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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
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?
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
Collective flow and properties of QGP, BNL, November 2003
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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
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 (?)
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
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
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
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
Collective flow and properties of QGP, BNL, November 2003
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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
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
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)
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
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}
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
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
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
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”.
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
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”.
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
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?
Collective flow and properties of QGP, BNL, November 2003
page 23 S.A. Voloshin
Non-identical particle correlations
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