A Nearly Perfect Ink !? Theoretical Challenges from RHIC
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Transcript of A Nearly Perfect Ink !? Theoretical Challenges from RHIC
A Nearly Perfect Ink !?Theoretical Challenges from RHIC
Dublin - 29 July 2005
LATTICE 2005
Berndt Mueller (Duke University)
A perfect ink…
Is brilliantly dark and opaque Yet flows smoothly and easily
A painful challenge to fountain pen designers
A delightful challenge to physicists: Are the two requirements really
compatible?Hint:
1f
The road to the quark-gluon plasma
STAR
…Is hexagonal and 2.4 miles long
Two wealths
ChallengesC
halle
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hallenge
sChallenge
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Challenges
Challenge
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Cha
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Challenge
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A wealth of …A wealth of …
D A T A
Cornerstone results from RHIC
Anisotropic transverse flow
“Jet” suppression
Baryon/meson enhancement
Azimuthal anisotropy v2
py
)(tan,2cos 12
x
y
p
pv
Coordinate space: initial asymmetry
Momentum space: final asymmetry
pxx
y
Semiperipheral collisions
Signals early equilibration (teq 0.6 fm/c)
Jet quenching in Au+Au
PHENIX Data: Identified 0
d+Au
Au+Au
No quenching
Quenching!
Baryons vs. mesons
baryons mesons
RC
P
pT (GeV/c)
behaves like meson ?
(also -meson)
coll
Yield( | )( )
( )Yield( )
b AAR b
N b pp
Overview
QCD Thermodynamics What are the dynamical degrees of freedom? Is there a critical point, and where is it?
Thermalization How can it be so fast?
Transport in a thermal medium Viscosity, energy loss, collective modes
Hadronization Recombination vs. fragmentation
QCD phase diagram
B
Hadronicmatter
Critical endpoint
?
Plasma
Nuclei
Chiral symmetrybroken
Chiral symmetryrestored
Color superconductor
Neutron stars
T
1st order line ?
Quark-Gluon
RHIC
Space-time picture
eqPre-equil. phase
final2
( ) /( )
( ) /
( / )
T
T
A
dE dy
dV dy
dE dy
R
3( ) 4.5 GeV/fm
at 1 fm/c
in Au+Au (200 GeV)
Bjorken formula
Stages of a r.h.i. collision
Initial collision ≈ break-up of the coherent gluon field (“color glass condensate”)
Pre-equilibrium: the most puzzling stage
Equilibrium (T > Tc): hydrodynamic expansion in longitudinal and transverse directions
Hadronization: are there theoretically accessible domains in pT ?
Hadronic stage (T < Tc): Boltzmann transport of the hadronic resonance gas
Initial state: Gluon saturation
~ 1/Q2
2 2 1/3s
2 2 2s s
gluon density area ( , ) ( )
= 1A s s
A
xG x Q Q A x
R Q Q
2s ( , )Q x A
Details of space-time picture depend on gauge!
Gribov, Levin, Ryskin ’83
Blaizot, A. Mueller ’87
McLerran, Venugopalan ‘94
“Color glass condensate (CGC)”
CGC dynamicsInitial state occupation numbers ~ 1/s 1 → classical fields generated by random color sources on light cone:
2 20 2 2
1( ) exp [ ( )]a a
s
P P d x xg Q
Boost invariance → Hamiltonian gauge field dynamics in transverse
plane (x,). 2-dim lattice simulation shows rapid equipartitioning of
energy (eq ~ Qs-1). Krasnitz, Nara & Venugopalan; Lappi (hep-ph/0303076 )
( )a x ( )a x
( , )aiA x
Challenge: (3+1) dim. simulation without boost invariance
Saturation and dN/dKharzeev & Levin
Pseudorapidity = - ln tan
Rapidity y = ln tanh(E+pL)/(E-pL)
Assume nucleus is “black” for all gluons with kT Qs:
Qs(x) → Qs(y)
with x = Qse-|Y-y| .
Also predicts beam energy dependence of dN/dy.
Challenge:
How much entropy is produced by simple decoherence, how much during the subsequent full equilibration?
The(rmalization) mystery
Experiment demands: th 0.6 fm/c “Bottom up” scenario (Baier, A. Mueller, Schiff, Son):
“Hard” gluons with kT ~ Qs are released from the CGC; Released gluons collide and radiate thermal gluons;
Thermalization time th ~ [s13/5 Qs]-1 ≈ 2-3 fm/c
Perturbative dynamics among gluons does not lead to rapid thermalization.
Quasi-abelian instability (Mrowczynski; Arnold et al; Rebhan et al): Non-isotropic gluon distributions induce exponentially
growing field modes at soft scale k ~ gQs ; These coherent fields deflect and isotropize the “hard”
gluons.
After thermalization…
... matter is described by (relativistic) hydrodynamics !
Requires f L and small shear viscosity .
HTL pert. theory (nf=3):
Dimensionless quantity /s.
Classical transp. th.: ≈ 1.5Tf, s ≈ 4 → /s ≈ 0.4Tf.
3
4 1106.7
ln
T
g g (Baym…; Arnold,
Moore & Yaffe)
( )
0 with
( trace)P u
T
uT uu Pg
Azimuthal anisotropy v2
py
)(tan,2cos 12
x
y
p
pv
Coordinate space: initial asymmetry
Momentum space: final asymmetry
pxx
y
Semiperipheral collisions
Signals early equilibration (teq 0.6 fm/c)
– How small can it be?
0 00 0 0
41
3s T
T s s
D. TeaneyBoost invariant hydro with T00 ~ 1 requires /s ~ 0.1.
N=4 SUSY Yang-Mills theory (g1):
/s = 1/4(Kovtun, Son, Starinets).
Absolute lower bound on /s ?
/s = 1/4 implies f ≈ (5 T)-1 ≈ 0.3 d
Challenge: (3+1) dim. relativistic viscous fluid dynamics
QGP(T≈Tc) = sQGP
First attempts
3 ( )
ret
1( , ) ( , )
6
tt ik
ikd x d e dt T x t T x t
Nakamura & Sakai
SU(3) YM
Related (warm-up?) problem: EM conductivity ≈ q2f/2T.
nf = 3 QGP → / ≈ 20 T2.
Caveat: f(glue) f(quarks)
Method: spectral function repr. of G and Gret, fit of spectral fct. to G.
Challenge: Calculate /s for real QCD
QCD equation of state2
4
30T
20%
Challenge: Devise method for determining from data
Challenge: Identify the degrees of freedom as function of T
Is the (s)QGP a gaseous, liquid, or solid plasma ?
Challenge: QCD e.o.s. with light domain wall quarks
A possible method
24
23
30
2
45
T
s T
4 4
2 3 3
12150.96
128
s s
Eliminate T from and s :
Lower limit on requires lower limit on s and upper limit on .
BM & K. Rajagopal, hep-ph/0502174
Measuring and s
Entropy is related to produced particle number and is conserved in the expansion of the (nearly) ideal fluid: dN/dy → S → s = S/V.
Energy density is more difficult to determine: Energy contained in transverse degrees of freedom is not
conserved during hydrodynamical expansion. Focus in the past has been on obtaining a lower limit on ; here
we need an upper limit. New aspect at RHIC: parton energy loss. dE/dx is telling us
something important – but what exactly?
Entropy Two approaches:
1) Use inferred particle numbers at chemical freeze-out from statistical model fits of hadron yields;
2) Use measured hadron yields and HBT system size parameters as kinetic freeze-out (Pratt & Pal).
Method 2 is closer to data, but requires more assumptions.
Good news: results agree within errors: dS/dy = 5100 ± 400 for Au+Au (6% central, 200 GeV/NN)
→ s = (dS/dy)/(R20) = 33 ± 3 fm-3
Jet quenching in Au+Au
PHENIX Data: Identified 0
d+Au
Au+Au
No quenching
Quenching!
High-energy parton loses energy by
rescattering in dense, hot medium.q
q
Radiative energy loss:2/ TdE dx L k
“Jet quenching” = parton energy loss
q q
g
Scattering centers = color chargesL
2 2T
22
2ˆ
dq q dq
dqk
Density of scattering centers
Range of color forceScattering power of the QCD medium:
Energy loss at RHIC2ˆ 5 10 GeV /fmq Data suggest large energy loss parameter:
RHIC
Eskola, Honkanen, Salgado & Wiedemann
pT = 4.5–10 GeV
Dainese, Loizides, Paic
The Baier plot
Plotted against , is the same for a gas and for a perturbative QGP.
Suggests that is really a measure of the energy density.
Data suggest that may be larger than compatible with Baier plot.
Nonperturbat. calculation is needed.
Pion gas
QGP
Cold nuclear matter
q̂
q̂
q̂
RHIC data
sQGP
Challenge: Realistic calculation of gluon radiation in medium
Eikonal formalism
quark
x
x -
0
( ) ( ; ) ( )
( ; ) exp ( , )L
q x W x L q x
W x L i dx A x x
P
+Gluon radiation: x = 0
x
( )2 2
†
2
( ) 1 ( ,0) (0, ) ( , )2
Tr[w
( ; ) ( ; )]( , )
1ith
ik x ys Fg
A A
c
C x yN k dx dy e C x C y C x y
x y
W x L W y LC x y
N
Kovner, Wiedemann
Eikonal form. II†
2
2 †
0 0
2 2
Tr[ ( ; ) ( ; )( , )
1
1( ) ( ) ( , ) ( ) ( , )
2
1 1( ) ( ) ˆ
2 2i
i F
c
xLi
i
W x L W y LC x y
N
x y dx dx F x W x x F x W x x
x y L x yF F qL
Challenge: Compute F+i(x)F+i(0) for x2 = 0 on the lattice
Not unlike calculation of gluon structure function, maybe moments are calculable using euclidean techniques.
Where does Eloss go?
STAR p+p Au+Au
Lost energy of away-side jet is redistributed to rather large angles!
Trigger jetAway-side jet
Wakes in the QGP
Mach cone requires collective mode with (k) < k:
J. Ruppert and B. Müller, Phys. Lett. B 618 (2005) 123
Colorless sound? Colored sound = longitudinal gluons? Transverse gluons
Angular distribution depends on energy fraction in collective mode and propagation velocity
T. Renk & J. Ruppert
Baryons vs. mesons
baryons mesons
RC
P
pT (GeV/c)
behaves like meson ?
(also -meson)
coll
Yield( | )( )
( )Yield( )
b AAR b
N b pp
Hadronization mechanisms
q
Baryon1
Meson
Fragmentation
q q
q q q
Baryon1
Meson
Recombination
M Q B Q2 3p p p p
Recombination wins…… for a thermal source
Baryons compete with mesons
Fragmentation dominates for a power-law tail
Quark number scaling of v2
In the recombination regime, meson and baryon v2 can be obtained from the quark v2 :
2 2 2 2v22
v3
v3v Btt
q tM q tp ppp
Hadronization RHIC data (Runs 4 and 5) will provide wealth of data on: Identified hadron spectra up to much higher pT (~10 GeV/c);
Elliptic flow v2 up to higher pT with particle ID;
Identified di-hadron correlations; Spectra and v2 for D-mesons….
D D
recombinationfragmentation
Challenge: Unified framework treating recombination as special case of QCD fragmentation “in medium”.
A. Majumder & X.N. Wang, nucl-th/0506040
Some other challenges
Where is the QCD critical point in (,T)?
What is the nature of the QGP in Tc < T < 2Tc ?
How well is QCD below Tc described by a weakly interacting resonance gas?
Thermal photon spectral function (m2,T).
Are there collective modes with (k) < k ?
Can lattice simulations help understand the dynamics of bulk (thermal) hadronization?
Don’t be afraid…
“Errors are the doors to discovery”
James Joyce
Back-up slides
Hard-soft dynamics
Nonabelian Vlasov equations generalizing “hard-thermal loop” effective theory.
Can be defined on (spatial 3-D) lattice with particles described as test charges or by multipole expansion (Hu & Müller, Moore, Bödeker, Rummukainen).
Poss. problem: short-distance lattice modes have wrong (k).
( ) ( ) ( ) (
ˆ(1, v) light-l
( )
ik
)
e
i i i
i
i
u
J x d Q u x x
D F gJ
k ~ gQs k ~ Qs
Challenge: Full (3+1) dim. simulation of hard-soft dynamics
Reco: Thermal quarks
2M
M3 3,
2B
B3 3, ,
( , ) ( , (1 ) ) ( )(2 )
' ( , ) ( , ' ) ( , (1 ') ) ( , ')(2 )
dN P uE d dxw R xP w R x P x
d P
dN P uE d dxdx w R xP w R x P w R x x P x x
d p
( , )w r p Quark distribution function at “freeze-out”
Relativistic formulation using hadron light-cone frame:
For a thermal distribution,
the hadron wavefunctions can be integrated out, eliminating the model dependence of predictions.
Remains exactly true even if higher Fock states are included!
( , ) exp( / )w r p p u T
Heavy quarks
Heavy quarks (c, b) provide a hard scale via their mass. Three ways to make use of this:
Color screening of (Q-Qbar) bound states;
Energy loss of “slow” heavy quarks;
D-, B-mesons as probes of collective flow.
RHIC program: c-quarks and J/;
LH”I”C program: b-quarks and .
RHIC data for J/ are forthcoming (Runs 4 & 5).
J/ suppression ?Vqq is screened at scale (gT)-1 heavy quark bound states dissolve above some Td.
Karsch et al.
Color singlet free energy
Quenched lattice simulations, with analytic continuation to real time, suggest Td 2Tc !
S. Datta et al. (PRD 69, 094507)
Challenge: Compute J/ spectral function in unquenched QCD
C-Cbar kinetics
J/
LHC
LHC
RHIC
RHIC
J/, can be ionized by thermal gluons. If resonances persist above Tc, J/ and can be formed by recombination in the medium: J/ may be enhanced at LHC!
Challenge: Multiple scattering theory of heavy quarks in a thermal medium
Analogous to the multiple scattering theory for high-pT partons, but using methods (NRQCD etc.) appropriate for heavy quarks.