Elliptic Flow and Constituent Quark Scaling

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

Elliptic Flow and Constituent Quark Scaling

Documents

Transcript of Elliptic Flow and Constituent Quark Scaling