Given at the 7th Workshop on Particle Correlations and Femtoscopy, Tokyo Japan, Sept 2011

1. Harmonic decomposition of two particle
angular correlations in Pb–Pb collisions at
√sNN = 2.76 TeV
Andrew Adare 7th Workshop on
Yale University Particle Correlations
for the and Femtoscopy
ALICE Collaboration September 21, 2011
Based on arXiv:1109.2501
(Submitted 12 Sep 2011)

2. Harmonics of Big and Little Bangs 2
Temperature anisotropy from CMB radiation
Power spectra hold a wealth of info from early epochs
WMAP
The Astrophysical Journal Supplement Series, 192:14 (15pp), 2011 February Jarosik et al.
Table 7
TeV-scale Pb-Pb collisions
S to k e s Q
K-band
Stokes U
Seven-year Spectrum χ 2 W-band Null Tests
Data Combinations 2
χEE PTEEE 2
χBB PTEBB
For DAs W1, W2, W3, and W4
{yr1} – {y2, y3, y4, y5, y6, y7} 0.944 0.56 0.976 0.50
{yr2} – {y1, y3, y4, y5, y6, y7} 0.800 0.78 0.956 0.54
{yr3} – {y1, y2, y4, y5, y6, y7} 0.934 0.57 1.166 0.24
{yr4} – {y1, y2, y3, y5, y6, y7} 0.850 0.70 0.920 0.59
Ka-band
Can we similarly make
{yr5} – {y1, y2, y3, y4, y6, y7} 0.737 0.85 1.286 0.13
{yr6} – {y1, y2, y3, y4, y5, y7} 0.769 0.82 1.101 0.32
“power spectra”
{yr7} – {y1, y2, y3, y4, y5, y6} 1.108 0.31 0.831 0.73
{yr1, yr2, y3} – {y4, y5, y6, y7} 0.608 0.96 0.98 0.49
from A+A collisions?
{yr1, yr3, y5, y7} – {y2, y4, y6} 0.860 0.69 1.06 0.38
For seven years of data
Q-band
{W1} – {W2, W3, W4}
{W2} – {W1, W3, W4} What can0.21 learned?
1.195
0.802 be 0.982 0.49
0.77 0.926 0.58
{W3} – {W1, W2, W4} 0.890 0.64 0.897 0.63
A. Adare{W4} – {W1, W2, W3}
(ALICE) 1.163 0.24 2.061 0.0005

3. 1
1.5
"#
Two-particle correlations 1
0.5
0
-0.5
-1 1
2
3 4 "! 3
0
-1.5 -1
Same and mixed event pair distributions
6
∆φ = φA − φB ∆η = ηA − ηB 60 $10
ALICE
58 |"#| < 0.8 performance
AB 56 Same-event
Nsame (∆φ, ∆η) dist.
54
pairs
52
50
48 Mixed-event dist.
46
-1 0 1 2 3 4
"! [rad]
AB
Nmixed (∆φ, ∆η)
Azimuthal correlation function:
AB AB
Nmixed dNsame /d∆φ
C(∆φ) ≡ AB · AB
Nsame dNmixed /d∆φ
A. Adare (ALICE)

4. Analysis and dataset 4
Pb-Pb at 2.76 TeV
13.5 M events in 0-90% after event selection
Centrality
centrality percentile resolution
4.5 Pb-Pb at sNN = 2.76 TeV
VZERO detectors ZDC vs ZEM (4.8<η<5.7)
4
resolution < 1% V0A (2.8< η<5.1)
V0C (-3.7< η<-1.7)
3.5 TPC (|η|<0.8)
SPD (|η|<1.4)
3
V0A+V0C
2.5
2
1.5
1
ALICE Performance
0.5 13/05/2011
0
0 10 20 30 40 50 60 70 80
Tracking centrality percentile
TPC points + ITS vertex
optimum acceptance + precision for correlations
A. Adare (ALICE)

5. distance between each track and the primary
in the longitudinal (radial) direction. At leas
Event structure and shape evolution track, out of which 50 TPC clusters must be5
of χ2 /nd.o.f. < 4 is imposed.
In central and low-pT “bulk-dominated” 3 < pt < 4 GeV/c
2<
T
pa < 2.5 GeV/c
Pb-Pb 2.76 TeV
0-10%
long-range correlations T
1.1
A near side ridge is observed 4 1.05
C("!, "#)
A very broad away side is observed, even doubly- 1
15 GeV/c,for 0-2% central
peaked and occupancy effects are negligible. Collision
1
h the TPC and SPD. Collisions at a longitudinal position " #0
-1 2
4
0 ]
inal high-pT “jet-dominated” The closest-approach
In interaction point are rejected. " ! [rad
the primary vertex is required to be within 3.2 (2.4) cm
correlations
on. Atnear-side ridge isrows visible traversed by each 1: Examples of two-particle (left) and atfunct
The least 70 TPC pad not must be Figure
intermediate transverse momentum
correlation
high
ersThe away-side jet is very strong; sharp like
must be assigned. In addition, a track fit requirement
proton-proton case
90 3. Two-particle correlation function an
2.76 TeV 8 < pt < 15 GeV/c Pb-Pb 2.76 TeV The two-particle correlation measure used
T
0-20%
6< pa < 8 GeV/c where the pair angles ∆φ and ∆η are measu
T
correlations induced by imperfections in detec
40 via division by a mixed-event pair distributio
C("!, "#)
95 event is paired with associated particles from
20 procedure results in correlations due only t
residual pair inefficiency effects, which are ne
0 pt , pa , and centrality interval, the correlation
T T
1
4 " #0 2
4
Nmixe
-1 0
" [rad
]
A.!Adare (ALICE) C(∆φ, ∆η) ≡

6. distance between each track and the primary
0.25
1.005 in the longitudinal (radial) direction. At leas
C("!)
Event structure and shape evolution 0.2
5
V n! [10-2]
1 track, out of which 50 TPC clusters must be
0.995
of χ2 /nd.o.f. < 4 is imposed. 0.15
0.1
In central and low-pT “bulk-dominated”
0.99 3< pt < 4 GeV/c = 33.3 / 35 Pb-Pb 2.76 TeV
T
$2/ndf
0-10%
0.05
0 <
2 pa < 2.5 GeV/c
2 4
long-range correlations
1.002 T
ratio
1.1 !
" [rad] 0
1
A near side ridge is observed 4 1.05
C("!, "#)
0.998
0 2 4 1 2 3
A very broad away side is observed, even doubly- 1 ! [rad]
"
15 GeV/c,for 0-2% central
peaked and occupancy effects are negligible. Collision
1
h the TPC and SPD. Collisions at a longitudinal position online)0 Left: C (∆φ) for particle pai
Figure 2: (Color "#
-1 2
4
0 ]
inal high-pT “jet-dominated” long-range
In interaction point are rejected. The closest-approach lower panel. Center: Amplitude of V
V5∆ are superimposed in color. Their sumadis shown as t
" ! [r
the primary vertex is required to be within is shown in cm
correlations 3.2 (2.4) the n∆
class. Right: Figurespectra for a variety of additional cen
V
on. Atnear-side ridge isrows visible traversed by eachn∆ 1: Examples of two-particle (left) and atfunct
The least 70 TPC pad not must be intermediate transverse momentum
correlation
high
ersThe away-side jet is very strong; sharp like
must be assigned. In addition, a track fit requirement Pb-Pb 2.76 TeV, 0-20% central
proton-proton case 2.5
8 < pt < 15 GeV/c
T
6 < pa < 8 GeV/c
90 3. Two-particle"#| < 1.8
T correlation
0.8 < |
function an
2
2.76 TeV 8 < pt < 15 GeV/c Pb-Pb 2.76 TeV The two-particle correlation measure used
T
0-20%
C("!)
6< pa < 8 GeV/c where the pair angles ∆φ and ∆η are measu
1.5
T
correlations induced by imperfections in detec
1
40 via division by a mixed-event pair distributio
C("!, "#)
95 event is paired with associated particles from
0.5
$2/ndf = 61.5 / 35
20 procedure results in correlations due only t
1.5 0 2 4
residual pair inefficiency "effects, which are ne
ratio
! [rad]
0 t a
pT , pT , and1 centrality interval, the correlation
1
4 " #0 2
4 0 2 4
Nmixe
-1 0 "! [rad]
" [rad
]
A.!Adare (ALICE) C(∆φ, ∆η) ≡

7. distance between each track and the primary
0.25
1.005 in the longitudinal (radial) direction. At leas
C("!)
Event structure and shape evolution 0.2
5
V n! [10-2]
1 track, out of which 50 TPC clusters must be
0.995
of χ2 /nd.o.f. < 4 is imposed. 0.15
0.1
In central and low-pT “bulk-dominated”
0.99 3< pt < 4 GeV/c = 33.3 / 35 Pb-Pb 2.76 TeV
T
$2/ndf
0-10%
0.05
0 <
2 pa < 2.5 GeV/c
2 4
long-range correlations
1.002 T
ratio
1.1 !
" [rad] 0
1
A near side ridge is observed 4 1.05
C("!, "#)
0.998
0 2 4 1 2 3
A very broad away side is observed, even doubly- 1 ! [rad]
"
15 GeV/c,for 0-2% central
peaked and occupancy effects are negligible. Collision
1
h the TPC and SPD. Collisions at a longitudinal position online)0 Left: C (∆φ) for particle pai
Figure 2: (Color "#
-1 2
4
0 ]
inal high-pT “jet-dominated” long-range
In interaction point are rejected. The closest-approach lower panel. Center: Amplitude of V
V5∆ are superimposed in color. Their sumadis shown as t
" ! [r
the primary vertex is required to be within is shown in cm
correlations 3.2 (2.4) the n∆
class. Right: Figurespectra for a variety of additional cen
V
on. Atnear-side ridge isrows visible traversed by eachn∆ 1: Examples of two-particle (left) and atfunct
The least 70 TPC pad not must be intermediate transverse momentum
correlation
high
ersThe away-side jet is very strong; sharp like
must be assigned. In addition, a track fit requirement Pb-Pb 2.76 TeV, 0-20% central
proton-proton case 2.5
8 < pt < 15 GeV/c
T
6 < pa < 8 GeV/c
90 3. Two-particle"#| < 1.8
T correlation
0.8 < |
function an
2
2.76 TeV 8 < pt < 15 GeV/c Pb-Pb 2.76 TeV The two-particle correlation measure used
T
0-20%
C("!)
6< pa < 8 GeV/c where the pair angles ∆φ and ∆η are measu
1.5
T
correlations induced by imperfections in detec
1
40 via division by a mixed-event pair distributio
C("!, "#)
95 event is paired with associated particles from
0.5
$2/ndf = 61.5 / 35
20 procedure results in correlations due only t
1.5 0 2 4
residual pair inefficiency "effects, which are ne
ratio
! [rad]
0 t a
pT , pT , and1 centrality interval, the correlation
1
4 " #0 2
4 0 2 4
Nmixe
-1 0 "! [rad]
" [rad
]
A.!Adare (ALICE) C(∆φ, ∆η) ≡

8. 4], but only after subtraction of a correlated componentreaches the of magnitude as 2 and 3 For more
mponents [31–38]. The azimuthal momentum distribution samethe wasandvat pt %v3 .GeV=c v4
whose shape emitted
2 GeV=c v3 becomes equal to v2
0.05
also
yto elliptic flow.
expressed as
Single vs. pair Fourier decomposition 6
central collisions 0%–2%, we observe that v3 becomes
equal to v2 at lower pt and reaches significantly larger
∞
dies suggest that fluctuations in the initial state geometry can generate 032301 (2011)
dN
∝ 1 + ∑ 2vazimuthal momentum ))
0
n (pT ) cos (n(φ − Ψn distribution of the emitted (1)
PRL 107 Centrality 30%-40% (a)
Single-particle anisotropy
mponents [31–38]. The
dφ 0.1
1 2 3 4 v 2 {2}
Centrality 0%-2%
v 3 {2}
5
(c)
n=1 0.3 v v{2}
4 2 {2}
y expressed as vn coefficients)
(the familiar v v{2}
5 {2}
3
v 2 ( /s = 0.0)
v v 4 {2} = 0.08)
( /s
itude of the nth order harmonic term relative to the angle of the initial-state
2
v v 5 {2} = 0.0)
3 ( /s
∞
dN
0.2
vn vn
v 3 ( /s = 0.08)
∝ 1 + ∑ 2vn (pT ) cos (n(φ − Ψn ))of v3 and 0.05 have been reported
metry Ψn . First measurements, in particular v5 (1)
dφ n=1 0.1
Pair the nth contribute to the previously-described of the initial-state
armonics can order
tude of anisotropyharmonic term relative to the anglestructures observed in
0
0
etry Ψn . First measurements, in particular of v3 and v5 have been reported 63
rticle correlations via the expression
ONLY form, but indep. of Ψn
Similar 0
1
1
2
2 3 Centrality 0%-5%
4
4
5
(b)
5
v 2 {2}
p (GeV/c)
v 3 {2}
t
0.1
∞
dNpairs
v {2}
FIG. 3 (color online). v2 , v3 , v4 , v5 as a function of transverse
4
∝ 1 + ∑ 2Vn∆ previously-described
armonics can contribute to the(pt , pa ) cos (n∆φ ) . structures observed in (2)
momentum andv5for three event centralities. The full and open
{2}
d∆φ parametrized T
be the T
correlations can vian=1 expressionat various momenta and centralities by
symbols are for Á 0:2 and Á 1:0, respectively. (a) 30%–
vn
ticle correlations 40% compared to hydrodynamic model calculations, (b) 0%–5%
0.05
iscrete Fourier harmonics, as done (for example) in [36, 38]. Following
centrality percentile, (c) 0%–2% centrality percentile.
∞
dNpairs we denote thet two-particle Fourier coefficients as Vn∆ (see
seExtract directly from 2-particle azimuthal
references,
∝ 1 + ∑ 2Vn∆ V T coefficients ) .
sent a measurement of the(pn∆, pa ) cos (n∆φfrom triggered, pseudorapidity-
T (2) 03230
correlations!
culate directly from C (∆φ ) as
d∆φ n=1
8) pair azimuthal correlations in Pb–Pb collisions in different centrality
0
Centrality 0%-2%
1 2 3 4 5
(c)
l transverse momentum intervals. Details of the experimental setup and
0.1
sent a measurement of the∑n∆ icoefficients from Ci .
Vn∆ ≡ cos (n∆φ ) = V C cos(n∆φi ) ∑ triggered, pseudorapidity-
v 2 {2}
(4) v 3 {2}
v 4 {2}
8) pair azimuthal correlations in Pb–Pb collisions in different centrality
i i v 5 {2}
lon: 268 :$) momentum intervals. Details is independent of thesetup 2011) :$
transverse is evaluated at ∆φ . Thus V of the+01000.05
$Date: 2011-02-04 22:40:50 experimental normaliza-
(Fri, 04 Feb and
vn
t the C (∆φ i n∆
A. Adare (ALICE)

9. 4], but only after subtraction of a correlated componentreaches the of magnitude as 2 and 3 For more
mponents [31–38]. The azimuthal momentum distribution samethe wasandvat pt %v3 .GeV=c v4
whose shape emitted
2 GeV=c v3 becomes equal to v2
0.05
also
yto elliptic flow.
expressed as
Single vs. pair Fourier decomposition 6
central collisions 0%–2%, we observe that v3 becomes
equal to v2 at lower pt and reaches significantly larger
∞
dies suggest that fluctuations in the initial state geometry can generate 032301 (2011)
dN
∝ 1 + ∑ 2vazimuthal momentum ))
0
n (pT ) cos (n(φ − Ψn distribution of the emitted (1)
PRL 107 Centrality 30%-40% (a)
Single-particle anisotropy
mponents [31–38]. The
dφ 0.1
1 2 3 4 v 2 {2}
Centrality 0%-2%
v 3 {2}
5
(c)
n=1 0.3 v v{2}
4 2 {2}
y expressed as vn coefficients)
(the familiar v v{2}
5 {2}
3
v 2 ( /s = 0.0)
v v 4 {2} = 0.08)
( /s
itude of the nth order harmonic term relative to the angle of the initial-state
2
v v 5 {2} = 0.0)
3 ( /s
∞
dN
0.2
vn vn
v 3 ( /s = 0.08)
∝ 1 + ∑ 2vn (pT ) cos (n(φ − Ψn ))of v3 and 0.05 have been reported
metry Ψn . First measurements, in particular v5 (1)
dφ n=1 0.1
Harmonic decomposition of two part
the nth contribute to the previously-described of the initial-state
tude of anisotropyharmonic term relative to the anglestructures observed in
order
armonics can
Pair 0
0
etry Ψn . First measurements, in particular of v3 and v5 have been reported 63
rticle correlations via the expression
ONLY form, but indep. of Ψn
Similar 0
1
1
2
2 3
4
4
5
(b)
5
Centrality 0%-5%
v 2 {2}
p (GeV/c)
v 3 {2}
t
0.1
Pb-Pb 2.76 TeV, 0-2% central
∞
dNpairs
v {2}
FIG. 3 (color online). v2 , v3 , v4 , v5 as pt 2.5 GeV/c
4
a function of transverse
∝ 1 + ∑ 2Vn∆ previously-described
armonics can contribute to the(pt , pa ) cos (n∆φ ) . structures observed in (2) v 5 {2} 2
1.015
momentum and for three event centralities. The full and open
T
1.5 pa 2 GeV/c
d∆φ parametrized T
be the T
correlations can vian=1 expressionat various momenta and centralities by
symbols are for Á 0:2 and Á 1:0, respectively. (a) 30%–
vn
ticle correlations
T
1.01 0.8 |#| 1.8 0%–5%
40% compared to hydrodynamic model calculations, (b)
0.05
iscrete Fourier harmonics, as done (for example) in [36, 38]. Following
centrality percentile, (c) 0%–2% centrality percentile.
1.005
C(!)
∞
dNpairs we denote thet two-particle Fourier coefficients as Vn∆ (see
seExtract directly from 2-particle azimuthal
references,
∝ 1 + ∑ 2Vn∆ V T coefficients ) .
sent a measurement of the(pn∆, pa ) cos (n∆φfrom triggered, pseudorapidity-
-2
T
1
(2) 03230
correlations!
culate directly from C (∆φ ) as
d∆φ n=1
8) pair azimuthal correlations in Pb–Pb collisions in different centrality
0
0.995
(c)
Centrality 0%-2%
1 2 3 4 5
l transverse momentum intervals. Details of the experimental setup and
0.1 0.99
$ /ndf = 33.3 / 35 2
sent a measurement of the∑n∆ icoefficients from Ci .
Vn∆ ≡ cos (n∆φ ) = V C cos(n∆φi ) ∑ triggered,1.002
v 2 {2}
0 (4)
pseudorapidity- 2 4 v 3 {2}
ratio
v 4 {2} ! [rad]
8) pair azimuthal correlations
i in Pb–Pb collisions
in different centrality
i 1 v 5 {2}
0.998
lon: 268 :$) momentum intervals. Details is independent of thesetup 2011)2:$
transverse is evaluated at ∆φ . Thus V of the+0100 (Fri, 04 normaliza-
$Date: 2011-02-04 22:40:50 experimental Feb and
vn
0.05
t the C (∆φ i n∆
A. Adare (ALICE)
0
! [rad]
4

10. Decomposition in bulk region 7
“Power spectrum” of pair Fourier components VnΔ
For ultra-central collisions, n = 3 dominates.
In bulk-dominated correlations, the n 5 harmonics are weak.
Harmonic decomposition of two particle correlations ALICE Collaboration
(But not necessarily zero...work in progress.)
Pb-Pb 2.76 TeV, 0-2% central
2 pt 2.5 GeV/c 0.35 5
1.015 T Centrality Centrality
1.5 pa 2 GeV/c
T 0.3 0-2% 40-50%
1.01 0.8 |#| 1.8 4
t
2 p 2.5 GeV/c
20-30%
0.25 T
1.005 a 10-20%
C(!)
1.5 p 2 GeV/c
0.2
T
3 2-10%
V n! [10-2]
V n! [10-2]
1
0-2%
0.15
0.995 2 t
2 p 2.5 GeV/c
T
0.1 a
1.5 p 2 GeV/c
0.99 T
$2/ndf = 33.3 / 35 1
0.05
1.002 0 2 4
ratio
! [rad] 0 0
1
0.998
0 2 4 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
! [rad] n n
Fig. 2: dominates as collisions become less central. The Fourier harmonics for V1∆ to V5∆
V2Δ (Color online) Left: C (∆φ ) for particle pairs at |∆η| 0.8.
re Collision geometry, rather than fluctuations,the dashed primary effect of data to the n ≤ 5 sum is
superimposed in color. Their sum is shown as becomes curve. The ratio
hown in the lower panel. Center: Amplitude of Vn∆ harmonics vs. n for the same ptT , pa , and centrality
T
lass. Right: Vn∆ spectra for a variety of centrality classes. Systematic uncertainties are represented with
A. Adare (ALICE)

11. Decomposition in bulk region 7
“Power spectrum” of pair Fourier components VnΔ
For ultra-central collisions, n = 3 dominates.
In bulk-dominated correlations, the n 5 harmonics are weak.
Harmonic decomposition of two particle correlations ALICE Collaboration
(But not necessarily zero...work in progress.)
Pb-Pb 2.76 TeV, 0-2% central
2 ptt 2.5 GeV/c 0.35 5
1.015 TT Centrality Centrality
1.5 pa 2 GeV/c
a
T
T 0.3 0-2% 40-50%
1.01 0.8 |#| 1.8 4
t
t
2 p 2.5 GeV/c
20-30%
0.25 T
T
1.005 a
a 10-20%
C(!)
1.5 p 2 GeV/c
0.2
T
T
3 2-10%
V n! [10-2]
V n! [10-2]
1
0-2%
0.15
0.995 2 t
t
2 p 2.5 GeV/c
T
T
0.1 a
a
1.5 p 2 GeV/c
0.99 T
T
$2/ndf = 33.3 / 35
2
1
0.05
1.002 0 2 4
ratio
! [rad] 0 0
1
0.998
0 2 4 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
! [rad] n n
Fig. 2: dominates as collisions become less central. The Fourier harmonics for V1∆ to V5∆
V2Δ (Color online) Left: C (∆φ ) for particle pairs at |∆η| 0.8.
re Collision geometry, rather than fluctuations,the dashed primary effect of data to the n ≤ 5 sum is
superimposed in color. Their sum is shown as becomes curve. The ratio
hown in the lower panel. Center: Amplitude of Vn∆ harmonics vs. n for the same ptT , pa , and centrality
T
lass. Right: Vn∆ spectra for a variety of centrality classes. Systematic uncertainties are represented with
A. Adare (ALICE)

12. Decomposition in bulk region 7
“Power spectrum” of pair Fourier components VnΔ
For ultra-central collisions, n = 3 dominates.
In bulk-dominated correlations, the n 5 harmonics are weak.
Harmonic decomposition of two particle correlations ALICE Collaboration
(But not necessarily zero...work in progress.)
Pb-Pb 2.76 TeV, 0-2% central
2 ptt 2.5 GeV/c 0.35 5
1.015 TT Centrality Centrality
1.5 pa 2 GeV/c
a
T
T 0.3 0-2% 40-50%
1.01 0.8 |#| 1.8 4
t
t
2 p 2.5 GeV/c
20-30%
0.25 T
T
1.005 a
a 10-20%
C(!)
1.5 p 2 GeV/c
0.2
T
T
3 2-10%
V n! [10-2]
V n! [10-2]
1
0-2%
0.15
0.995 2 t
t
2 p 2.5 GeV/c
T
T
0.1 a
a
1.5 p 2 GeV/c
0.99 T
T
$2/ndf = 33.3 / 35
2
1
0.05
1.002 0 2 4
ratio
! [rad] 0 0
1
0.998
0 2 4 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8
! [rad] n n
Fig. 2: dominates as collisions become less central. The Fourier harmonics for V1∆ to V5∆
V2Δ (Color online) Left: C (∆φ ) for particle pairs at |∆η| 0.8.
re Collision geometry, rather than fluctuations,the dashed primary effect of data to the n ≤ 5 sum is
superimposed in color. Their sum is shown as becomes curve. The ratio
hown in the lower panel. Center: Amplitude of Vn∆ harmonics vs. n for the same ptT , pa , and centrality
T
lass. Right: Vn∆ spectra for a variety of centrality classes. Systematic uncertainties are represented with
A. Adare (ALICE)

13. Decomposition in jet region 8
Di-jet Fourier components VnΔ
Very different spectral signature than bulk correlations!
- All odd harmonics 0, and finite to large n
Pb-Pb 2.76 TeV, 0-20% central
40 Centrality
8 pt 15 GeV/c
2.5 T
6 pa 8 GeV/c 40-50%
T 30
0.8 |#| 1.8 0-20%
2
20
C(!)
V n! [10-2]
1.5 10
1 0
-10
0.5
$2/ndf = 61.5 / 35
0 2 4 -20 8 pt 15 GeV/c
1.5 T
ratio
! [rad] 6 pa 8 GeV/c
1 -30 T
0 2 4 2 4 6 8 10 12
! [rad]
n
A. Adare (ALICE)

14. Aside: Gaussian Fourier transform 9
Away-side peak is (sort of) Gaussian:
The F.T. of a Gaussian(µ=π, σΔφ) is ±Gaussian(µ=0, σn =1/σΔφ).
Fit demonstration: when µ=π, odd VnΔ coefficients are negative.
Pb-Pb 2.76 TeV, 0-20% central
40 Centrality
8 pt 15 GeV/c
2.5 T
6 pa 8 GeV/c 40-50%
T 30
0.8 |#| 1.8 0-20%
2
20
C(!)
V n! [10-2]
1.5 10
1 0
-10
0.5
$2/ndf = 61.5 / 35
0 2 4 -20 8 pt 15 GeV/c
1.5 T
ratio
! [rad] 6 pa 8 GeV/c
1 -30 T
0 2 4 2 4 6 8 10 12
! [rad]
n
A. Adare (ALICE)

15. Aside: Gaussian Fourier transform 9
Away-side peak is (sort of) Gaussian:
The F.T. of a Gaussian(µ=π, σΔφ) is ±Gaussian(µ=0, σn =1/σΔφ).
Fit demonstration: when µ=π, odd VnΔ coefficients are negative.
Pb-Pb 2.76 TeV, 0-20% central
40 Centrality
8 pt 15 GeV/c
2.5 T
6 pa 8 GeV/c 40-50%
T 30
0.8 |#| 1.8 0-20%
2
20
Gaussian fit:
C(!)
V n! [10-2]
1.5 10
σΔφ = 0.34
1 0
-10
0.5
$2/ndf = 61.5 / 35
0 2 4 -20 8 pt 15 GeV/c
1.5 T
ratio
! [rad] 6 pa 8 GeV/c
1 -30 T
0 2 4 2 4 6 8 10 12
! [rad]
n
A. Adare (ALICE)

16. Aside: Gaussian Fourier transform 9
Away-side peak is (sort of) Gaussian:
The F.T. of a Gaussian(µ=π, σΔφ) is ±Gaussian(µ=0, σn =1/σΔφ).
Fit demonstration: when µ=π, odd VnΔ coefficients are negative.
Pb-Pb 2.76 TeV, 0-20% central
40 FT of fit: Centrality
8 pt 15 GeV/c
2.5
6
T
pa 8 GeV/c σn = 0.34-1 40-50%
T 30
0.8 |#| 1.8 0-20%
2
20
Gaussian fit:
C(!)
V n! [10-2]
1.5 10
σΔφ = 0.34
1 0
-10
0.5
$2/ndf = 61.5 / 35
0 2 4 -20 8 pt 15 GeV/c
1.5 T
ratio
! [rad] 6 pa 8 GeV/c
1 -30 T
0 2 4 2 4 6 8 10 12
! [rad]
n
A. Adare (ALICE)

17. Trigger pTt dependence of VnΔ 10
Similar trends as for vn
Rises with pTt to maximum near 3-4 GeV, then declines
pa (GeV/c)
0.3 Pb-Pb 2.76 TeV 0.3 0.3 0.3 0.3 T
0.25-0.5
0-2%
0.2 0.2 0.2 0.2 0.2 1-1.5
V n! [10-2]
0.1 0.1 0.1 0.1 0.1
0 0 0 0 0
-0.1 -0.1 -0.1 -0.1 -0.1
-0.2 -0.2 -0.2 -0.2 -0.2
n=1 n=2 n=3 n=4 n=5
0 5 10 0 5 10 0 5 10 0 5 10 0 5 10
trigger pt [GeV/c]
T
Centrality dependence:
V2Δ dominates as collisions become less central
A. Adare (ALICE)

18. Trigger pTt dependence of VnΔ 10
Similar trends as for vn
Rises with pTt to maximum near 3-4 GeV, then declines
1.4
0.3 1.4
Pb-Pb 2.76 TeV 0.3
1.4
0.3 1.4
0.3 1.4 pa (GeV/c)
0.3 T
1.2
0-10%
0-2%
1.2 1.2 1.2 1.2 0.25-0.5
1
0.2 1
0.2 1
0.2 1
0.2 1
0.2 1-1.5
V n! [10-2]
0.8 0.8 0.8 0.8 0.8 2-2.5
0.1
0.6 0.1
0.6 0.1
0.6 0.1
0.6 0.1
0.6
0.4 0.4 0.4 0.4 0.4
0
0.2 0
0.2 0
0.2 0
0.2 0
0.2
0
-0.1 0
-0.1 0
-0.1 0
-0.1 0
-0.1
-0.2 -0.2 -0.2 -0.2 -0.2
-0.2
-0.4 -0.2
-0.4 -0.2
-0.4 -0.2
-0.4 -0.2
-0.4
-0.6 n=1 -0.6 n=2 -0.6 n=3 -0.6 n=4 -0.6 n=5
0 5 10 0 5 10 0 5 10 0 5 10 0 5 10
trigger pt [GeV/c]
T
Centrality dependence:
V2Δ dominates as collisions become less central
A. Adare (ALICE)

19. Trigger pTt dependence of VnΔ 10
Similar trends as for vn
Rises with pTt to maximum near 3-4 GeV, then declines
6
1.4 6
1.4 6
1.4 6
1.4 6 T
1.4 pa (GeV/c)
0.3 Pb-Pb 2.76 TeV 0.3 0.3 0.3 0.3
5
1.2 5
1.2 5
1.2 5
1.2 5
1.2 0.25-0.5
40-50%
0-10%
0-2%
1
4
0.2 1
4
0.2 1
4
0.2 1
4
0.2 1
0.2
4 1-1.5
V n! [10-2]
0.8
3 0.8
3 0.8
3 0.8
3 0.8
3 2-2.5
0.1
0.6 0.1
0.6 0.1
0.6 0.1
0.6 0.1
0.6
2 2 2 2 2
0.4 0.4 0.4 0.4 0.4
1
0
0.2 1
0
0.2 1
0
0.2 1
0
0.2 0
1
0.2
0
0 0
0 0
0 0
0 0
0
-0.1 -0.1 -0.1 -0.1 -0.1
-1
-0.2 -1
-0.2 -1
-0.2 -1
-0.2 -1
-0.2
-2
-0.2
-0.4 -2
-0.2
-0.4 -2
-0.2
-0.4 -2
-0.2
-0.4 -2
-0.2
-0.4
-0.6
-3 n=1 -0.6 n=2
-3 -0.6 n=3
-3 -0.6 n=4
-3 -0.6 n=5
-3
0 5 10 0 5 10 0 5 10 0 5 10 0 5 10
trigger pt [GeV/c]
T
Centrality dependence:
V2Δ dominates as collisions become less central
A. Adare (ALICE)

20. rticles at large |∆η| is induced by a collective response to initial-state coordinat
The collision geometry andhypothesis In such a case, C (∆φ 11re
opy from
factorization fluctuations [38]. )
ism that affects all particles in the event, and Vn∆ depends only on the single-
hal distribution withtwo-particle anisotropysymmetry plane Ψn . Under these c
Factorization of respect to the n-th order
For pairs correlated to one another through a common symmetry plane Ψn,
Vn∆ factorizes [38] as
their correlation is dictated by bulk anisotropy:
Vn∆ (ptT , pa ) =
T ein(φa −φt )
in(φa −Ψn ) −in(φt −Ψn )
= e e
t a
= vn {2}(pT ) vn {2}(pT ) .
VnΔ would be generated from one vn(pT) curve,
evaluated at paveraging over events,
indicates an Tt and pTa. denotes averaging over both partic
and vn {2} specifies the use of a two-particle measurement to obtain vn . In con
w-dominated mechanism, dijet-related processes do not directly influence every p
Factorization expected:
fects are concentrated on a small number of fragments. For high-ptT , high-p
✔ For correlations correlated yields indicate dependence on initial geometry,
t fragmentation, the from collective flow.
Flow is global and affects all particles in the event.
xpectation from pathlength-dependent jet quenching. However, the azimuthal
e peaks are pairs from fragmenting pp or d–Au collisions (albeit suppressed), re
✘ Not for similar to those from di-jets.
ntation shapes are “local”, not strongly[10, 15]. to Ψn. this weak shape dependence
Di-jet rather than flow effects connected Given
ions between high-pT jet fragments are not expected to follow the factorization tr
A. Adare (ALICE)