Marcus Bleicher, Strange Quark Matter 2006 Elliptic Flow and Constituent Quark Scaling Marcus...

Marcus Bleicher, Strange Quark Matter 2006

Elliptic Flow and Constituent Quark ScalingElliptic Flow and Constituent Quark Scaling

Marcus Bleicher1 & Xianglei Zhu2

1Institut für Theoretische Physik2Frankfurt Institute for Advanced Studies

Goethe Universität Frankfurt

Germany


Thanks to the UrQMD group@ Frankfurt

Thanks to the UrQMD group@ Frankfurt

• Sascha Vogel (Resonances)

• Stephane Haussler (Event-by-Event Fluctuations)

• Hannah Petersen (Flow at FAIR)

• Diana Schumacher (Di-Leptons)

• Qingfeng Li (HBT)

• Xianglei Zhu (Elliptic Flow and Charm)

• and Horst Stoecker, Yan Lu, Paul Sorensen, Nu Xu


Parton Number Scaling of v2Parton Number Scaling of v2

P. Soerensen, UCLA & STAR @ SQM2003

•in leading order of v2, recombination predicts:

Bass, Nonaka, Mueller, Fries, 2003

Is this the only explanation?


ContentsContents

• Introduction

• Different methods for v2

• Constituent quark scaling

• Summary


The tool: UrQMDv2.2The tool: UrQMDv2.2

• Non-equilibrium transport model• Hadrons and resonances• String excitation and fragmentation• Cross sections are parameterized

via AQM or calculated by detailed balance• pQCD hard scattering at high energies

• Generates full space-time dynamics of hadrons and strings


Model check: Multiplicities Model check: Multiplicities

• Rapidity distributions in line with data (Phobos)

• Centrality dependence in line with data


Model check: -correlationsModel check: -correlationsQ

. Li

, M

.B.,

H.

Sto

ecke

r, n

ucl-

th/0

602

032;

D

ata:

ST

AR

• Correlations are well described except for most central reactions


Anisotropic flowAnisotropic flow

ϕϕ =

⎡ ⎤= + −Φ⎢ ⎥⎣ ⎦

= +

∑ i Ri 1t t t t

2 2t x y

dN 1 dN1 2v cos(i( ))

p dp dyd 2 p dp dy

p p p

Fourier expansion of the transverseangular distribution of the emitted particles:

v1 – directed flowv2 -- elliptic flow

Reaction PlaneReaction Plane

cos( ( ))n Rv n ϕ=< −Ψ >


Elliptic flowElliptic flow

coordinate-space-anisotropy momentum-space-anisotropy

€

ε =⟨y 2 − x 2⟩⟨y 2 + x 2⟩

v2 = cos2ϕ , ϕ = tan−1(pypx)

• Elliptic flow is a self-quenching effect shuts itself off after the early stage of the reaction

• Radial flow (<pT>) is an integral quantity developed over the whole reaction time


V2 at RHICV2 at RHIC

• Magnitude of v2 is large

• Meson-baryon ordering • Constituent quark scaling

• Decrease of v2 at high pT

Are these unique QGP signatures?


Cumulant: RapidityCumulant: Rapidity

• Differential flowAt large eta, the non-flow effects are less obvious. If the v2

fluctuations are also negligible to the cumulant method, the v2{2}, v2{4} and v2{6} should all agree with the exact v2.

At large eta, the non-flow effects are less obvious. If the v2

fluctuations are also negligible to the cumulant method, the v2{2}, v2{4} and v2{6} should all agree with the exact v2.

X.

Zhu

, M

.B.,

H.

Sto

ecke

r, P

hys.

Rev

.C7

2:0

6491

1,20

05


Cumulants: CentralityCumulants: Centrality

• Integral flow In the most central bin:The fluctuations give larger v2{6} but smaller v2{4}

In the very peripheral bins:The fluctuations give larger v2{6} and v2{4}

Agree with the prediction of MCG model

BUT:In the semi-central bins:the v2 fluctuations can be neglected.

In the most central bin:The fluctuations give larger v2{6} but smaller v2{4}

In the very peripheral bins:The fluctuations give larger v2{6} and v2{4}

Agree with the prediction of MCG model

BUT:In the semi-central bins:the v2 fluctuations can be neglected.

X. Zhu, M.B., H. Stoecker, Phys.Rev.C72:064911,2005


Compare apples to applesCompare apples to apples

• Differential flow

•v2{2} is heavily affected by the non-flow effects especially at large pT.

•The non-flow effects have been eliminated in v2{4} and v2{6}.

•But v2{4} is still a little larger than the exact v2.

Use Lee-Yang zero method

•v2{2} is heavily affected by the non-flow effects especially at large pT.

•The non-flow effects have been eliminated in v2{4} and v2{6}.

•But v2{4} is still a little larger than the exact v2.

Use Lee-Yang zero methodX

. Z

hu,

M.B

., H

. S

toec

ker,

Phy

s.R

ev.C

72:

064

911,

200

5

LYZ-method in UrQMD: nucl-th/0601049


Elliptic flow: MagnitudeElliptic flow: Magnitude

• Integral flow

• V2 from UrQMD is about 50% smaller than the data

• Space for parton rescattering?

STAR data is from nucl-ex/0409033

X. Zhu, M.B., H. Stoecker, Phys.Rev.C72:064911,2005


Energy dependenceEnergy dependenceH

. Pet

erse

n, X

. Zhu

, M.B

.

• Qualitative description OK

• Importance of potentials at low energies

• Lack of pressure shows up at lower SPS energies


When is v2 created?When is v2 created?

• The earlier a particle is emitted the larger is the elliptic flow

• The higher the pT of a particle the larger is the elliptic flow

• High pT particles are more sensitive to the initial v2

Y.

Lu,

M.B

., e

t al

., n

ucl-t

h/06

020

09


Initial ‘string matter’Initial ‘string matter’

• String matter dominates the early stages

lack of early pressure

‘string matter‘ = QGP?

H. P

eter

sen,

X. Z

hu, M

.B.

Strong color field or color glas or a hydrodynamical initial state fix the initial pressure problem


Back to the story line:Back to the story line:

Messengers from the mixed phase: Multi-strange hadrons

freeze-out early all v2 should be from QGP

Thus, if , and ϕ have sufficient v2

Proof of partonic collectivity (maybe QGP)


Indications of early freeze-outIndications of early freeze-out

• Two different groups: (a) ,K,p (b) ϕ,

• Multi-strange particle freeze-out earlier than bulk

Sensitivity to early (partonic) stage

K.

Sch

we

da,

ST

AR

Where will be the charm?


Early freeze-out: modelsEarly freeze-out: models

• Flow ordering

different hadronic cross sections

A. Dumitru, S. Bass, M.B., H. Stoecker, Phys.Lett.B460:411-416,1999

UrQMD, RHIC


Do multi-strange hadrons flow?Do multi-strange hadrons flow?P

. Sor

ense

n, S

QM

200

6

• Data indicates approximate 3:2 scaling with constituent quarks

• Baryons are generally below mesons

•Decrease of v2 at high pT

Is this rough scaling a signal for recombination?


V2(pT) for various hadronsV2(pT) for various hadrons

Open – MesonsFull -- Baryons

1) Clear separation of meson and baryon v2

2) Low pT, v2(meson)>v2(baryon)3) High pT, v2(m)<v2(b)4) v2’s of multi-strange hadrons comparable to light hadrons

1) Clear separation of meson and baryon v2

2) Low pT, v2(meson)>v2(baryon)3) High pT, v2(m)<v2(b)4) v2’s of multi-strange hadrons comparable to light hadrons

min. bias

Y.

Lu,

M.B

., e

t al

., n

ucl-t

h/06

020

09

UrQMD

Maybe its just the additive Quark

model?


NCQ-scalingNCQ-scaling

NCQ-scaling of v2 is roughly reproduced in UrQMD!NCQ-scaling of v2 is roughly reproduced in UrQMD!

•there might be an ordering of v2/n:<<<N

Y.

Lu,

M.B

., e

t al

., n

ucl-t

h/06

020

09

UrQMD

AQM cross sections:

N: 26 mb: 23 mb: 20 mb: 16 mb

: 18 mbK: 14 mb


B-M AsymmetryB-M Asymmetry

Inclusion of gluons in recombination was predicted to lead to a larger meson v2/n than baryon v2/n:B.Müller, et al. nucl-th/0503003


SummarySummary

At RHIC (transport models w/ strings and hadrons):

Part of v2 might also come from hadronic stage

non-flow correlations are correct

Mass ordering is correct

(B-M) Asymmetry has correct shape

Constituent quark scaling (w/o ReCo! but AQM)

However, transport models w/o QGP produce too few pressure in the early stage above 30 GeV


Back up slidesBack up slides


Model check: ExpansionModel check: Expansion

Transverse Expansion of the bulk is described

Model uncertainties on level of 30-50%

Uncertainties depend on:PYTHIA implementation and properties of high mass resonances

Bra

tkov

ska

ya,

M.B

. et

al.,

Phy

s.R

ev.C

69:0

549

07,2

004

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