J. Milošević, Measurement of Two- and Four-particle Correlations in pPb and PbPb Collisions at CMS

Measurement of Two- and Four-
particle Correlations in pPb and
PbPb Collisions at CMS
J. Milošević
University of Belgrade and
Vinča Institute of Nuclear Sciences,
Belgrade, Serbia
on behalf of the CMS Collaboration
28.04.2013 BW2013, Vrnjacka Banja, Serbia 1

28.04.2013
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Outline
v  CMS experiment
v  Azimuthal anisotropy
v  Two- and four-particle correlations as a tool to study azimuthal anisotropy
v  Results
v  Comparison to the theoretical predictions and results from other experiments
v  Conclusions

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Schematic view of the CMS detector
v  Higgs particle
v  supersymmetry
v  dark matter
v  extra dimensions
Although
designed to
study pp
collisions, CMS
is well suited to
study heavy ion
physics too
A multipurpose detector to search for:

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x!
y!
z!
Elliptic flow in a non-central
symmetric heavy ion collision
v The elliptic flow is one of, but most
famous, of collective movements
v  converts spatial anisotropy
momentum anisotropy
v  Experimentally it is measured with
respect to the event plane (EP)
v  But, there are methods which do not
require knowledge about the EP
!
!px > !py
dN
d!
~ [1+ 2 vn cos(n!)
n
! ]
ηΔ
-4
-2
0
2
4
φΔ
0
2
4
φΔdηΔd
pair
N2
d
trigN
1
1.6
1.7
1.8
110≥trk
offline
= 5.02 TeV, NNN
sCMS pPb
< 3 GeV/cT
1 < p
(b)
2D Δϕ-Δη correlation function
in asymmetric pPb collision
Phys.Lett.B718(2013)795
v For the first time seen in pPb collisions
v Long range structure in ϕ over wide
rapidity range is characteristic for
hydrodynamically driven flow
v  Does the effect seen in pPb has hydro
or Color-Glass-Condensate (CGC) origin?
v  How does it compare with the effect
seen in PbPb collisions?

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Azimuthal Anisotropy Harmonics from Two-particle Correlations
1
Ntrig
dN pair
d!!
=
Nassoc
2"
1+ 2Vn! cos(n!!)
n
"
#
$
%
&
'
(
Correlation:
1
Ntrig
d2
N pair
d!!d!"
= B(0,0)
S(!!,!")
B(!!!")
S(!!,!") =
1
Ntrig
d2
Nsame
d!!d!"
B(!!,!") =
1
Ntrig
d2
Nmix
d!!d!"
1D correlation is fitted with
Anisotropy harmonics vn{2, !! > 2}(pT ) =
Vn!(pT, pT
ref
)
Vn!(pT
ref
, pT
ref
)
!! = !!trigg
" !!assoc
!! = !!trigg
" !!assoc

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Four-particle correlations – Q cumulant method
Advantage wrt 2-part.corr.:
Four-particle correlations
remove two- and three-
particle non-flow
correlation
ein(!1+!2!!3!!4 )
! ein(!1!!3)
ein(!2!!4 )
! ein(!1!!4 )
ein(!2!!3)
cn 4{ }= 4 ! 2" 2
2
Reference flow: v2
ref
4{ }= !c2 4{ }4 Differential flow: v2 4{ } pT( )=
!d2 4{ } pT( )
(v2
ref
4{ })3
where in d2 4{ } pT( ) one of four reference particles is replaced with a particle
from a particular pT region.

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gen-level
chN
50 100 150 200
{4}2
c
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
-3
10×
= 5.02 TeV, Gen-levelNN
spPb HIJING
bin width of 2offline
trkN
trkN
trkN
offline
trkN
50 100 150 200
{4}2
c
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
-3
10×
= 5.02 TeVNN
spPb data
v  Hydro-flow is not incorporated in the HIJING MC model – c2{4} consistent with
zero for small bin width (2 or 5), while becomes nonzero for big bin width (30)
v  The effect becomes larger going to more peripheral collisions
v  In pPb data, c2{4} crosses zero and becomes negative at certain multiplicity. This
is an indication of the onset of multi-particle correlation effect
v  A bin width of 5 is chosen for the v2{4} analysis
tobesubmittedinPhys.Lett.B
h;ps://twiki.cern.ch/twiki/bin/view/CMSPublic/PhysicsResultsHIN13002

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Examples of 2-dimensional (2D) dihadron correlations
v  PbPb collisions:
the ridge – structure at Δϕ around zero and
elongated in Δη
v  Surprisingly seen in high-multiplicity pPb
and even in high-multiplicity pp collisions
v  Is the ridge in pPb collisions
related to hydrodynamical
flow like in PbPb collisions or
it is connected with CGC?
ηΔ
-4
-2
0
2
4
φΔ
0
2
4
φΔdηΔd
pair
N2
d
trigN
1
2.4
2.6
2.8
N < 260≤= 2.76 TeV, 220NNsCMS PbPb
< 3 GeV/c
trig
T
1 < p
< 3 GeV/c
assoc
T
1 < p
ηΔ
-4
-2
0
2
4
φΔ
0
2
4
φΔdηΔd
pair
N2
d
trigN
1
3.1
3.2
3.3
3.4
N < 260≤= 5.02 TeV, 220NNsCMS pPb
< 3 GeV/c
trig
T
1 < p
< 3 GeV/c
assoc
T
1 < p

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φΔ
0 2 4
ZYAM
-C
φΔd
pair
dN
trigN
1
0.0
0.1
0.2
0.3
0.4 = 2.76 TeVNNsCMS PbPb
|>2ηΔ|
< 1 GeV/c
trig
T
0.3 < p
< 260offline
trkN≤220
< 20offline
trkN≤0
Fourier fit
φΔ
0 2 4
ZYAM
-C
φΔd
pair
dN
trigN
1
0.0
0.2
0.4
0.6
0.8
|<1ηΔ|
φΔ
0 2 4
ZYAM
-C
φΔd
pair
dN
trigN
1
0.0
0.1
0.2
0.3
0.4
< 2 GeV/c
assoc
T
1 < p
< 2 GeV/c
trig
T
1 < p
φΔ
0 2 4
ZYAM
-C
φΔd
pair
dN
trigN
1
0.0
0.2
0.4
0.6
0.8
φΔ
0 2 4
ZYAM
-C
φΔd
pair
dN
trigN
1
0.0
0.1
0.2
0.3
0.4
< 4 GeV/c
trig
T
2 < p
φΔ
0 2 4
ZYAM
-C
φΔd
pair
dN
trigN
1
0.0
0.2
0.4
0.6
0.8
φΔ
0 2 4
ZYAM
-C
φΔd
pair
dN
trigN
1
0.0
0.1
0.2
0.3
0.4
< 6 GeV/c
trig
T
4 < p
φΔ
0 2 4
ZYAM
-C
φΔd
pair
dN
trigN
1
0.0
0.2
0.4
0.6
0.8
φΔ
0 2 4
ZYAM
-C
φΔd
pair
dN
trigN
1
0.0
0.1
0.2
0.3
0.4
< 12 GeV/c
trig
T
6 < p
φΔ
0 2 4
ZYAM
-C
φΔd
pair
dN
trigN
1
0.0
0.2
0.4
0.6
0.8
Averaged projection of 2D correlations onto Δϕ
for 2<|Δη|<4 (top) and |Δη|<1 (bottom)
PbPb case:
v  Cutting on |Δη|, jet contribution
largely suppressed in the long-range
region (2<|Δη|<4) w.r.t. the short-
range (|Δη|<1)
v  Low-multiplicity events: no near-
side correlations are observed in
the long-range region
v  Fourier fits are shown by lines

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φΔ
0 2 4
ZYAM
-C
φΔd
pair
dN
trigN
1
0.0
0.1
0.2
0.3
0.4 = 5.02 TeVNNsCMS pPb
|>2ηΔ|
< 1 GeV/c
trig
T
0.3 < p
< 260offline
trkN≤220
< 20offline
trkN≤0
Fourier fit
φΔ
0 2 4
ZYAM
-C
φΔd
pair
dN
trigN
1
0.0
0.2
0.4
0.6
0.8
|<1ηΔ|
φΔ
0 2 4
ZYAM
-C
φΔd
pair
dN
trigN
1
0.0
0.1
0.2
0.3
0.4
< 2 GeV/c
assoc
T
1 < p
< 2 GeV/c
trig
T
1 < p
φΔ
0 2 4
ZYAM
-C
φΔd
pair
dN
trigN
1
0.0
0.2
0.4
0.6
0.8
φΔ
0 2 4
ZYAM
-C
φΔd
pair
dN
trigN
1
0.0
0.1
0.2
0.3
0.4
< 4 GeV/c
trig
T
2 < p
φΔ
0 2 4
ZYAM
-C
φΔd
pair
dN
trigN
1
0.0
0.2
0.4
0.6
0.8
φΔ
0 2 4
ZYAM
-C
φΔd
pair
dN
trigN
1
0.0
0.1
0.2
0.3
0.4
< 6 GeV/c
trig
T
4 < p
φΔ
0 2 4
ZYAM
-C
φΔd
pair
dN
trigN
1
0.0
0.2
0.4
0.6
0.8
φΔ
0 2 4
ZYAM
-C
φΔd
pair
dN
trigN
1
0.0
0.1
0.2
0.3
0.4
< 12 GeV/c
trig
T
6 < p
φΔ
0 2 4
ZYAM
-C
φΔd
pair
dN
trigN
1
0.0
0.2
0.4
0.6
0.8
Averaged projection of 2D correlations onto Δϕ
for 2<|Δη|<4 (top) and |Δη|<1 (bottom)
pPb case:
v  In order to compare with the PbPb
results, 1D correlation function,
constructed in the same multiplicity
range
v  The yields in pPb case show a
similar structure as those from
PbPb collisions
v  As in PbPb, no near-side
correlations is observed

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The near-side associated yield vs trigger pT
in PbPb and pPb events
long-range short-range – long-range
v  The jet yield increases with pT
v  Explanation: higher jet energy –
more associated particles
v  Seen in both pPb and PbPb
collisions with similar magnitude
v  The ridge yield rises with pT
reaching maximum at pT ≈ 2-3GeV/c
and then decreases toward zero
v  The jet yield is obtained by
subtracting the ridge yield (from long-
range region)
(GeV/c)
T
trig
p
0 5 10
AssociatedYield/(GeV/c)
0
0.2
0.4
0.6 CMS Preliminary
|>2ηΔ(a) | < 260
offline
trkN≤220
< 2 GeV/c
assoc
T
1 < p
= 5.02 TeVNN
spPb
= 2.76 TeVNN
sPbPb
(GeV/c)
T
trig
p
0 5 10
0
0.2
0.4
0.6
|>2ηΔ|<1 minus |ηΔ(b) |

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offline
trkN
0 100 200 300
0.0
0.2
0.4
0.6
CMS
|>2ηΔ(a) | < 2 GeV/cassoc
T
, p
trig
T
1 < p
pPb CGC
= 5.02 TeV, 2013NN
spPb
= 2.76 TeVNN
sPbPb
= 5.02 TeV, 2012NN
spPb
= 7 TeVspp
2
(proton)=0.336 GeV2
0
Q
2
(proton)=1.008 GeV2
0
Q
2
(proton)=1.680 GeV2
0
Q
offline
trkN
0 100 200 300
0.0
0.2
0.4
0.6
|>2ηΔ|<1 minus |ηΔ(b) |
The near-side associated yield vs multiplicity
for 1<pT
trig,pT
assoc<2GeV/c in PbPb and pPb events
long-range short-range – long-range
v  The ridge yield: monotonic rise with
multiplicity
v  At a given multiplicity, the ridge yield
decreases going from PbPb trough pPb to
the smallest pp system
v  The CGC qualitatively describes
the ridge yield
v  The jet yield: moderate rise with
multiplicity
v  There is a slight, nearly no
significant difference between jet
yield in PbPb and pPb collisions
(arXiv:1302.7018)

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(GeV/c)T
p
2 4
2v
0.0
0.1
0.2
0.3 = 2.76 TeVNNsCMS PbPb
< 150trk
offline
N≤120
|>2}ηΔ{2, |2v
<20 sub.
offline
trk
, N|>2}ηΔ{2, |2v
{4}2v
(GeV/c)T
p
2 4
2v
0.0
0.1
0.2
0.3 = 5.02 TeVNN
sCMS pPb
>80 GeVPb
TEΣATLAS,
|>2}ηΔ{2, |2v
{4}2v
(GeV/c)T
p
2 4
2v
0.0
0.1
0.2
0.3
< 185trk
offline
N≤150
(GeV/c)T
p
2 4
2v
0.0
0.1
0.2
0.3 (GeV/c)T
p
2 4
2v
0.0
0.1
0.2
0.3
< 220trk
offline
N≤185
(GeV/c)T
p
2 4
2v
0.0
0.1
0.2
0.3 (GeV/c)T
p
2 4
2v
0.0
0.1
0.2
0.3
< 260trk
offline
N≤220
(GeV/c)T
p
2 4
2v
0.0
0.1
0.2
0.3
18≥part
= 4.4 TeV, NNN
spPb Hydro
2-nd Fourier harmonics vs pT in different multiplicity ranges
v  Hydrodynamics predicts the long-range
correlations (Phys.Rev.C 85(2012)014911)
v  Elliptic flow from1D Δϕ correllations
(v2{2,|Δη|>2})
v  To reduce non-flow correlations: v2
from 4-particle cumulant method (v2{4})
v  The v2 is larger in PbPb than in pPb
v  The difference between v2{2,|Δη|>2}
and v2{4} could come from event-by-event
fluctuations in the flow signal
v  Hydro describes v2{4}. It does not
includes event-by-event fluctuations
v  Comparison to the ATLAS results
(arXiv:1303.2084)
Long-range

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(GeV/c)T
p
2 4
3v
0.00
0.05
0.10
= 2.76 TeVNNsCMS PbPb
< 150trk
offline
N≤120
|>2}ηΔ{2, |3v
<20 sub.
offline
trk
, N|>2}ηΔ{2, |3v
(GeV/c)T
p
2 4
3v
0.00
0.05
0.10
= 5.02 TeVNN
sCMS pPb (GeV/c)T
p
2 4
3v
0.00
0.05
0.10
< 185trk
offline
N≤150
(GeV/c)T
p
2 4
3v
0.00
0.05
0.10
(GeV/c)T
p
2 4
3v
0.00
0.05
0.10
< 220trk
offline
N≤185
(GeV/c)T
p
2 4
3v
0.00
0.05
0.10
(GeV/c)T
p
2 4
3v
0.00
0.05
0.10
< 260trk
offline
N≤220
(GeV/c)T
p
2 4
3v
0.00
0.05
0.10
18≥part
= 4.4 TeV, NNN
spPb Hydro
3-rd Fourier harmonics vs pT in different multiplicity rangesLong-range
v  Triangular flow, v3{2,|Δη|>2}, is
extracted in the same way as v2{2,|Δη|>2}
v  Similar magnitude for v3{2,|Δη|>2} in
both, PbPb and pPb collisions
v  If jet-induced correlations are
independent of multiplicity in pPb
collisions, they could be removed by
subtracting low-multiplicity results from
from high-multiplicity events
v  The low-multiplicity-subtracted
v2{2,|Δη|>2} results are somewhere
between v2{2} and v2{4}, while the
triangular flow remains unchanged
under such a subtraction

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offline
trkN
0 100 200 300
2v
0.00
0.05
0.10
= 2.76 TeVNNs(a) PbPb
< 3 GeV/cT
0.3 < p
|>2}ηΔ{2, |2v
<20 sub.offline
trk
, N|>2}ηΔ{2, |2v
{4}2v
offline
trkN
0 100 200 300
2v
0.00
0.05
0.10
= 5.02 TeVNNs(b) pPb
offline
trkN
0 100 200 300
0.2
0.4
0.6
0.8
42
2+v22
2v
42
2-v22
2v
offline
trkN
0 100 200 300
0.2
0.4
0.6
0.8
2-nd Fourier harmonics vs multiplicity for 0.3<pT<3GeV/c
fluctuation
v  In the PbPb case, the v2 coefficients
increases moderately with multiplicity,
while in pPb case remain relatively
constant at high multiplicity
v  The PbPb data show a larger v2 than
those in the case of pPb collisions
v  The low-multiplicity-subtracted v2
gives almost the same values as
v2{2,|Δη|>2} in high-multiplicity events
v  40% in PbPb and 50-60% in pPb are
upper limits on the flow fluctuations

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offline
trkN
0 100 200 300
3v
0.00
0.01
0.02
0.03
|>2}ηΔ{2, |3v
<20 sub.
offline
trk
, N|>2}ηΔ{2, |3v
= 2.76 TeVNNs(a) PbPb
< 3 GeV/cT
0.3 < p
offline
trkN
0 100 200 300
3v
0.00
0.01
0.02
0.03
= 5.02 TeVNNs(b) pPb
3-rd Fourier harmonics vs multiplicity for 0.3<pT<3GeV/c
v  The magnitude of v3 in pPb collisions is similar to the PbPb case
v  The procedure of subtracting low-multiplicity results doesn’t change
v2 (2,|Δη|>2)
v  The v3 coefficient is largely determined by the event-by-event
geometry fluctuations

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offline
trkN
0 100 200 300
2v
0.00
0.05
0.10 |>2}ηΔ{2, |2v
<20 sub.
offline
trk
, N|>2}ηΔ{2, |2
v
{4}2v
= 5.02 TeVNN
sCMS pPb
< 5 GeV/cT
ATLAS, 0.3 < p
< 3 GeV/cT
0.3 < p
, 50-100% sub.|>2}ηΔ{2, |2v
{4}2v
Comparison to the ATLAS results
v  The v2{4} values from the ATLAS are higher than those from the CMS
although they agree within the errors
v  The applied cuts on compared ATLAS and CMS data are not precisely
equal

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Conclusions
v  The near-side features in pPb collisions at =5.02TeV are studied vs
transverse momentum, pT, and multiplicity
v  The near-side ridge yield increases with multiplicity. It has similar shape as
the one from PbPb collisions but with smaller magnitude
v  The short-range jet yield shows a weak multiplicity dependece in both pPb
and PbPb systems
v  The ridge yield rises and then falls, while the jet-yield rises monotonically
with pT
v  The extracted v2 and v3 values has pT dependence similar with the ridge-yield,
and a weak multiplicity dependence
v  In both systems, the v3 has comparable magnitude and similar dependence
on pT and multiplicity
v  As the data are studied over a broad range in multiplicity and in pT it could
provide significant constraints on theoretical predictions of the origin of the
long-range ridge phenomena
sNN

J. Milošević, Measurement of Two- and Four-particle Correlations in pPb and PbPb Collisions at CMS

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J. Milošević, Measurement of Two- and Four-particle Correlations in pPb and PbPb Collisions at CMS