S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page1 Azimuthal correlations and anisotropic flow: trends and questions Sergei A

Collective flow and properties of QGP, BNL, November 2003

page 1 S.A. Voloshin

Azimuthal correlations and anisotropic flow: trends and questions

Sergei A. Voloshin

1. Definitions: What is flow and what is non-flow? Spatial asymmetry?Let us speak the same language!

2. Continuous worry: is it really collective? Has anything to do with the impact parameter orientation (real flow)? q -distributions. Measuring non-flow in AA and pp.

3. Non-flow and many particle correlations. Mixed harmonics analysis.

4. Many reasons for flow fluctuations. Fluctuations contribution to mixed harmonic analysis.

5. 2-particle correlations at different angles to the Reaction Plane: High pt, azHBT,non-identical particles, balance functions.

6. Conclusions/Summary

Not a review, Not a presentation of STARresults



...) φ) ( v ) (φ v (dy dpN d

dφ dy dpN d

t t

2 2 2 121

2 1

2 3

cos cosπ

Directed flow Elliptic flow

Anisotropic flow correlationswith respect to the reaction plane

Term “flow” – not necessarily “hydro” flow – used only to emphasize the collectivebehavior multiparticle azimuthal correlation.

Anisotropic flow. Definitions: v’s

“… v2 in pp collisions is almost 100% …”“… event anisotropy at high pt, elliptic flow at low pt…”

The situation is not totally clear for 2-particle spectra. Discussed a little bit below.

Fourier decomposition of single particle inclusive spectra

Non-zero v4 – is it bad?



Anisotropic flow. Definitions: ’s

2 2

2 2

y x

y x

Other similar/same quantities:

Ollitrault: s

Heiselberg: Sorge: A2

Shuryak: s2

22

22

2

)cos(

xy

xy

n sn

And more recent ones:

Those have clear meaning only for particlesproduced at the point x=y=0.

The physics is (due to Sorge) that v2 is proportional to any of them. Better to use the samedefinition to allow cross comparison (unless a new physics based relation established). (Low density limit (Heiselberg) is probably the best to check the meaning)Note: -- it is not at all trivial what should be used (if any) for higher harmonics (no simple form) -- s2 parameter in the Blast Wave fit to v2(pt) in general is a different parameter-- do not confuse initial and final state anisotropy



Such absorption corresponds to suppression for inclusive yield in central collisionsabout factor of 4-5

b/2RA

V2

b/2RA

V4

Flow due to absorption. v2, v4; e2, e4See also: nucl-th/0310044 A. Drees, H. Feng, J. Jia

<cos(4)> would behave quite differently (sign, etc.)

WS density,finite absorption

Surface emission limit,hard sphere

Not clear what should be used for 4



Looking for collectivity: q-distributions

Two more:1) q-distributions:2) Q vector products

MQq /||

2dqdN

q

2dqdN

q

;* δ 2221 vuu

Distribution in the magnitude of the flow vector 2222 2| | iiQ e Q e

Correlations due to flow: shift of the peak

Non-flow contribution: widening of the distribution

Used in the very first E877 analysis

Better shape description higher moments (cumulant orders) new method of Ollitrault (?)



v2 from q-distributions

-- The results are very close to those from 4-particle correlation analysis.-- Difficult to trace the contribution of flow fluctuations.

STAR, PRC 66 (2002) 034904



Azimuthal correlation in pp collisions

Goals (from “flow” point of view):

1. Check if non-flow estimates/measurements reported for Au+Au are consistentwith measurements in pp. (One could expect the difference of the order of factor of <~2. Examples: Extra particles in jets non-flow ; B-to-B jet suppression - )

2. Use pp data to estimate non-flow effects in Au+Au in the regions where othermethods do not work well (like high pt region; Kaon and Lambda ? )

Approach/method:

1. “Scalar product”. The basic quantity in this approach is

Advantages: simpler to work with and much simpler to interpret.

*2; 2;

22; 2; 2; 2cos(2 2 ) ; ia b a b aba bv u evu u

Subscript “2” is omitted in equations on a next few slides.

Flow non-flow



uQ* in pp and AA collisions

2

" "

;

iii i

i pool

Q u u e

* * AA AA ppb b p bu Q v v M u Q Non-flow looks exactly the same in pp

and AA Directly “correctible”.

* ( )

AA AAb b p bp

pp pp ppbp bpAA

bp AAcoll

u Q v v M

M

N M



pp vs. AA * * AA AA ppb b p bu Q v v M u Q

The plot above, showing the rise and fall of azimuthal correlations ( M<uu*>)can be explained only by flow: no any other known source of the azimuthal correlation is able to give such a dependence.

The origin of such dependence: ~ M *

STAR Preliminary

Most peripheral

5% central

0 pt 7 GeV

M<~10

M>~500

STAR results are presented by A. Tang at this workshop



Mixed harmonics: how it works* 2

,1 ,2 ; inn n nu u v u e

What to do when the reaction plane is known: (AMP, SV: PRC “method” paper)

21cos( )cos( ) sin( )sin( ) cos( 2a RP b RP a RP b RP a b RP v

sin( )sin( ) / 2a RP b RP

21cos( )cos( ) / 2a RP b RP v

21

cos( )cos( ) sin( )sin( )

cos( 2 ) cos(2 2 )

a EP b EP a EP b EP

a b EP EP RPv

21 2,cos( ) cos( ) sin( )sin( )

cos( 2 )

a c b c a c b c c

a b c

v v

… and when it is not exactly known:

Similar for v4 via 2cos(4 4 )

Borghini, Dinh, Ollitrault



Non-flow and mixed harmonics

422

22

*22 10)2025(}4{}2{

vvuu

flownon

424

*44 105.2}2{

vuu

flownon

824*422 1025)105(~

flownonuuu

422

*4224 10/}3{ vuuuv

2 *1 2 3 1 3 2 3 2 2 2cos(2 2 4 ) cos(2 2 )cos(2 3 ) 2

non flowv u u

* 34 2 22 10

non flowv u u

Compare to 5—6 10-3 reported.

-- Totally relies on non-flow estimates for v2.-- Higher order cumulants do not help



Non-flow or Fluctuations?

42

**

222* ;

vuuuu

vvuu

dcba

vba

222

42

**

222

*

222

;

vvuuuu

euvuu

dcba

iba Correct if v is constant

in the event sample

Should be used even in a case of =0

Several reasons for v to fluctuate in a centrality bin:1) Variation in impact parameter in a given exp. centrality bin

(taken out in STAR PRC flow paper)2) Real flow fluctuations (due to fluctuations in initial conditions, in local

particle density, or in the system evolution)



Fluctuations in eccentricity fluctuations in v2

1/ 6

36 4 2 212

1/ 4

2 2 2

22 42 2 2

22

2

2

4

{4}

{2}

{6} 12

2

9

v

v

v v v v v

v

v v

2 2

2 2

y x

y x

x,y – coordinates of “wounded” nucleons

v2 ~ fluctuations in flow

Calculations: R. Snellings and M. Miller



Compare to data

R. Snellings

Fluctuations in initial geometrycould explain the entire differencebetween v2{2} and v2{4}



On the other hand, it is noticed that224 ~ vv

it will be interesting to study fluctuationsin 2

2

Flow fluctuations: mixed harmonics

Calculations by R. Snellings.<cos(4s) used as e4

224 ~ vv

The effect can be as large as factor of 3



Where we are – checking with “oldstuff”

S.V. RHIC Winter Workshop, Berkeley, January 1999http://www-rnc.lbl.gov/~nxu/oldstuff/workshop/rww99.html



2-particle correlations wrt RP

);,( 2121

2

RPxxdxdx

Nd x – azimuthal angle, transverse momentum, rapidity, etc.

J. Bielcikova, P. Wurm, K. FilimonovS. Esumi, S.V. nucl-ex/0311007

“a” == “trigger particle”

)2cos(21 ,,

,2,2,

baoutin

abba

flowpairs vv

d

dN

2

22

2

22 4

2

4

2

v

vv

v

vv outin

CERES, nucl-ex/0303014

Selection of one (or both) of particles in- or out- of the reaction plane “distorts” the RP determination

Approach: - “remove” flow contribution- parameterize the shape of what is left- study RP orientation dependence of the parameters



STAR Results

STAR preliminary

STAR preliminary

Back-to-back suppression is larger in the out-of-plane direction

K. Filimonov, STAR, DNP 2003

Complications: particles in the “trigger” pt region could have different originand correspondingly different “flow”.



Approach: “Same” –”Opposite”

Next step: compare differences for 2 different pseudorapidity windowsused to count the associated particles get numbers of “Same” and “Opposite” separately. Here one has to use one of the assumptions: - the eta distribution of associated particles in “opposite” direction is flat, or- it is the same as in pp collisions

Work with differences: (# of associated particles in the SAME direction)

-(# of associated particle in the OPPOSITE direction)

Advantage: Flow contribution cancels out exactly.

STAR, PRL 90 (2003) 082302



Only sketch…

central

Out-of-planeIn-plane

Number ofassociatedparticles.“Same” – “Opposite”

peripheral

(!) Larger difference values correspond to either larger “same” or smaller “opposite”.



azHBTS.V. LBNL 1998 annual report # R20

http://ie.lbl.gov/nsd1999/rnc/RNC.htm RQMD v 2.3, AuAu @ RHIC

~/ ( / ) /T T

HBT T

v vR v t

dv dx L t L

- thermal velocity

/ - expansion velocity gradient

- expansion time

- source size at freeze-out

Tv

dv dx

t

L



azHBT-2

IPES initial conditions, U. Heinz, P. Kolb PL B542 (2002) 216

Should we try very lowkT at RHIC?



Non-identical particle correlations



Summary: trends, questions

1. Please avoid (unnecessary) introduction of new terms

2. Not clear what, if any, to use instead of e2 for higher harmonics

3. How to get rid of non-flow effects at the level of 0.1% level (vn)

4. How to disentangle non-flow and flow fluctuations effects

5. 2-particle correlations with respect to the RP- future direction?

6. How to disentangle “jet” and “soft” flow at intermediate pt?

7. Is the azHBT sensitive to the in-plane expansion?

8. …

9. Plasma of constituent quarks?

Thanks to STAR “flow group” for discusion

Documents

S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page1 Azimuthal correlations and anisotropic flow: trends and questions Sergei A