Chiho Nonaka

RHICRecombination plus Fragmentation Model

5 @

Chiho Nonaka

Outline Introduction

– QCD Phase diagram, Experimental data Hadronization mechanism

– Recombination + Fragmentation Model– Hadron spectra, hadron ratios, nuclear modification factors

Elliptic Flow– Comparison with experimental data– Quark number scaling

• v2 for resonances• v2 for exotic particles• v2 at SPS

Summary

Chiho Nonaka

Phenomenological Analyses QCD phase diagram

• Phase transition Quark Gluon PlasmaQGP phase Hadron phase

•Recent QCD phase diagram–Critical End Point–cc bound state–Color superconductor phase

Hadron phase

ggcc

qqCEP

QGP phaseT

µΒ

QCD Experiment

Chiho Nonaka

EOS from Lattice QCD

Karsch, Laermann, Peikert, PLB478(2000)447

Chiho Nonaka

Relativistic Heavy Ion Collider

PHOBOS BRAHMS

PHENIX

Chiho Nonaka

RHIC QCD Phase diagram Experiment

• Difficulty in QGP search quarks and gluon: Confinement

• ObservablesHadron spectra single, two particle correlationflowFluctuation(charge transverse momentumPhoton, lepton etc.

Collisions Initial State Thermalization Hadronization Freeze outFinal Interactions

LHC

RHIC

Chiho Nonaka

Experimental Data ( I ) Proton Puzzle at RHIC

p/π ratio ~ 1 (PT>2 GeV) in central collisions

(PHENIX:nucl-ex/0307022)

• Hadronization from Fragmentation at high PT

g qq

: KKP fragmentation function)(zDha!

p/π ratio << 1

p/π

Chiho Nonaka

Au+Au at sqrt(sNN)=200GeVr.p. |η=3~4min. bias

Experimental Data ( II )

• Saturation in v2 of baryon occurs at higher PT than one of meson.PHENIX : nucl-ex/0305013

))2cos(2)cos(21( 210 !!!

vv ++" vd

dN

(STAR : nucl-ex/0306007)

Hydro : Huovinen et al.,PLB503,58(2001)

At low PTAt Low PTHydro works well

Chiho Nonaka

Experimental Data ( III )

Sorensen@SQM2003

• There are some correlations between RAA and v2.

• Suppression in RAA of baryon occurs at higher PT than one of meson.

22

coll

22

/)(

/)(

Tpp

TAA

AAdPNdbN

dPbNdR uu

+

+=

Nuclear modification factor

• Intermediate PT# of valence quarks

• High PTFragmentation

Hints from experimental data

Chiho Nonaka

Recombination + Fragmentation Model Recombination at moderate PT

– Recombination occurs in an instant.

– The parton spectrum is shifted to higher pT in the hadron spectrum.

– Entropy and energy conservation– No gluon dynamics

Fragmentation at high PT– The parton spectrum has a power law tail (quarks and gluons) from pQCD.– The parton spectrum is shifted to lower pT in the hadron spectrum.

recombiningpartons:p1+p2=ph

fragmenting parton:ph = z p, z<1

Recomb.

Frag.

Chiho Nonaka

Formalism of Recombination Number of meson

Effective wave function

Covariant form on hadronizaion hypersurface Σ

mesonparton

Integral over q in terms of light cone coordinates

: phase space distribution of parton: degree of freedom of meson: Wigner function

: Meson states with momentum P: density matrix for systems of parton

)2/)(( 21 ppq !=

Chiho Nonaka

Recombination vs. Fragmentation

i. Parton spectrum:

ii. Parton spectrum: (power law)

(exponential)Recomb.

Recomb.

Frag.

Frag.

: KKP fragmentation function

• Important feature

• Important feature

Recombination

Fragmentation

Chiho Nonaka

Input for Quantitative Calculation Recombination

Fragmentation

• K=1.5 :roughly account for higher order corrections• C, B, β are taken from a leading order pQCD calculation

Energy Loss :

γ : fugacity factor, Δ: rapidity widthf(ρ,φ): transverse distribution

T=175 MeV, τ=5 fm, vT=0.55

Spectrum of parton

Spectrum of parton

Hadron SpectraHadron Spectra

RF

R+FRF

RF

R+FRF

2 4 6 8 10 12PT [GeV]

Chiho Nonaka

Hadron Ratios vs. PTR + FR

Statistical model

ThermalRecomb.

Frag

• Up to 4 GeV, thermal model describes data well.

• supports transition from recomb to fragmentation at intermediate PT.

• Up to PT ~ 6 GeV, recombination pQCDcalculation p/π ratio << 1

Chiho Nonaka

Centrality dependence0!

PRC68,044902(2003) • Centrality dependence of

• In peripheral collision, fragmentation becomes more and more important.

p/π0

Chiho Nonaka

Nuclear Modification Factors ( I )Nuclear modification factor

• Central collision• Both results are consistent with

data.• Peripheral collision

• Uncertainty in pQCD is large.• Jet quenching effects are much

weaker.

Chiho Nonaka

• 2 < PT < 4 GeV RCP (baryon) > RCP (meson) Recombination• 4 < PT < 6 GeV steep drop Transition from Recom. to Frag.• High PT suppression Fragmentation

Nuclear Modification Factors ( II )Nuclear modification factor

RF

φ ?

Chiho Nonaka

Intermediate PT

22

coll

22

coll

/)()0(

/)0()(

TAA

TAA

CP

dPbNdN

dPNdbNR

uu

uu

+

+=

Nuclear modification factor

Velkovska(PHENIX)@QM2004

• Recombination mechanism works!

φ

Chiho Nonaka

Elliptic Flow

))2cos(2)cos(21( 210 !!!

vv ++" vd

dN

Anisotropy of collective flow

• Thermalization• Equation of state

• Sensitive to initial geometry

• At intermediate PT Recombination• At high PT Fragmentation

• Hadronization mechanism RHIC

Chiho Nonaka

Quark Number Scaling in v2

Hadronization from recombination

• number of constituent quark

Voloshin, NPA715(2003)379Molnar and Voloshin, PRL91 (2003)092301Lin and Molnar, PRC68 (2003) 044901Greco and Ko, PRC68 (2003) 034904Our group, PRC68,044902(2003) , PLB587,73(2004)

P. Sorensen

Chiho Nonaka

Elliptic Flow

Recomb.

Frag.

Elliptic flow is sensitive to initial geometry

Total elliptic flow

At moderate PTrecombination

• Pressure gradient• Collision plane > Perpendicular plane

r(pt): relative weight of the recombination contribution in spectra

At high PTfragmentation

• Energy loss• Perpendicular plane > Collision plane

Chiho Nonaka

Elliptic Flow

Mesons

Baryons

• v2 of baryons saturates at a higher value than for mesons.• At high PT, v2 is dominated byfragmentation. v2 of baryon and meson is identical.

Hydrodynamical model• v2 of φ is almost the same as that of K.

• For saturation feature, the mass effect in v2 is negligible. # of valence quarks

PLB587,73(2004)

Chiho Nonaka

Comparison with Hydrodynamical Model

• # of valence quarks

Universal v2 curve

• Low PT

• Intermediate PT

• High PT

• Mass effect

• Fragmentation

• Saturation feature

(Blast wave model) Hydrodynamical Model

Recombination + Fragmentation

φ : mass effect ? recombination ?

Chiho Nonaka

Intermediate PT

22

coll

22

coll

/)()0(

/)0()(

TAA

TAA

CP

dPbNdN

dPNdbNR

uu

uu

+

+=

Nuclear modification factor

Velkovska(PHENIX)@QM2004

• Recombination mechanism works!

φ

Chiho Nonaka

• Up to intermediate PT

Quark number scaling from quark recombination

• At high PTUniversal curve from fragmentation

Recombination & Fragmentation Model

RCP of φ (STAR, PHENIX)

Brief Summary for Elliptic FlowElliptic Flow

Key: Quark Number Scaling

Resonances ? final interactionsExotic particles ? hadron structure

v2

PT

?v2 quark

v2 hadron

Chiho Nonaka

v2 for resonance particles QGP resonances:

hadronizing QGP, no rescattering

HG resonances: hadron final stage, h-h rescattering

Key: v2 is additive for composite particles

TotalHG

2

QGP

2

full

2 ))(1()( vPrvPrvTT

!+=

is determined by experiments and related to width of particles and cross section in the hadronic medium.

Final Interactionsfreeze-out process

7.0:)(TPr

7.0:)(TPr

quarks n=2 scaling

n=4 scalingn=4 scaling

Chiho Nonaka

v2 for exotic particles

compact 5 quark state ?K-N molecular state ?

5 q reco. + direct fragmentation

K + N reco. + direct fragmentation(molecule)

• QGP hadronization (direct)

•

at high PT

Structure of exotic particlesn=5scaling

 

K N

5q

At intermediate PT , there are measurable differences (up to 20 %) between them.

Other exotic candidates

• 3rd possible scenario

and so on

n=3 scaling

Chiho Nonaka

Elliptic Flow at SPS ( I ) Hadrons in QGP?

Shuryak@QM2004• Lattice QCD Bielefeld group, Asakawa-Hatsuda and Umeda et al.

survive up to and

Quark number scaling

Quark number scaling ?

• RHIC q-q melts.

• SPS q-q exists.

Ex.

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Elliptic Flow at SPS ( II )

• Fragmentation mechanism should be negligible.

Assumption Thermalization is achieved.

Quark number scaling is broken down !

If q-q exists,

Chiho Nonaka

Summary

• Up to intermediate PTQuark number scaling from quark recombination

• At high PTUniversal curve from fragmentation

Recombination & Fragmentation Model Hadronization Mechanism

Elliptic Flow –– Useful tool ––PT

Hydro(Thermal) Recombination Fragmentation

• Quark number scalingFinal inteructions, Hadron structure, Phase structure

Correlations

Fluctuations

Chiho Nonaka

Impact Parameter Dependence

STAR:nucl-ex/0407007

Peripheral Collisions

?

•Recombination mechanismShuryak,PRC66,027902(2002)X-N.Wang, nucl-th/0305010

Chiho Nonaka

Chiho Nonaka

Fluctuation Bialas hep-ph/0205047

?• Recombination mechanism

Two-particle correlation