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
1
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)
 ……………
2
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
3
Enhancement of multistrange baryons
But enhancement is even larger in HI collisions at lower energies
4
J/Ψ production at RHIC
Kinetic rate equation with
g + Ψ ↔ c + c ; (g, q, q) + Ψ ↔ (g, q, q) + c + c
Au+Au @ 200 GeV
Grandchamp, Rapp, Brown,
PRL 92, 212301 (04)
5
Pion interferometry
open: without Coulomb
solid: with Coulomb
STAR
Au+Au @ 130 GeV
STAR Au+Au @ 130 AGeV
C ( q)
 1  exp(  qo2 Ro2  qs2 Rs2  ql2 Rl2 )
 1  exp(  q R )
2
inv
2
inv
Ro/Rs~1 smaller than expected ~1.5
6
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
String melting: PRC 65, 034904 (02); PRL 89, 152301 (02)
 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
7
Zhang’s parton cascade (ZPC)
Bin Zhang, Comp. Phys. Comm. 109, 193 (1998)
p    f1 (x,p,t)   dp2d v1  v 2 (d /d)(f1'f 2'-f1f 2 )
9 s2
9 s2
d
1

,


dt 2(t- 2 )2
2 2 1   2 / 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
d
 t   d
(1  cos )  1.5mb
d
 σ=6 mb → μ≈0.44 GeV, σt≈2.7 mb
 σ=10 mb → μ≈0.35 GeV, σt≈3.6 mb
8
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 be
due to quasi bound states in QGP and/or multiparton dynamics (gg↔ggg)
9
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
10
High PT hadron suppression
Wang & Wang, PRL 87, 142301 (01)
Parton energy loss due to
radiation and reabsorption
¢ E (b; r; Á)
¼ ² 0 (E =¹ ¡ 1:6) 1:2 =(7:5 + E =¹ )
Z ¢L
¿ ¡ ¿0
£
d¿
½g (¿; b; ~
r+~
n ¿)
¿0 ½0
¿0
ε0=1.07 GeV/fm, μ=1.5 GeV
Also Gyulassy, Levai & Titev,
PRL 85, 5535 (00)
Jet quenching → initial energy density → 5-10 GeV/fm3
11
Puzzle: Large proton/meson ratio
PHENIX, nucl-ex/0304022
R AA 
dN Au+Au
N bin dN p+p
π0 suppression: evidence of jet
quenching before fragmentation
PHENIX, nucl-ex/0212014
 Fragmentation leads to p/π ~ 0.2
 Jet quenching affects both
 Fragmentation is not the dominant
mechanism of hadronization at
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pT < 4-6 GeV
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
13
Unexpected: Appreciable charm flow
14
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).
15
Coalescence model
PRL 90, 202102 (2003); PRC 68, 034904 (2003)
Number of hadrons with n quarks and/or antiquarks
n
N n =g   pid i
i=1
Spin-color
statistical factor
Quark distribution
function
Coalescence
probability
function
x  p  
gM
dpi
 2 
e.g.
3
Ei
f q,i  x i , pi  f n (x1 ,...,x n ;p1 ,...,p n )
g   g K  1 / 36 g   g K  1 / 12
*
g p  g p  1 / 108, g   g   1 / 54
f q ( x , p)
d 3p
 p  d (2)3 E fq (x, p)  Nq
f M (x 1 , x 2 ; p1 , p 2 ) = f 2 ( x1 - x 2 ; p1 - p 2 )
= exp[(x 1 - x 2 ) 2 /2Δ 2x ]
× exp{[(p 1 - p 2 ) 2 - (m1 - m 2 ) 2 ]/2Δ 2p }
For baryons, Jacobi coordinates for three-body system are used.
16
Parton transverse momentum distributions
T=170 MeV
 Thermal QGP pT  2 GeV
 Power-law minijets pT  2 GeV
 Choose R = 8 fm
τ = 5 fm ,
| y |≤0.5
⇒ V  1100 fm 3
soft
hard
L/l3.5
P. Levai et al., NPA 698 (02) 631
N u  N d  245, N s  149
dET
dy
 788 GeV
y  0.5
Consistent with data
(PHENIX)
17
Other inputs and assumptions
 Minijet fragmentation via KKP fragmentation functions
(Kniehl, Krammer, Potter, NPB 582, 514 (2000))
2
p had
dN
dN D had / jet (z, Q )
   dz 2 
, z
2
2
d p had jet
d p jet
z
p jet
 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
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Pion and proton spectra
ρ  ππ
Au+Au @ 200AGeV (central)
Similar results from other groups
 Oregon: parton distributions extracted from pion spectrum
 Duke group: no resonances and s+h but uses harder parton spectrum
19
Baryon/Meson ratio
TAMU
 > 
OREGON
DUKE
20
Elliptic flow
Quark v2 extracted from pion and kaon v2 using coalescence model 21
Momentum-space quark coalescence model
Only quarks of same momentum
can coalescence, i.e., Δp=0
Quark transverse momentum distribution
f q (pT )  1  2v 2,q (pT )cos(2 )
Meson elliptic flow
v 2,M ( pT ) 
2v 2,q ( pT / 2)
1  2 v ( p T / 2)
2
2,q
 2 v 2,q ( pT / 2)
Baryon elliptic flow
v 2,B ( pT ) 
3v 2,q ( pT / 3)
1  6v ( pT / 3)
2
2,q
 3v 2,q ( pT / 3)
Quark number scaling
of hadron v2 (except pions):
1
v 2 ( pT / n)
n
same for mesons and baryons
22
Effects of hadron wave function and resonance decays
Effect of resonance decays
Wave function effect
Higher fock states → similar effect (Duke)
Wave fun.+ res. decays
23
Charm spectra
Charm quark
D meson
J/ψ
dNc
 2.5
dy
D
e-
Au+Au @ 200 A GeV
Bands correspond to flow velocities
between 0.5 and 0.65
T=0.72 GeV
T=0.35-0.50 GeV
NJ/ψ =2.7 . 10-3
NJ/ψ =0.9 . 10-3
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Charmed meson elliptic flow
Smaller charm v2 than light quark
v2 at low pT due to mass effect
S. Kelly,QM04
v2 of electrons
Greco, Rapp, Ko, PLB595 (04) 202
Data consistent with thermalized
charm quark with same v2 as light
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quarks
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
26
Charm elliptic flow from AMPT
Zhang, Chen & Ko, PRC 72, 024906 (05)
15
10
5
0
-5
Current light quark masses are used in AMPT. Charmed meson
elliptic flow will be larger if constituent quark masses are used.
27
Higher-order parton anisotropic flows
Including 4th order quark flow Kolb, Chen, Greco, Ko, PRC 69 (2004) 051901
f q (pT )  1  2v 2,q (pT )cos(2 )  2v 4,q (p T )cos(4 )
Meson elliptic flow
v 2,M =
2v 2,q + 2v 2,q v 4,q
1 + 2(v
2
2,q
2
4,q
+v )
, v 4,M =
2v 4,q + v 22,q
1 + 2( v 22,q + v 24,q )
Baryon elliptic flow
v 2,B =
3v 2,q + 6v 2,q v 4,q + 3v 32,q + 6v 2,q v 24,q
2
2,q
2
4,q
2
2,q 4,q
1 + 6( v + v + v v )
, v 4,B =
3v 4,q + 3v 22,q + 6v 22,q v 4,q + 3v 34,q
1 + 6(v 22,q + v 24,q + v 22,q v 4,q )
v 4,M 1 1 v 4,q v 4,B 1 1 v 4,q
⇒ 2 = + 2 , 2 = + 2
v 2,M 4 2 v 2,q v 2,B 3 3 v 2,q
28
Higher-order anisotropic flows
Data can be described by
a multiphase transport
(AMPT) model with large
parton cross sections.
Data
v4
2

1.2

v

2v
4,q
2,q
v 22
Parton cascade gives v4,q~v2,q2
29
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.
30
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.
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