energy dependence of anisotropic flow

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


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?


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


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


The perfect liquid


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


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


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!?


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


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


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


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


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


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


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


Rapidity dependence

No boost invariance!

Hirano: Nucl Phys A715 821 824 2003


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


Rapidity dependence of eccentricity

Is the /S independent of rapidity?


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


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).


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


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


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


v2 and v4 at 200 GeV

STAR preliminary

Y. Bai, AGS users meeting 2006


200 GeV v4{EP2}/v2{4}2


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


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



Rapidity dependence

Ratio increases towards midrapidity contrary to expectations

A. Tang


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!

energy dependence of anisotropic flow

Documents

qcd eos

eos particular

ptparticles flow

different eos qp

hadron gas eos

flownon flow correlation

strong radial flow

softest pointelliptic