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![Page 1: S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page1 Azimuthal correlations and anisotropic flow: trends and questions Sergei A.](https://reader035.fdocuments.in/reader035/viewer/2022070409/56649e985503460f94b9b65f/html5/thumbnails/1.jpg)
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
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Collective flow and properties of QGP, BNL, November 2003
page 2 S.A. Voloshin
...) 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?
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Collective flow and properties of QGP, BNL, November 2003
page 3 S.A. Voloshin
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
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Collective flow and properties of QGP, BNL, November 2003
page 4 S.A. Voloshin
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
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Collective flow and properties of QGP, BNL, November 2003
page 5 S.A. Voloshin
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 (?)
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Collective flow and properties of QGP, BNL, November 2003
page 6 S.A. Voloshin
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
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Collective flow and properties of QGP, BNL, November 2003
page 7 S.A. Voloshin
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
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Collective flow and properties of QGP, BNL, November 2003
page 8 S.A. Voloshin
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
![Page 9: S.A. Voloshin Collective flow and properties of QGP, BNL, November 2003page1 Azimuthal correlations and anisotropic flow: trends and questions Sergei A.](https://reader035.fdocuments.in/reader035/viewer/2022070409/56649e985503460f94b9b65f/html5/thumbnails/9.jpg)
Collective flow and properties of QGP, BNL, November 2003
page 9 S.A. Voloshin
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
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Collective flow and properties of QGP, BNL, November 2003
page 10 S.A. Voloshin
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
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Collective flow and properties of QGP, BNL, November 2003
page 11 S.A. Voloshin
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
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Collective flow and properties of QGP, BNL, November 2003
page 12 S.A. Voloshin
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)
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Collective flow and properties of QGP, BNL, November 2003
page 13 S.A. Voloshin
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
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Collective flow and properties of QGP, BNL, November 2003
page 14 S.A. Voloshin
Compare to data
R. Snellings
Fluctuations in initial geometrycould explain the entire differencebetween v2{2} and v2{4}
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Collective flow and properties of QGP, BNL, November 2003
page 15 S.A. Voloshin
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
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Collective flow and properties of QGP, BNL, November 2003
page 16 S.A. Voloshin
Where we are – checking with “oldstuff”
S.V. RHIC Winter Workshop, Berkeley, January 1999http://www-rnc.lbl.gov/~nxu/oldstuff/workshop/rww99.html
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Collective flow and properties of QGP, BNL, November 2003
page 17 S.A. Voloshin
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
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Collective flow and properties of QGP, BNL, November 2003
page 18 S.A. Voloshin
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”.
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Collective flow and properties of QGP, BNL, November 2003
page 19 S.A. Voloshin
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
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Collective flow and properties of QGP, BNL, November 2003
page 20 S.A. Voloshin
Only sketch…
central
Out-of-planeIn-plane
Number ofassociatedparticles.“Same” – “Opposite”
peripheral
(!) Larger difference values correspond to either larger “same” or smaller “opposite”.
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Collective flow and properties of QGP, BNL, November 2003
page 21 S.A. Voloshin
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
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Collective flow and properties of QGP, BNL, November 2003
page 22 S.A. Voloshin
azHBT-2
IPES initial conditions, U. Heinz, P. Kolb PL B542 (2002) 216
Should we try very lowkT at RHIC?
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Collective flow and properties of QGP, BNL, November 2003
page 23 S.A. Voloshin
Non-identical particle correlations
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Collective flow and properties of QGP, BNL, November 2003
page 24 S.A. Voloshin
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