S.A. Voloshin STAR QM’06: Energy and system size dependence of elliptic flow and v 2 / scaling...
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Transcript of S.A. Voloshin STAR QM’06: Energy and system size dependence of elliptic flow and v 2 / scaling...
QM’06: Energy and system size dependence of elliptic flow and v2 / scaling
page 1 S.A. Voloshin
STAR
Sergei A. Voloshin
Wayne State University, Detroit,
Michigan
for the STAR Collaboration
Energy and system size dependence of charged
particle elliptic flow and v2 / scaling
Outline:
1. Introduction: Elliptic flow and the system initial eccentricity. Flow fluctuations and non-flow.
2. Measuring flow with STAR detector (Main TPC, Forward TPCs, ZDC-SMD).
3. Estimates of flow fluctuations with Monte-Carlo Glauber model.4. v / scaling(s).
QM’06: Energy and system size dependence of elliptic flow and v2 / scaling
page 2 S.A. Voloshin
STAR
Elliptic flow and the system initial geometry
Note: uncertainty in the centrality definition- sqrt(s)=130 GeV data: 0.075 < pt < 2.0 GeV/c- sqrt(s)=200 GeV data: 0.15 < pt < 2.0; - the data scaled down by a factor of 1.06 to account for change in (raw) mean pt.- AGS and SPS – no low pt cut- STAR and SPS 160 – 4th order cumulants - no systematic errors indicated
2
1 dN
Sv
dy 2 2S x y
Motivation for the plot:
2 2
2 2
y x
y x
2 cos 2 i RPv Hydro limits: slightly depend on initial conditionsData: no systematic errors, shaded area –uncertainty incentrality determinations.Curves: “hand made”
S.V. & A. Poskanzer, PLB 474 (2000) 27
QM’06: Energy and system size dependence of elliptic flow and v2 / scaling
page 3 S.A. Voloshin
STAR
v2{2}, v2{4}, non-flow, and flow fluctuations
* 2 21 2 2
* 1/ 22 1 2
* * 4 2 21 2 3 4 2 2
1/ 4* 2 * *2 1 2 1 2 3 4
;
{2}
2 2 2
{4} 2
iu u v u e
v u u
u u u u v v
v u u u u u u
Several reasons for v to fluctuate in a centrality bin:1) Variation in impact parameter in a centrality bin
(taken out in STAR results)2) Real flow fluctuations (due to fluctuations in the
initial conditions or in the system evolution)
* 22 2 2
2
22 12 2
vv uu v vv v
22
2 2* * * 24 42
22 2
2
4 2 12
vv
v uu uuu u v vv
2 equations, at least 3 unknowns: v, δ, σ
Non-flow Flow fluctuations
Non-flow (not related to the orientationof the reaction plane) correlations:- resonance decays- inter and intra jet correlations, etc.
Different directions to resolve the problem:- Find methods which suppress / eliminates non-flow or flow fluctuations
- Add more equations assuming no new unknowns
- Estimate flow fluctuations by other means
- Measure flow fluctuations
22 2 2 2 2; {2} / {2}/v v v v
Correlations with large = |1-2|Lee-Yang Zeroes (Bessel Transform)
Subject of this talk
Use equations for v2{n}, n>4
Talk by P.Sorensen (STAR)
QM’06: Energy and system size dependence of elliptic flow and v2 / scaling
page 4 S.A. Voloshin
STAR
Data
This analysis used the data taken during RHIC Run IVand based on (after all quality cuts)Au+Au 200 GeV ~ 10.6 M Minimum Bias eventsAu+Au 62 GeV ~ 7 M Minimum Bias eventsCu+Cu 200 GeV ~ 30 M Minimum Bias eventsCu+Cu 62 GeV ~ 19 M Minimum Bias events
Tracking done by two Forward TPCs (East and West)and STAR Main TPC.
Tracks used: | η |<0.9 (Main TPC) -3.9 < η < -2.9 (FTPC East) 2.9 < η < 3.9 (FTPC West)
0.15 < pT < 2.0 GeV/c
Results presented/discussed in this talk: elliptic flow in the Main TPC region (|η|<0.9)
ZDC
Barrel EM Calorimeter
Magnet
Coils
ZDC
FTPC west
Central Trigger Barrel
Main TPC
Silicon Vertex Tracker
FTPC east
QM’06: Energy and system size dependence of elliptic flow and v2 / scaling
page 5 S.A. Voloshin
STAR
Shown in black are resultsobtained by correlatingtwo random particles from Main TPC. Non-flow contribution can be largeand positive.
In blue are results forv2 in the Main TPC regionobtained from correlations (Forward*Main) and(East*West). Relative systematic error at maximum flow ~< 3% (AuAu 200 GeV)~< 5% (AuAu 62 GeV)~< 12% (CuCu 200 GeV) ~< 20% (CuCu 62 GeV)
Note: significantly largerrelative difference between black and blue points in Cu+Cu case compared to Au+Au
v2 from ( Forward TPC * Main TPC ) correlations
The difference (blue and red) is due to non-flow assuming that flow fluctuates coherently in the Main and Forward TPC regions
QM’06: Energy and system size dependence of elliptic flow and v2 / scaling
page 6 S.A. Voloshin
STAR
v2{FTPC}(pt) , 20-60% centrality
There still indications of non-flow contribution in v2{FTPC}, especially at high transverse momenta.
The green points show the results “AA-pp” [G.Wang (STAR), QM2005]
AuAu 200 GeV
CuCu 200 GeV
Non-flow contribution in v2{2}, relatively smallin AuAu @200 GeV, increases with pt
QM’06: Energy and system size dependence of elliptic flow and v2 / scaling
page 7 S.A. Voloshin
STAR
CuCu 200 GeV, v2{FTPC}(pt)
S
TA
R P
reli
min
ary
Indicates strong non-flow contribution in v2{2} (measured within Main TPC).
Non-flow might be still present at high pt in v2{FTPC}
QM’06: Energy and system size dependence of elliptic flow and v2 / scaling
page 8 S.A. Voloshin
STAR
Initial eccentricity: “optical”, “standard”, “participant”.
“New” coordinate system –rotated, shifted
2 2
2 2Std
y x
y x
2 2
2 2
' '
' 'part
y x
y x
S. Manly, QM2005
x
'x
y'y
“Optical” Glauber calculations: “Monte-Carlo” Glauber model:
[neglecting shift ]
cos(2 )std part
QM’06: Energy and system size dependence of elliptic flow and v2 / scaling
page 9 S.A. Voloshin
STAR
Eccentricity fluctuations: ‘Standard’ vs ‘Participant’
Note:- Relative fluctuations in part are much smaller than in std
- “participant” eccentricity values are larger compared to “standard” std ≈ part cos(Ψ).-In Cu+Cu Std{4} fails almost at all centralities- The difference between std and part is bigger for Cu+Cu than Au+Au- Very weak dependence on collision energy (not shown)
- Very small values of part{4} for central collisions difficult to use it to rescale v2{4}
Monte Carlo Glauber nTuples from J. Gonzales (STAR)
22 2 22
24 2 44 2
Black line on the left is optical used earlier in STAR and NA49 publi-cations. Note that it is about 15%
larger than part almost at all centralities.
Main idea: use proper ε{n} torescale corresponding v2{n}:
{ } { }/v n v n
QM’06: Energy and system size dependence of elliptic flow and v2 / scaling
page10 S.A. Voloshin
STAR
One more equation: Flow fluctuations from v2{4}/v2{6}
Assuming:- non-flow does not fluctuate- non-flow exist only on 2-particle level
- Gaussian type of fluctuations
- (For the last approximation)small relative fluctuations
* 2 * * 4 2 2
* * 4 2 2
; 4 2 ;
4 2 ;
uu v uuu u v v
uuu u v v
2 4 22 2 2 2 4
6 4 26 2 4 6
; 6 3
15 15
v v v v v
v v v v
2
2yv
1/ 42
1/ 22
1 24
2 1 /
y yv
v y v
1/ 42 2
1/ 6 2
1 241
6 1 4 6
y yv
v y v
One finds:
where :
Cu+Cu 200 GeV
Au+Au 200 GeV
- Fluctuations in std (green points) are too strong (noticed earlier by R. Snellings.)- Gaussian approximation works rather poorly(no agreement between red and blue points)
QM’06: Energy and system size dependence of elliptic flow and v2 / scaling
page11 S.A. Voloshin
STAR
Eccentricity fluctuations in AuAu, MC Glauber vs data
Flow fluctuations from data are somewhat stronger compared to those in eccentricity (shown in blue)though would be within sytematics.
STAR Phys. Rev. C 72 (2005) 014904
22 2 22
24 2 44 2
22 1/ 4
1/ 6 2
4 (1 2 ),
6 (1 4 )v
v y yy
v y v
QM’06: Energy and system size dependence of elliptic flow and v2 / scaling
page12 S.A. Voloshin
STAR
Effect of fluctuations in eccentricity
If compare to the “original” v2 / plot (page 2) note the difference in eccentricityoptical, old (using parameterization made for SPS energies) and part (optical, old ~ (1.1– 1.2) * part ) ! )
2{ }/ {2}v FTPC 2{ }/ partv FTPC
Systematic error on dn/dy ~10%, similarly on v2 and S.
Hydro results (Kolb, Sollfrank, Heinz, PRC 62 (2000) 054909 )are rescaled with optical
Scaling with ε should be used ifv2’s in the Main and ForwardTPCs are not correlated.
QM’06: Energy and system size dependence of elliptic flow and v2 / scaling
page13 S.A. Voloshin
STAR
v2{ZDC-SMD} and eccentricity scaling
Au +Au 200 GeV
STAR
prelimi
nary
G. Wang (STAR) QM2005
Note that under assumption that the directedflow of spectator neutrons is not correlatedto the elliptic shape of the system at midrapidty,
v2{ZDC-SMD} should follow std .(This assumption requires further study with MC Glauber model).
QM’06: Energy and system size dependence of elliptic flow and v2 / scaling
page14 S.A. Voloshin
STAR
v2/ scaling
Scaling holds rather well, thoughAuAu 62 GeV results are somewhat higher.
Hydro curves are obtained from calculationsKolb, Sollfrank, Heinz, PRC 62 (2000) 054909,made at b=7 fm and rescaled by ‘optical’ eccentricity value. The centrality dependence is not fullyreflected by these curves, as it is more ‘flat’ at eachgiven collision energy (very roughly indicatedby strait lines)
QM’06: Energy and system size dependence of elliptic flow and v2 / scaling
page15 S.A. Voloshin
STAR
Conclusions
1. The results for elliptic flow at midrapidity in Au+Au and Cu+Cu collisions
have been presented for collision energies √sNN = 200 and 62 GeV using
correlations of particles in the Main TPC and FTPCs regions.
2. Initial eccentricity and its fluctuations have been studied with Monte Carlo
Glauber model.
3. Flow fluctuations have been estimated from v2{4}/v2{6} ratio using Gaussian
approximation.
4. The v2 /2 scaling holds well for all four systems ( Au+Au and Cu+Cu at different
energies ) once the fluctuations in eccentricity have been taken into account.
v2{ZDC-SMD} scales well with std
QM’06: Energy and system size dependence of elliptic flow and v2 / scaling
page16 S.A. Voloshin
STAR
Backup slides
QM’06: Energy and system size dependence of elliptic flow and v2 / scaling
page17 S.A. Voloshin
STAR
v2{2}/eps{2} and v2{4}/eps{4}
QM’06: Energy and system size dependence of elliptic flow and v2 / scaling
page18 S.A. Voloshin
STAR
Eccentricity for the ‘standard’ STAR centrality bins
AuAu200 CuCu200
No multiplicity weight!
Centrality bin 1 2 3 4 5 6 7 8 9 10Fraction of cross section (%) >80 70-80 60-70 50-60 40-50 30-40 20-30 10-20 5-10 0-5
QM’06: Energy and system size dependence of elliptic flow and v2 / scaling
page19 S.A. Voloshin
STAR
Observation of non-flow in azimuthal correlations
- In Cu+Cu collisions the azimuthal correlationsin the main TPC are dominated by non-flow.
-The relative contribution of non-flow is at least 2 times smaller in correlations between Forward and Main TPCs.
Main * ForwardMain_a * Main_b
FTPC_east * FTPC_west“a” and “b” are two random particles from Main TPC
In this kind of plots non-flow correlation contributionshould be either flat or slightly increasing