C.C.Tscherning, Niels Bohr Institute, University of Copenhagen
Niels Bohr Institute - indico.nbi.ku.dk · Angular Correlations 3 For very peripheral collisions or...
Transcript of Niels Bohr Institute - indico.nbi.ku.dk · Angular Correlations 3 For very peripheral collisions or...
Angular Correlations
1
Raimond SnellingsUtrecht University
7-11-2011
Niels Bohr Institute
Angular Correlations at the LHC
2
q6
-10
12
34 d6-5-4-3
-2-101 2 3 4
0.99
1
1.01
1.02
0-1%
q6
-10
12
34 d6-5-4
-3-2-10 12 3 4
1
1.02
0-5%
q6
-10
12
34 d6-5-4-3
-2-10 1 23 4
0.98
1
1.02
1.04
0-10%
q6
-10
12
34 d6-5-4
-3-2-10 1 2 3 4
0.95
1
1.05
1.1
10-20%
q6
-10
12
34 d6-5-4-3
-2-101 2 3 4
1
1.1
20-30%
q6
-10
12
34 d6-5-4
-3-2-10 12 3 4
0.9
1
1.1
1.2
30-40%
q6
-10
12
34 d6-5-4-3
-2-10 1 23 4
0.9
1
1.1
1.2
40-50%
q6
-10
12
34 d6-5-4
-3-2-10 1 2 3 4
0.9
1
1.1
50-60%
q6
-10
12
34 d6-5-4-3
-2-101 2 3 4
0.9
1
1.1
60-70%
q6
-10
12
34 d6-5-4
-3-2-10 12 3 4
0.9
1
1.1
1.2
70-80%
q6
-10
12
34 d6-5-4-3
-2-10 1 23 4
0.8
1
1.2
1.4
80-90%
ATLAS Preliminary
-1bµ Ldt = 8 0 < 3 GeVb
T, pa
T2 < p
Contributions to the two-particle ΔΦ,Δη angular correlation
come from anisotropic flow, jets, resonances,
HBT, etc
C(���⌘) ⌘ Nmixed
Nsame
d2Nsame
/d��d�⌘
d2Nmixed
/d��d�⌘
Angular Correlations
3
For very peripheral collisions or when triggered with a high-pt charged particle the dominant contribution to two particle angular correlations is due to
jet-correlationsMore central heavy-ion collisions
look very very different!
[rad]!"0
24
#"-1
01
)#
", !
"C
(
0
2
4
6-8, 0-20%a
T 8-15, pt
Tp
Pb-Pb 2.76 TeV
) < 5!"0 < C(zoomed to
q6
-10
12
34 d6-5-4-3
-2-10 1 23 4
0.8
1
1.2
1.4
80-90%
4
q6
-10
12
34 d6-5-4
-3-2-10 12 3 4
1
1.02
0-5%
0.98
1.02
1.04
ATLAS
ATLAS
q6
-10
12
34 d6-5-4-3
-2-101 2 3 4
0.99
1
1.01
1.02
0-1%
q6
-10
12
34 d6-5-4
-3-2-10 12 3 4
1
1.02
0-5%
q6
-10
12
34 d6-5-4-3
-2-10 1 23 4
0.98
1
1.02
1.04
0-10%
q6
-10
12
34 d6-5-4
-3-2-10 1 2 3 4
0.95
1
1.05
1.1
10-20%
q6
-10
12
34 d6-5-4-3
-2-101 2 3 4
1
1.1
20-30%
q6
-10
12
34 d6-5-4
-3-2-10 12 3 4
0.9
1
1.1
1.2
30-40%
q6
-10
12
34 d6-5-4-3
-2-10 1 23 4
0.9
1
1.1
1.2
40-50%
q6
-10
12
34 d6-5-4
-3-2-10 1 2 3 4
0.9
1
1.1
50-60%
q6
-10
12
34 d6-5-4-3
-2-101 2 3 4
0.9
1
1.1
60-70%
q6
-10
12
34 d6-5-4
-3-2-10 12 3 4
0.9
1
1.1
1.2
70-80%
q6
-10
12
34 d6-5-4-3
-2-10 1 23 4
0.8
1
1.2
1.4
80-90%
ATLAS Preliminary
-1bµ Ldt = 8 0 < 3 GeVb
T, pa
T2 < p
ATLAS
measure anisotropic flow
4
• since the common symmetry plane cannot be measured event-by-event, we measure quantities which do not depend on it’s orientation: multi-particle azimuthal correlations
• assuming that only correlations with the symmetry plane are present - not a very good assumption (jets, resonances, etc)!
hhein(�1��2)ii = hhein(�1� n�(�2� n))ii= hhein(�1� n)ihe�in(�2� n)ii= hv2ni
hvni = hhein(�1� n)ii
Can we isolate the flow?• flow is a collective effect
• flow “factorizes”
• <vivj>/<vj> = <vivk>/<vk>
• correlate particles separated in rapidity
• correlate particles separated in pt
• multi-particle correlation
• build cumulants
5
Collective Motion
6
p+pA+A independent # of p+p
A+A collective behavior
tests if we are dealing with a common symmetry plane!
multi-particle correlations• for detectors with uniform acceptance 2nd and 4th
cumulant are given by:
7
we got rid of two particle nonflow correlations!
we can remove nonflow order by order
Borghini, Dihn and Ollitrault, PRC 64, 054901 (2001)
8
v2 from cumulants M
etho
d us
ed :
A.B
iland
zic,
R.S
nelli
ngs,
S. V
olos
hin,
Ph
ys.R
ev. C
83 (2
011)
044
913
centrality percentile0 10 20 30 40 50 60 70 80
> 1
)η
Δ (* b
Q aQ
0
5
10
-310×
= 2.76 TeVNNsALICE Preliminary, Pb-Pb events at
charged hadrons
centrality percentile0 10 20 30 40 50 60 70 80
QC
{4}
-60
-40
-20
0
-610×
centrality percentile0 10 20 30 40 50 60 70 80
QC
{6}
0
0.5
1
1.5
-610×
centrality percentile0 10 20 30 40 50 60 70 80
QC
{8}
-0.1
-0.05
0
-610×
cumulants show behavior as expected when correlations are dominated by collective flow
QC{2} = v2{2}QC{4} = �v4{4}QC{6} = 4v6{6}
QC{8} = �33v8{8}
What about p-p?
9
Multiplicity (uncorr.)0 10 20 30 40 50 60
QC
{2}
0
0.01
0.02
0.03 = 0.052vData (7 TeV)
Multiplicity (uncorr.)0 10 20 30 40 50 60
QC
{4}
0
0.2
0.4
0.6
0.8
-310=
ALICE preliminary
ALICE preliminary
)b()a(
remember QC{2} = v2, QC{4} = -v4
the 2 and 4-particle correlations decrease with increasing number of particles produced which is typical behavior of correlations involving only few particles
the 4-particle cumulant, QC{4}, even has the wrong sign compared to true flow!
What about p-p?
10
Multiplicity (uncorr.)0 10 20 30 40 50 60
QC{2
}
0
0.01
0.02
0.03
PythiaPhojet
= 0.052vData (7 TeV)
Multiplicity (uncorr.)0 10 20 30 40 50 60
QC{4
}
0
0.2
0.4
0.6
0.8
-310!
ALICE preliminary
ALICE preliminary
(a) (b)
remember QC{2} = v2, QC{4} = -v4
models like PYTHIA and PHOJET have the correct sign for the correlations and capture the general trends observed in p-p
no evidence for elliptic flow in this multiplicity range
11
The Perfect Liquid
The system produced at the LHC behaves as a very low viscosity fluid (a perfect fluid), constraints dependence of η/s versus temperature
K. A
amod
t et a
l. (A
LICE
Col
labo
ratio
n)
PRL
105,
252
302
(201
0)
(GeV)NNs
1 10 210 310 410
2v
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
ALICESTARPHOBOSPHENIXNA49CERESE877EOSE895FOPI
Flow Analysis Methods
12
flow analysis methods have different sensitivity to
nonflow and fluctuations
I focus on the cumulants
excellent opportunity to study flow fluctuations and from these get a handle on initial conditions!
Borghini, Dihn and Ollitrault, PRC 64, 054901 (2001)
Bilandzic, Snellings and Voloshin, PRC 83, 044913 (2011)
v2n{2} = v̄2n + ⇥2v + �
v2n{4} = v̄2n � ⇥2v
v2n{6} = v̄2n � ⇥2v
v2n{8} = v̄2n � ⇥2v
Flow Fluctuations
13
when (2-particle) nonflow is corrected for or negligible!
in limit of “small” (not necessarily Gaussian) fluctuations
in limit of only (Gaussian) fluctuations
vn{4} = 0
vn{2} =2��v̄n
v2n{2} = v̄2n + �2v
v2n{4} = v̄2n � �2v
v2n{2}+ v2n{4} = 2v̄2n
v2n{2}� v2n{4} = 2�2v
14
v2 versus centrality in ALICE
centrality percentile0 10 20 30 40 50 60 70 80
2v
0
0.05
0.1
= 2.76 TeVNNsALICE Preliminary, Pb-Pb events at
(charged hadrons)2v > 0)ηΔ ({2}2v > 1)ηΔ ({2}2v
{4}2v{6}2v{8}2v
Two particle v2 estimates depend on Δη
Higher order cumulant v2 estimates are consistent within
uncertainties
Two particle v2 estimates are corrected for nonflow based on
HIJINGThe estimated nonflow
correction for Δη > 1 is included in the systematic uncertainty
centrality percentile0 10 20 30 40 50 60 70 80
2v
0
0.05
0.1
= 2.76 TeVNNsALICE Preliminary, Pb-Pb events at
> 0}d6{2, 2v > 1}d6{2, 2v
corrected > 0}d6{2, 2v corrected > 1}d6{2, 2v
{4}2v
v2 Fluctuations
15
Fluctuations are significant and for more central collisions not in agreement with the eccentricity fluctuations in MC-
Glauber and MC-KLN CGCtune initial conditions? what are the other contributions?
need to compare to full model calculations!
�vn ⇥ [1
2
�v2n{2}� v2n{4}
�]12
�vn
v̄n'
✓v2n{2}� v2n{4}v2n{2}+ v2n{4}
◆ 12
centrality percentile0 5 10 15 20 25 30 35 40 45 50
2vσ
0.02
0.04
0.06
= 2.76 TeVNNsALICE Preliminary, Pb-Pb events at
2vσ ≈ 21
)/2)2{4}2 - v2{2}2
((v
centrality percentile0 5 10 15 20 25 30 35 40 45 50
2ε/ 2εσ
or
2v/ 2vσ
0.2
0.4
0.6
0.8
1 = 2.76 TeVNNsALICE Preliminary, Pb-Pb events at
21
))2{4}2 + v2{2}2
)/(v2{4}2 - v2{2}2
ALICE ((v
21
))2{4}2ε + 2{2}2ε)/(2{4}2ε - 2{2}2εMC-KLN ((
21
))2{4}2ε + 2{2}2ε)/(2{4}2ε - 2{2}2εMC-Glauber ((
2ε/ 2ε
σMC-KLN (2.76 TeV)
2ε/ 2ε
σMC-Glauber (64 mb)
16
v2 as function of pt
Elliptic flow as function of transverse momentum does not change much from RHIC to LHC energies, can we understand that?
K. A
amod
t et a
l. (A
LICE
Col
labo
ratio
n)
PRL
105,
252
302
(201
0)
)c (GeV/t
p0 1 2 3 4 5
{4}
2v
0.05
0.1
0.15
0.2
0.25
10-20%20-30%30-40%10-20% (STAR)20-30% (STAR)30-40% (STAR)
17
v2 for identified particles
the mass splitting increased compared to RHIC energies
pion and kaon v2 are described well with hydrodynamic predictions using MC-KLN CGC initial conditions and η/s = 0.2
(GeV/c)t
p0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
2v
0
0.05
0.1
0.15
0.2
0.25 = 2.76 TeVNNsALICE preliminary, Pb-Pb events at (PHENIX data: Au-Au@200 GeV)
(PHENIX)-K-/ (PHENIX)p
|>1}d6{2, |2
, v±/
|>1}d6{2, |2
, v±K|>1}d6{2, |
2, vp
centrality 20%-40%
RHIC hydroLHC hydro(CGC initial conditions)
/s=0.2)d(
Hydro: Shen, Heinz, Huovinen & Song, arXiv:1105.3226
(GeV/c)t
p0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
2v
0
0.05
0.1
0.15
0.2
0.25 = 2.76 TeV, Heinz&ShenNNsHydro prediction for Pb-Pb events at /s=0.2dCGC initial conditions,
/
Kp
centrality 20%-40%
RHIC hydroLHC hydro
(GeV/c)t
p0 0.5 1 1.5 2 2.5 3 3.5
2v
0
0.1
0.2
0.3centrality 40%-50%
|>1}d6{2, |2
, v±/|>1}d6{2, |
2, v±K
|>1}d6{2, |2
, vp
hydro LHC(CGC initial conditions)
/s=0.2)d(
= 2.76 TeVNNsALICE preliminary, Pb-Pb events at
18
v2 for identified particles
at small (mt-m0)/nq the scaling in the data resemble the scaling as observed in hydrodynamics
(GeV/c)q)/n0-mt
(m0 0.2 0.4 0.6 0.8 1
q/n 2v
0
0.05
0.1
0.15 = 2.76 TeVNNsALICE preliminary, Pb-Pb events at centrality 10%-20%
|>1}d6{2,|2
, v±/
|>1}d6{2,|2
, v±K
|>1}d6{2,|2
, vp
(GeV/c)q)/n0-mt
(m0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
q/n 2v
0
0.05
0.1
0.15 = 2.76 TeVNNsALICE preliminary, Pb-Pb events at centrality 40%-50%
|>1}d6{2,|2
, v±/
|>1}d6{2,|2
, v±K
|>1}d6{2,|2
, vp
(GeV/c)q)/n0-mt
(m0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
q/n 2v
0
0.05
0.1
0.15 = 2.76 TeV, Heinz&ShenNNsHydro prediction for Pb-Pb events at centrality 40%-50%
hydro/
K hydro
p hydro
hydro LHC(CGC initial conditions)
/s=0.2)d(
Hyd
ro: S
hen,
Hei
nz, H
uovi
nen
& S
ong,
arX
iv:1
105.
3226
19
Initial conditions and vn
6 4 2 0 2 4 66
4
2
0
2
4
6
y(fm)
x(fm)
G. Qin, H. Petersen, S. Bass, and B. Muller
initial spatial geometry not a smooth almond (for which all odd harmonics are zero due to reflection symmetry)
may give rise to higher odd harmonics which give additional independent constraint on the initial conditions!!!
x, b
y z
2⇡
N
dN
d�= 1 +
1X
n=1
2vn cosn(�� n)2⇡
N
dN
d�= 1 +
1X
n=2,4,6,...
2vn cosn(�� R)
20
Shear Viscosity!=0.4 fm/c
-10 -5 0 5 10
x [fm]
-10
-5
0
5
10
y [fm
]
0
100
200
300
400
500
600
" [fm
-4]
!=6.0 fm/c, ideal
-10 -5 0 5 10
x [fm]
-10
-5
0
5
10
y [fm
]
0
2
4
6
8
10
12
" [fm
-4]
!=6.0 fm/c, #/s=0.16
-10 -5 0 5 10
x [fm]
-10
-5
0
5
10
y [fm
]
0
2
4
6
8
10
12
" [fm
-4]
Music, Sangyong Jeon
initial conditions ideal hydro η/s=0 viscous hydro η/s=0.16
0
0.02
0.04
0.06
0.08
0.1
0.12
0 0.5 1 1.5 2 2.5 3
v 3
!/s=0.08
!/s=0.16
pionskaons
protons
p (GeV/c)t
Hydro: Alver, Gombeaud, Luzum & Ollitrault, Phys. Rev. C82 (2010)
Larger η/s clearly smoothes the distributions and suppresses the higher harmonics (e.g. v3)
21
Shear Viscosityη/s = 0
η/s > 0
u1
u2
u3u1 > u2 > u3 shear viscosity will make
them equal and destroy the elliptic flow v2
higher harmonics represent smaller differences which get destroyed more easily, and which, if measurable, makes
them more sensitive probes to η/s
22
Triangular Flow
ALICE Collaboration, arXiv:1105.3865 accepted for PRL
The v3 with respect to the reaction plane determined in the ZDC and with the v2 participant plane is consistent with zero as expected if v3 is due to fluctuations of the initial eccentricity
The v3{2} is about two times larger than v3{4} which is also consistent with expectations based on initial eccentricity fluctuations
centrality percentile0 10 20 30 40 50 60 70 80
0
0.05
0.1
ALICE > 1}ηΔ{2, 2v > 1}ηΔ{2, 3v > 1}ηΔ{2, 4v
{4}3vRPΨ3/v
22Ψ3/ v×100
Alver, Gombeaud, Luzum & Ollitrault, Phys. Rev. C82 034813 (2010)/s=0.08η Glauber 3v
/s=0.16η CGC 3vWe observe significant v3 which compared to v2 has a different centrality dependence
The centrality dependence and magnitude are similar to predictions for MC Glauber with η/s=0.08 but above MC-KLN CGC with η/s=0.16
23
Triangular Flow
(GeV/c)q)/n0-mt
(m0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
q/n 3v
-0.01
0
0.01
0.02
0.03
0.04
0.05
0.06 = 2.76 TeVNNsALICE preliminary, Pb-Pb events at
centrality 10%-20%
±/ {2}3v± K{2}3v
p {2}3v
(GeV/c)t
p0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
3v
0
0.05
0.1
0.15
0.2 = 2.76 TeVNNsALICE preliminary, Pb-Pb events at
centrality 10%-20%
±/ {2}3v± K{2}3v
p {2}3v
The behavior of v3 as function of pt for pions, kaons and protons shows the same features as observed for v2
(the mass splitting, the crossing of the pions with protons at intermediate pt)
24
Geometry and Harmonics
(GeV/c)Tp0 0.5 1 1.5 2 2.5 3 3.5 4
nv
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
1 v2 v3 v4 v5 v6 v
Au+Au 200 GeV (b = 0 fm)
G-L Ma and X-N Wang, arXiv:1011.5249v2
0 1 2 3 4 5
nv
0
0.1
0.2
0.3
(a)Centrality 30-40%{2}2v{2}3v{2}4v{2}5v
/s = 0.0)η (2v/s = 0.08)η (2v/s = 0.0)η (3v/s = 0.08)η (3v
0 1 2 3 4 5
nv
0
0.05
0.1
(b)Centrality 0-5%
{2}2v
{2}3v
{2}4v
{2}5v
)c (GeV/t
p0 1 2 3 4 5
nv
0
0.05
0.1 (c)Centrality 0-2%{2}2v{2}3v
{2}4v{2}5v
ALIC
E Collaboration, arX
iv:1105.3865 accepted for PRL
For central collisions at intermediate pt the higher harmonics v3 and v4 cross v2 and become the dominant harmonics
For more central collisions this occurs already at lower pt
25
Geometry
(rad.)φΔ-1 0 1 2 3 4
)φΔ
C(
0.9920.9940.9960.998
11.0021.0041.0061.008
1.01
< 3.0t,trig2.0 < p < 2.0t,assoc1.0 < p
| < 0.8ηCentrality 0-1%, || > 1ηΔ|
| > 1}ηΔ{2, |2,3,4,5v
ALI
CE
Col
labo
ratio
n, a
rXiv
:110
5.38
65 a
ccep
ted
for
PRL
0 1 2 3 4 5
nv
0
0.1
0.2
0.3
(a)Centrality 30-40%{2}2v{2}3v{2}4v{2}5v
/s = 0.0)! (2v/s = 0.08)! (2v/s = 0.0)! (3v/s = 0.08)! (3v
0 1 2 3 4 5
nv
0
0.05
0.1
(b)Centrality 0-5%
{2}2v
{2}3v
{2}4v
{2}5v
)c (GeV/t
p0 1 2 3 4 5
nv
0
0.05
0.1 (c)Centrality 0-2%{2}2v{2}3v
{2}4v{2}5v
We observe a doubly-peaked structure in the azimuthal correlation function opposite to the trigger particle before the subtraction of v2
The red line shows the sum of the measured anisotropic flow Fourier coefficients. The flow coefficients give a natural explanation of the observed correlation structure known as the Mach cone and ridge
C(��) ⌘ Nmixed
Nsame
dNsame
/d��
dNmixed
/d��
ALI
CE
Col
labo
ratio
n, a
rXiv
:110
5.38
65
Conclusions• Anisotropic flow measurements provided strong constraints on
the properties of hot and dense matter produced at RHIC and LHC energies and have lead to the new paradigm of the QGP as the so called perfect liquid
• At the LHC we observe even stronger flow than at RHIC which is expected for almost perfect fluid behavior
• The first measurements of v3, v4 and v5 have recently been made at RHIC and the LHC and indicate that these flow coefficients behave as expected from fluctuations of the initial spatial eccentricity (geometry!) and a created system which has a small η/s
• provide new strong experimental constraints on η/s and initial conditions
26
Thanks
27