Pb-Pb 2.76TeV

300

Pb-Pb 2760GeV

b)

0
0

−0.05
-0.05
100

200

300

400

100

100

Npart

200

200

300

300

400

400

NN
part
part

(P. Bozek, J. Phys. G38, 124097)✦ R 2side,3 / R 2side,00.05

Pb-Pb 2760GeV

R 2os,3/R 2s,0c)
✓ Npart dependence of R 2side,3 / R 2side,0 can be reproduced by 3+1D hydrodynamic
model within the systematic uncertainty0✓ R 2out,3 / R 2side,0 and R 2os,3 / R 2side,0 will be compared with hydrodynamic model✓ Need kT dependence !!

-0.05
12

Summary✦ Azimuthal angle dependence of HBT radii w.r.t. Ψ3•••

Rout and Rside oscillate in-phase
Explicit oscillation of Rout and small oscillation of Rside can be seen
Rlong and λ have almost no oscillation✦ Relative amplitude of squared HBT radii••-2R 2out,3/R 2out,0 is positive in centrality 10-50% and small centrality dependence
2R 2side,3/R 2side,0 is negative in centrality 10-40%✦ Hydro dynamical model comparison•

Bozek R 2side,3/R 2side,0 calculation shows good agreement within Syst. error

Outlook✦ Azimuthal angle dependence of HBT w.r.t. Ψ3 in centrality 0-10% is ongoing✦ kT dependence of HBT w.r.t. Ψ3 for more precise understanding✦ Azimuthally sensitive HBT with Event shape engineering (J. Schukraft et al., arXiv:1208.4563 )✓ Selecting of event by event vn by the magnitude of flow vector➡ Impact on final source shape by larger triangular flow (initial ε3)13

Backup14

Event plane resolution correction■ Event Plane Resolution Correction (Phys. Rev. C66, 044903 (2002) )bins
よる方位角方向の HBT 半径の補正 nX
⇥ exp
⇤
exp
⇠n,m ( ) Nc,n(q) cos(n j ) + Ns,n(q) sin(n j )N (q, j ) = Nexp (q, j ) + 2

n=1に実験的には真のイベント平面を求めることはできない。求めexpとは必ずずれがある。これは図??を見るとよくわかる。独立なNc,n(q) cos(nj ) = hNexp (q, j ) cos(n )i =C side) で求めた 2 次のイベント平面の 2 次元プロットであが求められるならば N
2 exp
つの検出器で求めたイベント平面は等し(q) sin(n ) = hN (q, ) sin(n )i =
s,n

j

exp

j

) のラインまたはイベント平面の対称性から Ψ2 (V ZEROA) =

nX
bins

1

nbins n=1

nX
bins

1

nbins n=1n /2ずである。しかし、測定したイベント平面のずれにより図のようの⇠n,m ( ) =sin(n /2)hcos (n (mntrue ))in

Nexp (q,j ) cos(n j )Nexp (q,j ) sin(n j )➡ event plane resolution•

correction for q-distribution with EP resolution

図 80 イベント平面分解能が HBT 半径に与える影響のイメージ図15