Elliptic and higher order flow measured in a

large phase space in large phase space in

Pb+Pb Collisions2.76NN

s TeV=

Soumya Mohapatra

for the ATLAS Collaboration

Stony Brook University

• Initial spatial fluctuations of nucleons lead to higher moments of deformations in the fireball, each with its own orientation.

• The spatial anisotropy is transferred to momentum space by collective flow

Introduction and Motivation

dN

d φ∝1+ 2v

ncosn φ − Ψ

n( )n

∑Singles:

dN

d ∆φ∝1+ 2v

n

a vn

b cos n∆φ( )∑Pairs:

EP method

2PC method

2

• The harmonics vn carry information about the medium: initial geometry, η/s

• Understanding of higher order vn can shed light on the physics origin of “ridge” and “cone” seen in 2P correlations

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

d ∆φ∝1+ 2v

nv

ncos n∆φ( )

n

∑Pairs: 2PC method

ATLAS Detector3.3<|η|<4.8

3

• Tracking coverage : |η|<2.5

• FCal coverage : 3.3<|η|<4.8 (used to determine Event Planes)

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

|η|<2.5

Event Plane Method4

Bands indicate

systematic errors

Centrality dependence of vn

•5% Centrality bins + 0-1%

centrality bin

•v2 has a stronger centrality

dependence.

•Other vn are flatter.

5

•In most central collisions, v3,v4

can be larger than v2 at high

enough pT

pT Dependence of vnv

n

6

• Similar trend across all harmonics (increase till 3-4GeV then decrease)

• In most central collisions(0-5%): v3, v4 can be larger than v2.

Soumya Mohapatra : Stony Brook University

vn

vn scaling(v

n1

/n /

v2

1/2

)

7

• Observe scaling: vn1/n =kv2

1/2, where “k” is only weakly dependent on pT.

• R.Lacey et al. (http://arxiv.org/abs/1105.3782)

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

v2 Comparison to RHIC8

• Similar magnitude and pT dependence in overlapping pT range

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

|η|<1

η Dependence of vn

•weak dependence on

η (~5% drop within

acceptance)

9

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

• For Correlations:

relation is true only if

the η dependence is

weak

,

, v v va b a b

n n n n= ×

Two Particle ∆η−∆φ correlations

Near-side jet peak

is always visible

Ridge seen in

central and mid-

central collisions,

weak η

dependence

Ridge strength first

increases then

decreases with

10

Away side has

double hump

structure in most

central events

Peripheral events have near side peak truncated

decreases with

centrality

Peripheral events

have jet related

peaks only

Obtaining harmonics from correlationsa) The 2D correlation function in

∆η,∆φ.

b) The corresponding 1D

correlation function in ∆φ for

2<|∆η|<5 ( the |∆η| cut

removes near side jet)

c) The vn,n obtained using a

Discrete Fourier

11

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

Discrete Fourier

Transformation(DFT)

d) Corresponding vn values

( ) ( ), v = v ,a a a

n T n n T Tp p p

Bands indicate systematic errors

Comparison between the two methods 12

Centrality Dependence

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

pT Dependence of v2

13

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

�The 2PC vn for |∆η|<0.5 deviates from the EP results (for all pT)

� Good agreement seen for |∆η|>2 at pT<4 GeV.

�See deviations for pT>4 GeV even for |∆η|>2 due to increased away-side

jet contribution (which swings along ∆η).

pT Dependence of other vn

14

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

We see similar trend as v2

Recovering the correlations from EP vn

From 2PC method From EP method

C ∆φ( ) = b2P (1+ 2v1,1

2P cos ∆φ + 2 vn

EPvn

EP cosn∆φn=2

6

∑ )

� Chose v1,1 and

normalization to be

same as original

correlation function, but

all other harmonics are

15

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

all other harmonics are

from EP analysis.

� Correlation function is

well reproduced, ridge

and cone are recovered!

� Common physics origin

for the near and away-

side long range

structures.

• Measured v2-v6 by both correlation and event-plane analysis.

– Significant and consistent v2-v6 were observed by the two methods.

– Measured in phase space much larger than at RHIC.

– Each vn can act as independent cross-check for η/s.

• Noted that v2 doesn’t change drastically from RHIC to LHC

• Observed that the vn follow a simple scaling relation: vn1/n ∝ v2

1/2.

Summary16

∝

• Concluded that the features in two particle correlations for |∆η|>2 at low

and intermediate pT (pT<4.0GeV) can be accounted for by the collective

flow of the medium.

– Double hump and ridge arise due to interplay of even and odd

harmonics

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

• ATLAS vn analysis note : http://cdsweb.cern.ch/record/1352458

• ATLAS HI public results page : • https://twiki.cern.ch/twiki/bin/view/AtlasPublic/HeavyIonsPublicResults

For more results see:

BACKUP SLIDES

BACKUP SLIDES17

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

18

Vn of Charged Hadrons: from RHIC to LHC

vn(Ψn)

From

Arkadiy Taranenko

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

Arkadiy Taranenko

EPIC@LHC Talk

∆η dependence of vn

•Repeat procedure

in narrow ∆η slices

to obtain vn vs ∆η.

•vn values peak at

low ∆η, due to jet

bias.

19

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

•Relatively flat

afterwards, so we

require a |∆η| >2

gap (to remove

near-side jet).

Bands indicate systematic errors

v1,1

20

• Left panel: : v1(pTa) vs ∆η for four fixed-pT correlations.

– We see that v1 ,1(pTa ) can become negative showing eta dependence of v1

• Right panel: v1(pTb) vs for target pT in (1.4,1.6) GeV

– We see that v1(pTb) depends on pT

a showing the breakdown of the scaling relation

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

Universality of vn

vn,n

pT

a ,pT

b( )=vn

pT

a( )vn

pT

b( )

vn

pT

a( ) = vn,n

pT

a ,pT

a( )

21

� vn,n is expected to factorize

into single vn for flow

� Obtain vn using “fixed pT”

correlations

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

vn

pT

b( )=v

n,np

T

a ,pT

b( )v

np

T

a( )

� cross-check via “mixed-pT”

correlation

� Indeed, vn,n factorizes! (above

certain ∆η)

v2 out to 20GeV

central

22

• Charged hadrons, pT=0.5-20 GeV, mid-rapidity, |η|<1

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

peripheral

pT evolution of ∆φ correlations 23

• pT evolution of two-particle ∆φ correlations for 0-10% centrality selection, with a large rapidity gap (|∆η|>2) to suppress the near-side jets and select only the long range components.

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

vn,n and vn vs ∆η for other centralities24

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

pT Dependence of v3 (2PC)25

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

pT Dependence of v4 (2PC)26

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

pT Dependence of v5 (2PC)27

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

ATLAS Detector3.3<|η|<4.8

28

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

• Tracking coverage : |η|<2.5

• FCal coverage : 3.3<|η|<4.8 (used to determine Event Planes)

• “Flipped side FCal” used to study η dependence (reduces Jet bias)

• The EP is determined with the Q-vector method using ET

flow in FCal

• In mid-central collisions, the Q2 vector is distributed in a ring-like structure indicating the excellent ability of the FCal in determining the reaction plane

Q vector example

,1

, ,

,

1cos( ) ; sin( ) ; tan ( )

y n

x n i i y n i i n

i i x n

QQ E n Q E n

n Qφ φ −= = Ψ =∑ ∑

29

• In Central and mid-central collisions and for higher harmonics, the ring blurs out

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

Two Particle Correlations30

� The correlations are constructed by dividing foreground pairs by mixed

background pairs.

� Mixed background pairs account for detector acceptance. Final correlation

contains only physical effects.

� The detector acceptance causes fluctuations ~ 0.001 in the foreground

pairs, which mostly cancels out in the ratio.

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

ForegroundPairs( )( )

MixedPairs( )C

φφ

φ

∆∆ =

∆

Recovering 0-1% correlation31

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

Recovering 0-5% correlation32

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration

33

Soumya Mohapatra : Stony Brook University : ATLAS Collaboration