Transcript Slide 1
Searching for the Quark-Gluon Plasma
in Relativistic Heavy Ion Collisions
Che-Ming Ko
Teaxs A&M University
Introduction: concepts and definitions
- Quark-gluon plasma (QGP)
- Heavy ion collisions (HIC)
Experiments and theory
- Signatures of QGP
- Experimental observations
Largely based on slides by Vincenzo Greco
Big Bang
• e. m. decouple (T~ 1 eV , t ~ 3.105 ys)
“thermal freeze-out “
• but matter opaque to e.m. radiation
• Atomic nuclei (T~100 KeV, t ~200s)
“chemical freeze-out”
• Hadronization (T~ 0.2 GeV, t~ 10-2s)
• Quark and gluons
We’ll never see what happened at
t < 3 .105 ys (hidden behind the curtain of
the cosmic microwave background)
Bang
HIC can do it!
Little Bang
N D N “Elastic”
finite Dt
Freeze-out
Hadron Gas
Phase Transition
Plasma-phase
Pre-Equilibrium
Heuristic QGP phase transition
Free massless gas
E
g 3
4 gtot g g 78 ( gq gq )
d p p f ( p) gtot T
3 0
V (2 )
30 g g 16 , gq gq Nc Ns N f
Bag Model
EH
C
PH
B
V
4R4
P 0 RH
Pressure exceeds the Bag
pressure -> quark liberation
37 2 904 1/ 4 B1/4 ~ 210 MeV
Tc T
2 B B
> Tc~ 145 MeV
37
90
1/ 4
Extension to
finite mB , mI
Quantum ChromoDynamics
1
m
m a
ψi γ m i gAa ψi mi ψi ψi Fam Fam
2
4 a
i 1
nf
Fam m Aa Aam i f abc Abm Ac
Similar to QED, but much richer structure:
SU(3) gauge symmetry in color space
Approximate Chiral Symmetry in the light sector
which is broken in the vacuum.
UA(1) ciral
Scale Invariance broken by quantum effects
Phase Transition in lattice QCD
Enhancement of the degrees
of freedom towards the QGP
0.7 GeV / fm 3
Tc 173 15 MeV
Noninteracting massless partons
qq
2 7
4
g
6n f 16 T
30 4
Gap in the energy density
(Ist order or cross over ?)
QCD phase diagram
From high rB regime
to high T regime
AGS
SPS
RHIC
2
sNN ( pA pB )2 ECMS
We do not observe hadronic systems
with T> 170 MeV (Hagedon prediction)
Definitions and concepts
in HIC
Kinematics
Observables
Language of experimentalist
The RHIC Experiments
Au+Au
STAR
Soft and Hard
SOFT (non-pQCD) string fragmentation in e+e , pp … or
(pT<2 GeV)
string melting in AA (AMPT, HIJING, NEXUS…)
QGP
HARD minijets from first NN collisions
Independent Fragmentation : pQCD + phenomenology
• Small momentum transfer
• Bulk particle production
– How ? How many ? How are they
distributed?
• Only phenomenological
descriptions available (pQCD
doesn’t work)
99% of particles
Collision Geometry - “Centrality”
Spectators
Participants
S. Modiuswescki
15 fm
0
b
N_part
For a given b,
Glauber model
0 fm predicts N
part
394 and Nbinary
Kinematical observables
1 E pz
y ln
2 E pz
Additive like Galilean velocity
y j / CM y j / LAB yLAB / CM
Transverse mass
mT m p
2
2 1/ 2
T
E mT cosh y , pz mT sinh y
Angle with respect to beam axis
1 | p | pz
ln tan( / 2) ln
2 | p | pz
PHOBOS
Rapidity -pseudorapidity
dN
m2
dN
1 2
2
ddpT
mT cosh y dyd pT
PHOBOS
Energy Density
| Dy | 0.5
Energy density a la Bjorken:
dET
1 dET
ε
2
AT dz πR τ dy
Particle streaming from origin
z
v z tanh y
t
dz cosh y dy
R 1.18 A
1/3
7 fm
τSPS 1 fm/c
τ RHIC 0.4 1 fm/c
Estimate for RHIC:
dET/dy ~ 720 GeV
Time estimate from hydro:
0.6 fm/c ~ 8 GeV/fm3
Tinitial ~ 300-350 MeV
Some definitions I: radial collectiv flows
Slope of transverse momentum spectrum
is due to folding temperature with radial
collective expansion <bT> from pressure.
Absence
1
Non relativistic pT m , Tsl Tf m v T
2
1 vT
Ultra relativistic pT >> m, Tsl Tf
1 vT
2
Slopes for hadrons with different masses
allow to separate thermal motion
from collective flow
Tf ~ (120 ± 10) MeV
<bT> ~ (0.5 ± 0.05)
Collective flow II: Elliptic Flow
Fourier decomposition of particle
momentum distribution in x-y plane
dN
dN
1 2 vn cos(n )
dpT d dpT
n
z
y
x
Anisotropic Flow
Measure of the pressure gradient
Good probe of
early pressure
v2 is the 2nd Fourier coeff. of particle
transverse moment distribution
px2 p y2
v2 cos 2 2
px p y2
Anisotropic flow
Anisotropic flow vn
d3N
dN
1
dN
E 3
1
2v
(p
,
y)cos(n
)
n T
d p pT dpT d dy 2 pTdpTdy n=1
Sine terms vanish because of the symmetry in A+A collisions
Initial
x spatial
anisotropy
Pressure
gradient
anisotropy
Anisotropic
flows
Statistical Model
Temperature
Yield
Maximum entropy principle
Mass
Chemical Potential
Quantum Numbers
Is there a dynamical evolution that
leads to such values of temp. &
abundances?
Hydro adds radial flow &
freeze-out hypersurface
for describing the
differential spectrum
Yes, but what is Hydro?
HYDRODYNAMICS
Local conservation Laws 5 partial diff. eq. for 6 fields (p,e,n,u)
+ Equation of State p(e,nB)
m
mT ( x ) 0 T m ( x) e( x) p( x)u m ( x)u ( x) p( x) g m
m
j
m B ( x ) 0 jBm ( x) nB ( x)u m ( x)
No details about collision dynamics (mean free path >0)
Transport Model
Follows time evolution of particle distribution
f q , g ( r , p, t )
from initial non-equilibrium partonic phase
f p
r f rU p f I coll
t m
drift
2 2
coll
Ip
m
m
f ( fI3
1 2 3
mean field
Non-relativistically
collision
I
I
4 12
2
2
2
3
f 4 f1 f 2 )W1234 ( p1
coll
coll
coll
gg>ggg
Relativistically
p
p
2... 3 p4 )
g>gg
To be treated:
- Multiparticle collision (elastic and inelastic)
- Quantum transport theory (off-shell effect, … )
- Mean field or condensate dynamics
at High density
Transport
Spectra still appear thermal
Hydro
Elliptic Flow
rapidity
rapidity
• Chemical equilibrium with a limiting Tc ~170MeV
• Thermal equilibrium with collective behavior
- Tth ~120 MeV and <bT>~ 0.5
• Early thermalization ( < 1 fm/c, ~ 10 GeV/fm3)
- very large v2
We have not just crashed 400 balls to get fireworks,
but we have created a transient state of plasma
A deeper understanding of the system
is certainly needed!
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)
……………
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
Strangeness Enhancement
Basic Idea:
Production threshold is lowered in QGP
In the QGP:
qq ss
QQGP 2ms 250 300 MeV
g g s s
Hadronic channels:
K K (Q 2mK 2m 710 MeV )
NN NK
(Q m mK mN 670 MeV )
N K
(Q m mK mN m 530 MeV )
Equilibration timescale? How much time do we have?
QGP Scenario
Hadronic Scenario
Decreasing threshold in
a Resonance Gas
N D N K
(Q 380 MeV )
D K (Q 240 MeV )
DD NK
r
(Q 90 MeV )
(Q 80 MeV )
To be weighted with
the abundances
npQCD calculation with quasi particle picture
and hard-thermal loop still gives t~5-10 fm/c
How one calculates the Equilibration Time
d3p
Tm 2 1 nm
req g
K2
3 f ( p)
2 n 1 n T
(2 )
dr S
g12 v
dt
r1r2 v
12 SS
72 qq
g12 N N N f
256 gg
2
c
2
s
r
SS 12
2
S
Similarly in hadronic case
but more channels
Reaction dominated by gg
6 fm/c
(pQCD) Equilibration time in
QGP teq ~10 fm/c > tQGP
Hadronic matter teq ~ 30 fm/c
Experimental results
Strangeness enhancement 1
Ej
Y /N
Y / N
j
wound
j
wound ref
AA
Strangeness enhancement 2
2ss
S
uu dd
e+e- collisions
Schwinger mechanism
J/Y suppression
In a QGP enviroment:
• Color charge is subject to screening in QGP
> qq interaction is weakened
• Linear string term vanishes in the deconfined phase
(T) > 0 deconfinement
q
V / TC
q
q,q,g distribution modified
Coulomb > Yukawa
V
eff
r
eff
r
e
r
D
rTC
=0 doesn’t mean no bound !
Screening Effect
• Abelian
• Non Abelian
(gauge boson self-interaction)
eff (T )
1
H
e
2 mr 2
r
Bound state
TBound
0.84
r
D ( T )
solution
dE(r )
0
dr
m
2 eff
D >
210 MeV
9
150 MeV
V
2
c c g (T )
4
One loop pQCD
Nc N f
D
6
3
1.2
eff m
4 r
1.2 rBohr
1
2
gT
1
2 / 3 gT
1
1
latt
0
.
3
T
D
TBound is not Tc !
In HIC at √s ~ SPS, J/Y should be suppressed !
Lattice result for V channel (J/y)
A(w) w2r (w)
J/y (p 0) disappears
between 1.62Tc and 1.70Tc
cu , cd D cs Ds
c u, c d D
J/Y
Initial production
Dissociation
In the plasma
c s Ds
Suppression
respect
Recombine
with to
extrapolation
from pp
light quarks
For light quarks rBohr ~ 4 fm >> D , dissociation is more effective
but of course also recombination
Associated suppression of charmonium resonances Y’, cc , …
as a “thermometer”, like spectral
lines for stellar interiors
B quark in similar condition at RHIC as Charmonium at SPS
NUCLEAR ABSORBTION
pre-equilibrium cc formation time and
absorbtion by comoving hadrons
HADRONIC ABSORBTION
rescattering after QGP formation
J / Y h ( , r,w,...) D D
DYNAMICAL SUPPRESSION
(time scale, g+J/Y > cc,…)
pA (models)
abs ~ 6 mb
Fireball dynamical evolution
Dynamical dissociation
J/y + g
c+c+X
gluon-dissociation,
inefficient for
my≈ 2 mc*
“quasifree” dissoc.
[Grandchamp ’01]
• RHIC central: Ncc≈10-20,
• QCD lattice: J/y’s to ~2Tc
If c-quarks
thermalize:
dNy
d
Regeneration in QGP / at Tc
J/y + g
c+c+X
y ( Ny Nyeq )
→
←
[Grandchamp
+Rapp ’03]
Charmonia in URHIC’s
RHIC
• dominated by regeneration
• sensitive to:
mc* , open-charm degeneracy
SPS
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
Source radii from hydrodynamic model
Fails to explain the extracted source sizes
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)
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
Jet quenching
Decrease of mini-jet hadrons (pT> 2 GeV) yield,
because of in medium radiation.
Ok, what is a mini-jet?
why it is quenched ?
High pT Particle Production
High pT (>
~ 2.0 GeV/c) hadron production in pp collisions
Jet: A localized collection of hadrons which
come from a fragmenting parton
hadrons
Parton Distribution Functions
Hard-scattering cross-section
c
a
b
d
hadrons
Fragmentation Function
leading
particle
phad= z pc , z <1 energy needed
to create quarks from vacuum
h
d pp
0
D
d
2
2
h/c
K
dx
dx
f
(
x
,
Q
)
f
(
x
,
Q
)
(
ab
cd
)
a
b a
a
b
b
dyd 2 pT
dtˆ
zc
abcd
“Collinear factorization”
Jet Fragmentation-factorization
, K, p ...
c
b
dNh
dNc
dzc 2 Dch ( zc )
2
d ph
d pc
c
a
A
B
d
ph= z pc , z <1 energy needed
to create quarks from vacuum
AB= pp (e+e)
a,b,c,d= g,u,d,s….
dNc distribution after pp2collision 2
Parton
dx dx f ( x , Q ) f ( x , Q )
2
d pc
a
b
a
A
a
b
B
b
c
sˆ dσ
( ab cd ) δ( sˆ tˆ uˆ )
π dtˆ
(+ phenomenological kT smearing
due to vacuum radiation)
Dc p ( z )
Dc ( z )
0.2
p/ < 0.2
B.A. Kniehl et al., NPB 582 (00) 514
High pT Particle Production in A+A
h
AB
dN
2
2
ABK
dx
dx
d
k
d
kb
a
b
a
2
abcd
dyd pT
f a / A ( xa , Q 2 ) f b / B ( xb , Q 2 )
g (k a ) g (k b )
pc* pc (1 )
zc* zc /(1 )
Parton Distribution Functions
Intrinsic kT , Cronin Effect
S A ( xa , Qa2 ) S B ( xb , Qb2 )
Shadowing, EMC Effect
d
(ab cd ) Hard-scattering cross-section
dtˆ
1
zc*
Partonic Energy Loss
0 dP( )
zc
Dh0/ c ( zc* , Qc2 )
Fragmentation Function
zc
c
a
b
d
hadrons
leading particle
suppressed
Energy Loss
~ Brehmstralung radiation in QED
Color makes a difference
k
pi
pi
pf
×
×
pi
pf
a
pf
c
k
×
Gluon multiple scattering
Static scattering centers assumed
thickness
dE
s Nc qˆ L DE qˆL2
dx
t form
Non-Abelian gauge
Transport coefficient
qˆ
q
2
2
m Debye
x
v
scatt
coh
N
1 w
k k
lcoh
lcoh / > 1
Medium Induced Radiation
c
M 2,1,1
Clearly similar Recursion Method is needed
to go toward a large number of scatterings!
Ivan Vitev, LANL
Jet Quenching
L/ opacity
Large radiative energy loss
in a QGP medium
DE/E ~ 0.5
Jet distribution
Non – abelian energy loss
DE ( 0) 3α μL 2E
log 2
E
4 g
μ L
DE E weak pT dependence
of quenching
Quenching
Energy Loss and expanding QGP
qL
2
eff
2E
d r ( , ) ln
2
m
(
)
r ( ) r0 / 0
out
0
Probe the density
m ( ) gT ( ) g r ( ) / 2
In the transverse plane
Quenching is angle dependent
dN
dN
1 2 vn cos(n )
dpT d dpT
n
px2 p y2
v2 cos 2 2
px p y2
1/ 3
How to measure the quenching
Self-Analyzing (High pT) Probes of the Matter at RHIC
Nuclear
Modification
Factor:
d 2 N AA / dpT d
RAA ( pT )
2
NN
N coll d N / dpT d
nucleon-nucleon
cross section
<Ncoll>
AA
If R = 1 here, nothing new
going on
Centrality Dependence
Au + Au Experiment
d + Au Control
• Dramatically different and opposite centrality evolution of
Au+Au experiment from d+Au control.
• Jet suppression is clearly a final state effect.
Is the plasma a QCD-QGP?
Consistent with L2 non-abelian plasma behavior
Consistent with ~ 10 GeV (similar to hydro)
Baryon-Meson Puzzle
pions
protons
PHENIX,nucl-ex/0212014
PHENIX, nucl-ex/0304022
0 suppression: evidence of jet
quenching before fragmentation
Fragmentation p/ ~ 0.10.2
Jet quenching should affect both
Fragmentation is not the dominant
mechanism of hadronization at
pT ~ 1-5 GeV !?
Coalescence vs. Fragmentation
Parton spectrum
Fragmentation:
Leading parton pT
ph= z pT
according to a probability Dh(z)
z < 1, energy needed to create quarks
from vacuum
Coalescence:
BM
partons are already there
$ to be close in phase space $
ph= n pT ,, n = 2 , 3
baryons from lower momenta
Even if eventually
Fragm. takes over …
p p
C ( pT ) T T
2 2
p
F ( pT ) T
z
C 4
F z pT
Coalescence
dN m
2
3
3
VF d p1d p2 f q ( p1 ) f q ( p2 ) Μ(qq m)
3
d P
Our implementation
Mqqm
2
npQCD
1 dN q
f q ( p)
VF d 3 p
2
3
W
(3)
p1 , p2 | P, m gm d r f m (r , q) δ ( P p1 p2 )
9π
f D2x ( x1 x2 ) 2 D2p ( p1 p2 ) 2 (m1 m2 ) 2
2
D x 1/ D p coal . parameter
|Mqq->m|2 depends only on the
gm spin color probabilit
y
phase space weighted by wave
function (npQCD also encoded
Energy not conserved
in the quark masses , mq=0.3
No confinement constraint
GeV, ms=0.475 GeV)
W
m
Coalescence Formula
n
d 3 pi
dNH
pi dσ i
f ( xi , pi ) f H ( x1 ...xn , p1 ... pn )δ( pT piT )
2
3 q
d pT
( 2π )
i 1
fq invariant parton distribution function
thermal (mq=0.3 GeV, ms=0.47 GeV)
with radial flow b0.5)
+
quenched minijets (L/3.5
fH hadron Wigner function
fM
9π
2
2
2
2
2
D
(
x
x
)
D
(
p
p
)
(
m
m
)
x
1
2
p
1
2
1
2
2(D x D p )3
Dx = 1/Dp coalescence radius
2
( p1 p2 ) In the rest frame
Distribution Function
T=170 MeV
| Dy | 0.5
soft
ET ~ 700 GeV
b(r) ~ 0.5 r/R
T ~ 170 MeV
hard
L/3.5
P. Levai et al., NPA698(02)631
V ~ 900 fm-3
~ 0.8 GeV fm-3)
Hadron from coalescence may
have jet structure (away suppr.)
REALITY: one spectrum with correlation kept also at pT < 2 GeV
Pion & Proton spectra
Au+Au @200AGeV (central)
ρ ππ
V. Greco et al., PRL90 (03)202302
PRC68(03) 034904
R. Fries et al., PRL90(03)202303
PRC68(03)44902
R. C. Hwa et al., PRC66(02)025205
Proton enhancement
due to coalescence!
Baryon/Meson ratio
Be careful , there are mass effects !
Resonance decays r >
Shrinking of baryon phase
space
p
Fragmentation not included for
Momentum-space coalescence model
Including 4th order quark flow Kolb, Chen, Greco, & Ko, PRC 69 (2004) 051901
fq (pT ) 1 2v2,q (pT )cos(2) 2v4,q (pT )cos(4)
Meson flow
v 2,M =
2v 2,q + 2v 2,qv 4,q
1 + 2(v22,q + v 24,q )
, v4,M =
2v 4,q + v 22,q
1 + 2( v 22,q + v 24,q )
Baryon flow
v 2,B =
3v 2,q + 6v 2,qv 4,q + 3v 32,q + 6v 2,qv 24,q
2
2,q
2
4,q
2
2,q 4,q
1 + 6( v + v + v v )
, v4,B =
3v 4,q + 3v 22,q + 6v 22,qv 4,q + 3v 34,q
1 + 6(v22,q + v 24,q + v 22,qv 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
Elliptic Flow from Coalescence
Enhancement
partonic v2
Coalescenceofscaling
v 2,M (p1T ) 2v
pT2,q (p T /2)
V2
v 2,B (pnT ) 3vn 2,q (pT /3)
Wave function effects
> scaling breaking 10% q/m
5% b/m
wave function effect
Effect of Resonances on Elliptic Flow
Pions from resonances
w.f. + resonance decay
K&p
*
K, , moved
p … v2 not
affected
coal.
towards
data
by resonances!
nucl-th/0402020
Higher-order anisotropic flows
Data can be described by
a multiphase transport
(AMPT) model
Parton cascade
Data
v4,q v22,q
v4
2
1.2
⇒
v
2v
4,q
2,q in naivequark coalescence model
2
v2
Back-to-Back Correlation
trigger
Assoc.
quenched
Trigger is a particle at
4 GeV < pTrig < 6 GeV
Associated is a particle at
2 GeV < pT < pTrig
Away Side: quenching
has di-jet structure
Same Side: Indep. Fragm.
equal (?!) to pp
Coalescence from s-h leads to away side suppression,
While same side is reduced if no further correlation …
Unexpected: Appreciable charm flow
Does Charm quark thermalize?
v2 of D meson (single e)
coalescence/fragmentation?
energy loss?
pT Spectra and Yield of J/Y
From hard pp collision
D meson spectra
V. Greco , PLB595 (04) 202
S. Batsouli,PLB557 (03) 26
D mesons
D mesons
B mesons
No B mes.
Single electron does not
resolve the two scenarios
Elliptic flow better probe of interaction
Charmed Elliptic Flow
Flow mass effect
V2q from , p, ,
Coalescence can predict
v2D for v2c = 0
&
v2c = v2q
V2 of electrons
S. Kelly,QM04
Quenching
VGCMKRR, PLB595 (04) 202
Quark gluon plasma was predicted to be a weakly
interacting gas of quarks and gluons
The matter created is not a firework of multiple minijets
Strong Collective phenomena
Hydrodynamics describes well the bulk of the matter
Transport codes needs a quite large npQCD cross section
Charm quark interacts strongly in the plasma
Recent lattice QCD finds bound states of cc at T>Tc
Rethinking the QGP at Tc < T < 2Tc
“Strong” QGP
Summary
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.
Conclusions
Matter with energy density too high for simple hadronic
phase ( > c from lattice)
Matter is approximately thermalized (T >Tc )
Jet quenching consistent with a hot and dense medium
described by the hydrodymic approach
Hadrons seem to have typical features of recombination
Strangeness enhancement consistent with grand canonical
ensemble
J/y ...
Needed : - Thermal spectrum
- Dilepton enhancement
A Lot of work to do …
Lattice QCD
Effective field theory
Transport theory (quantum, field condensate,…)
pQCD
Understanding of Non-Abelian Interaction !
Scientific approach to an important part
of the evolution of the primordial plasma
can be achieved