energy dependence of anisotropic flow
DESCRIPTION
Energy dependence of anisotropic flow. Raimond Snellings. RHIC: the first 3 years. RHIC Scientists Serve Up “Perfect” Liquid New state of matter more remarkable than predicted -- raising many new questions April 18, 2005. Outline. The perfect liquid at RHIC - PowerPoint PPT PresentationTRANSCRIPT
Energy dependence of anisotropic flow
Raimond Snellings
5 July 2006 [email protected] 2
RHIC: the first 3 yearsRHIC Scientists Serve Up “Perfect” LiquidNew state of matter more remarkable than predicted -- raising many new questionsApril 18, 2005
5 July 2006 [email protected] 3
Outline
The perfect liquid at RHIC How do we approach the perfect liquid? What can we expect at the LHC?
What can we learn from higher harmonics?
5 July 2006 [email protected] 4
Anisotropic Flow
Anisotropic flow ≡ azimuthal correlation with the reaction plane the cleanest signal of final-state
reinteractions Unavoidable consequence of
thermalization Natural description in hydrodynamic
language, however when we talk about flow we do not necessary imply (ideal) hydrodynamic behavior
Flow in cascade models: depends on constituent cross sections and densities, partonic and/or hadronic
Non-flow ≡ contribution to vn from azimuthal correlations between particles not due to their correlation with the reaction plane (HBT, resonances, jets, etc)
1
2
3
3
cos),(21dd
d
2
1
pd
d
nrtn
tt
nypvypp
NNE
rn nv cos
5 July 2006 [email protected] 5
Measuring Anisotropic Flow
222 2 vv
)ψ( r)(cos inrn env
2 1 2 1 21 ( ) ( ) (( ) 2) ( ) ( {2})r r r rinn
in in in ine e e ee v
Assumption: all correlations between particles due to flow
Non flow correlation contribute order (1/N), problem if vn≈1/√N
1 2 3 4 3 4 3 21 2 1 4( ) ( ) ( )( ) ( ) 4( {4})in in inin in
n ve e e e e Non flow correlation contribute order (1/N3), problem if vn≈1/N¾
N. Borghini, P.M. Dinh and J.-Y Ollitrault, Phys. Rev. C63 (2001) 054906
Measuring the cumulants of different order provides constraints on both fluctuations and non-flow. Can be conveniently calculated using generating functions, extended to vn{∞} using Lee-Yang zeros, reliable vn>1/N
4/1
42
2222 24
vvv
5 July 2006 [email protected] 6
The perfect liquid
5 July 2006 [email protected] 7
The “nearly perfect” liquid
Magnitude and transverse momentum dependence of v2
A strongly interacting, more thermalized system which is for more central collisions behaves consistent with ideal fluid behavior!
v2{4} 130 GeV
Zhixu Liu
HYDRO: Kolb, Sollfrank, Heinz, PRC 62 (2000) 054909
STAR PRL 86, 402 (2001)
P.F. Kolb et al., PLB 500 (2001) 0012137
5 July 2006 [email protected] 8
Viscosity and parton cascade
Viscosity needs to be small Parton cascades need huge opacities
Partially solved by coalescence Microscopic picture responsible for large v2 still not understood (E. Shuryak
sQGP is being understood)
D. Teaney PRC68:034913,2003 D. Molnar and P. Huovinen, PRL94:012302,2005
5 July 2006 [email protected] 9
Strong Collective Motion, v2(m,pt)
Particles flow with a common velocity The most compact representation of the strong radial
flow and its azimuthal variation Best described by QGP EoS!?
5 July 2006 [email protected] 10
The QCD EoS and Cs
Test the effect of four different EoS; qp is lattice inspired, Q has first order phase transition, H is hadron gas with no phase transition and T a smooth parameterization between hadron and QGP phase
Pasi Huovinen, arXiv:nucl-th/0505036
F. Karsch and E. Laermann, arXiv:hep-lat/0305025
5 July 2006 [email protected] 11
v2(m,pt) and the softest point
Elliptic flow as function of pt and mass very sensitive to EoS (particular the heavier particles)
Before we can draw conclusions about the EoS much more work needed in theory (test different EoS, influence viscosity, hadronic phase)
EoS Q and EoS T (both have significant softening) do provide the best description of the magnitude of the mass scaling in v2(pt)
The lattice inspired EoS (EoS qp) in ideal hydro does as poorly as a hadron gas EoS! (opposite to conclusion Kämpfer)
Pasi Huovinen, arXiv:nucl-th/0505036
5 July 2006 [email protected] 12
Energy dependence
Energy dependence missed by ideal hydro Hydro + cascade describes v2 from SPS to
RHIC At higher energies ideal hydro contribution
dominates Hydro + cascade follows “low density limit”??
NA49, Phys. Rev. C(68), 034903 (2003) Kolb, Sollfrank, Heinz, PRC 62 (2000) 054909
D. Teaney, J. Lauret, E.V. Shuryak, arXiv:nucl-th/0011058; Phys. Rev. Lett 86, 4783 (2001).
Heiselberg and Levi PRC 59
dy
dN
Sv tr
2
5 July 2006 [email protected] 13
v2, eccentricity and fluctuations
2 2
2 2
y x
y x
2v
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
M. Miller and RS, arXiv:nucl-ex/0312008
5 July 2006 [email protected] 14
v2, eccentricity and fluctuations
“standard” v2{2} overestimates v2 by 10%, higher order cumulant underestimate v2 by 10% at intermediate centralities
Measuring the cumulants of different order provides constraints on both fluctuations! and on non-flow contributions!
M. Miller and RS, arXiv:nucl-ex/0312008
5 July 2006 [email protected] 15
PHOBOS eccentricity fluctuations
Large effect for small systems over whole centrality range
x
'x
y'y
S. Manly, QM2005
2 2
2 2
' '
' 'part
y x
y x
5 July 2006 [email protected] 16
v2/ revisited
By using participant eccentricity Cu+Cu and Au+Au at two energies follow the v2/ scaling
Although fluctuations in part are reduced to compared to ”standard” using {2} and v2{4}/{4} could be an improvement
Why does it work that well?
S. Voloshin CIPANP-’06
5 July 2006 [email protected] 17
Rapidity dependence
No boost invariance!
Hirano: Nucl Phys A715 821 824 2003
5 July 2006 [email protected] 18
Rapidity dependence
dN/d scales versus -ybeam
v2/ ~ 1/S dN/dy Rapidity dependence no surprise?
PHOBOS PRL 94, 122303 (2005)PHOBOS nucl-ex/0509034
5 July 2006 [email protected] 19
Rapidity dependence of eccentricity
Is the /S independent of rapidity?
5 July 2006 [email protected] 20
LHC energies
Using dN/dy scaling of multiplicity and v2/eps extrapolation
Values a bit above hydro predictions (from T. Hirano)
2v
ddNch
E. Simili
5 July 2006 [email protected] 21
Energy dependence
The higher the beam energy the more dominant the QGP (here ideal hydro) contribution becomes
T. Hirano
D. Teaney, J. Lauret, E.V. Shuryak, arXiv:nucl-th/0011058; Phys. Rev. Lett 86, 4783 (2001).
5 July 2006 [email protected] 22
Viscosity/entropy versus T
Important to quantitatively calculate the effect of viscosity on v2
Would reduce further the elliptic flow
Csernai, Kapusta and McLerran arXiv:nucl-th/0604032
Hirano and Gyulassy arXiv:nucl-th/0506049
5 July 2006 [email protected] 23
Higher Harmonics
STAR, Phys. Rev. Lett.(92), 062301 (2004)
Higher harmonics are expected to be present, for smooth azimuthal distributions the higher harmonics will be small vn ~ v2
n/2
v4 - a small, but sensitive observable for heavy ion collisions (Peter Kolb, PRC 68, 031902)
v4 - magnitude sensitive to ideal hydro behavior (Borghini and Ollitrault, arXiv:nucl-th/0506045) Ideal hydro v4/v2
2 = 0.5
Peter Kolb, PRC 68, 031902
5 July 2006 [email protected] 24
What do we learn from v4?
Ratio v4/v22 is sensitive to degree of
thermalization (Borghini and Ollitrault nucl-th/0506045) v4(pt)/v2(pt)2 is 1/2 for ideal hydro (more accurate
for increasing values of pt) Observed integrated ratio is larger than unity
Do we have intuitive test if the ratio is related to the degree of thermalization? ratio v4/v2
2 expected to decrease as the collisions become more central
ratio v4/v22 expected to increase as function of
transverse momenta rapidity & energy dependence
5 July 2006 [email protected] 25
v2 and v4 at 200 GeV
STAR preliminary
Y. Bai, AGS users meeting 2006
5 July 2006 [email protected] 26
200 GeV v4{EP2}/v2{4}2
Y. Bai, AGS users meeting 2006
v4/v22 decreases with pt below 1 GeV/c after which is starts to
increase again (expected) Magnitude and centrality dependence do not follow intuitive
expectations
5 July 2006 [email protected] 27
62 GeV v4{EP2}/v2{4}2
Centrality and pt dependence similar to 200 GeV magnitude of v4/v2
2 even somewhat lower! Energy dependence does not follow intuitive expectations
Y. Bai, AGS users meeting 2006
5 July 2006 [email protected] 28
Rapidity dependence
Ratio increases towards midrapidity contrary to expectations
A. Tang
5 July 2006 [email protected] 29
Conclusions Strong collective motion at RHIC energies, consistent with perfect
liquid behavior No microscopic picture available Constraining the EoS requires more detailed calculations
Energy dependence No obvious horns, kinks or steps Collapse of the proton v2 at SPS (next talk) Measurements of v2{2}, v2{4}, v2{6} allow for estimates of the
fluctuations and non flow as function of energy (detailed measurement still needs to be done, strong argument for energy scan)
v2 measurement at LHC will provide critical test of our understanding of the almost perfect liquid, testing the “hydro limit”
Au+Au and Cu+Cu follow v2/ scaling when using part Why does it work that well?
v4 is promising new observable to test hydrodynamic behavior Detailed high statistics measurement available Are the non-flow and fluctuation contributions to v4 under control? Challenge to theory!