1

Searching for the QGP at RHIC

Che-Ming Ko Texas A&M University

Signatures of QGP Quark coalescence Baryon/meson ratio Hadron elliptic flows and quark number scaling Effects of resonance decays and hadron wave function Charm flow Higher-order anisotropic flow Summary

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Signatures of quark-gluon plasma

Dilepton enhancement (Shuryak, 1978)

Strangeness enhancement (Meuller & Rafelski, 1982)

J/ψ suppression (Matsui & Satz, 1986)

Pion interferometry (Pratt; Bertsch, 1986)

Elliptic flow (Ollitrault, 1992)

Jet quenching (Gyulassy & Wang, 1992)

Net baryon and charge fluctuations (Jeon & Koch; Asakawa, Heinz & Muller, 2000)

Quark number scaling of hadron elliptic flows (Voloshin 2002)

……………

3

-

Dilepton spectrum at RHIC

MinBias Au-Au

thermal

• Low mass: thermal dominant (calculated by Rapp in kinetic model)• Inter. mass: charm decay

No signals for thermal dileptons yet

4

Enhancement of multistrange baryons

But enhancement is even larger in HI collisions at lower energies

5

J/Ψ production at RHIC

Au+Au @ 200 GeV

c+c+)qq,(g,↔Ψ+)qq,(g, ;c+c↔Ψ+g

withequationrateKinetic

Grandchamp, Rapp, Brown, PRL 92, 212301 (04)

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Pion interferometry

STAR Au+Au @ 130 AGeV

)exp(1

)exp(1

)(

22

222222

invinv

llssoo

Rq

RqRqRq

qC

open: without Coulombsolid: with Coulomb

Au+Au @ 130 GeV

STAR

Ro/Rs~1 smaller than expected ~1.5

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A multiphase transport (AMPT) model

Default: Lin, Pal, Zhang, Li & Ko, PRC 61, 067901 (00); 64, 041901 (01);

72, 064901 (05); http://www-cunuke.phys.columbia.edu/OSCAR

Initial conditions: HIJING (soft strings and hard minijets) Parton evolution: ZPC Hadronization: Lund string model for default AMPT Hadronic scattering: ART

Convert hadrons from string fragmentation into quarks and antiquarks Evolve quarks and antiquarks in ZPC When partons stop interacting, combine nearest quark and antiquark to meson, and nearest three quarks to baryon (coordinate-space coalescence) Hadron flavors are determined by quarks’ invariant mass

String melting: PRC 65, 034904 (02); PRL 89, 152301 (02)

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1 2 1 2 1 2 1 2p f (x,p,t) dp d v v (d /d )(f 'f '-f f )

2 2

2 2 2 2

9 9d 1,

dt 2(t- ) 2 1 /s s

s

Using αs=0.5 and screening mass μ=gT≈0.6 GeV at T≈0.25 GeV, then <s>1/2≈4.2T≈1 GeV, and pQCD gives σ≈2.5 mb and a transport cross section

σ=6 mb → μ≈0.44 GeV, σt≈2.7 mb σ=10 mb → μ≈0.35 GeV, σt≈3.6 mb

t

dd (1 cos ) 1.5mb

d

Zhang’s parton cascade (ZPC)

Bin Zhang, Comp. Phys. Comm. 109, 193 (1998)

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Two-Pion Correlation Functions and source radii from AMPT

Lin, Ko & Pal, PRL 89, 152301 (2002)

Au+Au @ 130 AGeV

Need string melting and large parton scattering cross section which may bedue to quasi bound states in QGP and/or multiparton dynamics (gg↔ggg)

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Emission Function from AMPT

• Shift in out direction (<xout> > 0)• Strong positive correlation between out position and emission time• Large halo due to resonance (ω) decay and explosion → non-Gaussian source

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High PT hadron suppression

Parton energy loss due toradiation and reabsorption

ε0=1.07 GeV/fm, μ=1.5 GeV

Wang & Wang, PRL 87, 142301 (01)

¢ E (b;r;Á)

¼²0(E =¹ ¡ 1:6)1:2=(7:5+E =¹ )

£Z ¢ L

¿0

d¿¿ ¡ ¿0

¿0½0½g(¿;b;~r +~n¿)

Also Gyulassy, Levai & Titev, PRL 85, 5535 (00)

Jet quenching → initial energy density → 5-10 GeV/fm3

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Fragmentation leads to p/π ~ 0.2 Jet quenching affects both Fragmentation is not the dominant mechanism of hadronization at pT < 4-6 GeV

PHENIX, nucl-ex/0212014PHENIX, nucl-ex/0304022

Puzzle: Large proton/meson ratio

π0 suppression: evidence of jet quenching before fragmentation

Au+AuAA

bin p+p

dNR

N dN

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Surprise: quark number scaling of hadron elliptic flow

Except pions, v2,M(pT) ~ 2 v2,q(pT/2) and v2,B(pT) ~ 3 v2,q(pT/3) consistent with hadronization via quark recombination

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Unexpected: Appreciable charm flow

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Coalescence model in heavy ion collisions

Extensively used for light clusters production. First used for describing hadronization of QGP by Budapest group Revived by Oregon: Hwa, Yang (PRC 66 (02) 025205), ……… Duke-Minnesota: Bass, Nonaka, Meuller, Fries (PRL 90 (03) 202303; PRC 68 (03) 044902 ) Ohio and Wayne States: Molnar, Voloshin (PRL 91 (03) 092301; PRC 68 (03) 044901) Texas A&M: Greco, Levai, Rapp, Chen, Ko (PRL (03) 202302; PRC 68 (03) 034904) Most studies are schematic, based on parameterized QGP parton distributions. Study based on parton distributions from transport models has been developed by TAMU group (PRL 89 (2002) 152301; PRC 65 (2002) 034904 ) and also pursued by D. Molnar (nucl-th/0406066).

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Coalescence model

qq3

3

N)p,x(fE)2(

pddp

36/1gg K Mg

ni

n i i q,i i i n 1 n 1 n3i=1 i

dpN =g p d f x ,p f (x ,...,x ;p ,...,p )

2 E

Quark distribution function

Spin-color statistical factor

e.g. 12/1gg *K

Coalescence probabilityfunction

)p,x(fq

PRL 90, 202102 (2003); PRC 68, 034904 (2003)

Number of hadrons with n quarks and/or antiquarks

54/1gg,108/1gg pp

}]/2Δ)m-(m-)p-exp{[(p×

]/2Δ)x-exp[(x=

)p-p;x-x(f=)p,p;x,(xf

2p

221

221

2x

221

212122121M

px

For baryons, Jacobi coordinates for three-body system are used.

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5.0≤||,fm5= yτ

Thermal QGP Power-law minijets Choose

GeV2pT GeV2pT

fm8=R

GeV7885.0

y

T

dy

dE

3fm1100⇒ V

Consistent with data (PHENIX)

Parton transverse momentum distributions

149,245 sdu NNN

P. Levai et al., NPA 698 (02) 631

L/

T=170 MeV

quenchedsoft hard

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jet

had

jet2

2jet/had

jet2

had2 p

pz,

z

)Q,z(D

pd

dNdz

pd

dN

Minijet fragmentation via KKP fragmentation functions (Kniehl, Krammer, Potter, NPB 582, 514 (2000))

Gluons are converted to quark-antiquark pairs with equal probabilities in all flavors. Quark-gluon plasma is given a transverse collective flow velocity of β=0.5 c, so partons have an additional velocity v(r)=β(r/R). Minijet partons have current quark masses mu,d=10 MeV and

ms=175 MeV, while QGP partons have constituent quark masses

mu,d=300 MeV, ms=475 MeV (Non-perturbative effects, Levai &

Heinz, PRC 57, 1879 (1998)) Use coalescence radii Δp=0.24 GeV for mesons and 0.36 GeV for baryons

Other inputs and assumptions

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Au+Au @ 200AGeV (central)

ππρ

Pion and proton spectra

Similar results from other groups Oregon: parton distributions extracted from pion spectrum Duke group: no resonances and s+h but uses harder parton spectrum

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Baryon/Meson ratio

DUKEOREGON

TAMU

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Elliptic flow

Quark v2 extracted from pion and kaon v2 using coalescence model

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Momentum-space quark coalescence model

Quark transverse momentum distribution

q T 2,q Tf (p ) 1 2v (p )cos(2 )

Meson elliptic flow

Baryon elliptic flow

)2/p(v2)2/p(v21

)2/p(2v)p(v T2,q

T22,q

T2,qTM2,

)3/p(v3)3/p(v61

)3/p(3v)p(v T2,q

T22,q

T2,qTB2,

Quark number scaling of hadron v2 (except pions):

n)/p(vn

1T2

Only quarks of same momentumcan coalescence, i.e., Δp=0

same for mesons and baryons

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Effects of hadron wave function and resonance decays

Wave function effectEffect of resonance decays

Wave fun.+ res. decays

Higher fock states → similar effect (Duke)

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Charm spectra

Charm quark D meson J/ψ

Bands correspond to flow velocities between 0.5 and 0.65

NJ/ψ =2.7 . 10-3

NJ/ψ =0.9 . 10-3

T=0.72 GeVT=0.35-0.50 GeV

D

e-

5.2dy

dNc

Au+Au @ 200 A GeV

25Greco, Rapp, Ko, PLB595 (04) 202

S. Kelly,QM04

Charmed meson elliptic flow

v2 of electrons

Data consistent with thermalizedcharm quark with same v2 as lightquarks

Smaller charm v2 than light quarkv2 at low pT due to mass effect

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Charm quark elliptic flow from AMPT

PT dependence of charm quark v2 is different from that of light quarks. At high pT, charm quark has similar v2 as light quarks. Charm elliptic flow is also sensitive to parton cross sections

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Charm elliptic flow from AMPT

Zhang, Chen & Ko, PRC 72, 024906 (05)

Current light quark masses are used in AMPT. Charmed meson elliptic flow will be larger if constituent quark masses are used.

15

10

5

0

-5

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Higher-order parton anisotropic flows

Including 4th order quark flow

q T 2,q T 4,q Tf (p ) 1 2v (p )cos(2 ) 2v (p )cos(4 )

Meson elliptic flow

Baryon elliptic flow

v

v

3

1+

3

1=

v

v ,

v

v

2

1+

4

1=

v

v ⇒ 2

2,q

4,q2

B2,

B4,22,q

4,q2

M2,

M4,

)v+v(2+1

v+v2= v,

)v+2(v+1

vv2+v2=v 2

4,q22,q

22,q4,q

M4,24,q

22,q

4,q2,q2,q

M2,

)vv+v+6(v+1

v3+vv6+v3+v3= v,

)vv+v+v(6+1

vv6+v3+vv6+v3=v

4,q22,q

24,q

22,q

34,q4,q

22,q

22,q4,q

B4,4,q

22,q

24,q

22,q

24,q2,q

32,q4,q2,q2,q

B2,

Kolb, Chen, Greco, Ko, PRC 69 (2004) 051901

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22,q4,q2

2

4 2v v 1.2 v

v

Data can be described by a multiphase transport (AMPT) model with largeparton cross sections.

Data Parton cascade gives v4,q~v2,q

2

Higher-order anisotropic flows

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Summary on quark coalescence

Quark coalescence can explain observed Large baryon/meson ratio at pT~ 3GeV Quark number scaling of hadron v2

→ signature of deconfinement? Coalescence of minijet partons with thermal partons is significant → medium modification of minijet fragmentation. Scaling violation of pion v2 can be explained by resonance decays.

Coalescence of thermalized charm quarks can explain preliminary charmed meson spectrum and v2 as well as J/ψ yield.

Required quark v2 is consistent with that from parton cascade.

Appreciable parton v4 is seen in parton cascade.

Entropy violation (~16%) is not as large as one naively thinks and is related to

corresponding energy violation.

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Summary on QGP search

Most proposed QGP signatures are observed at RHIC.

Strangeness production is enhanced and is consistent with formation of hadronic matter at Tc.

Large elliptic flow requires large parton cross sections in transport model or earlier equilibration in hydrodynamic model.

HBT correlation is consistent with formation of strongly interacting partonic matter.

Jet quenching due to radiation requires initial matter with energy density order of magnitude higher than that of QCD at Tc.

Quark number scaling of elliptic flow of identified hadrons is consistent with hadronization via quark coalescence or recombination.

Studies are needed for electromagnetic probes and heavy flavor hadrons.

Theoretical models have played and will continue to play essential roles in understanding RHIC physics.