A Nearly Perfect Ink Theoretical Challenges from RHIC

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A Nearly Perfect Ink !?Theoretical Challenges
from RHIC

• Dublin - 29 July 2005
• LATTICE 2005

Berndt Mueller (Duke University)
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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?

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The road to the quark-gluon plasma
Is hexagonal and 2.4 miles long
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Two wealths
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Cornerstone results from RHIC

• Anisotropic transverse flow
• Jet suppression
• Baryon/meson enhancement

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Azimuthal anisotropy v2
py
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Jet quenching in AuAu
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Baryons vs. mesons
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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

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QCD phase diagram
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Space-time picture
Pre-equil. phase
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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 gt Tc) hydrodynamic expansion in
  longitudinal and transverse directions
• Hadronization are there theoretically accessible
  domains in pT ?
• Hadronic stage (T lt Tc) Boltzmann transport of
  the hadronic resonance gas

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Initial state Gluon saturation
Gribov, Levin, Ryskin 83 Blaizot, A. Mueller
87 McLerran, Venugopalan 94
Color glass condensate (CGC)
Details of space-time picture depend on gauge!
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CGC dynamics
Initial state occupation numbers 1/as ? 1 ?
classical fields generated by random color
sources on light cone
Boost invariance ? Hamiltonian gauge field
dynamics in transverse plane (x?,t). 2-dim
lattice simulation shows rapid equipartitioning
of energy (teq Qs-1). Krasnitz, Nara
Venugopalan Lappi (hep-ph/0303076 )
Challenge (31) dim. simulation without boost
invariance
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Saturation and dN/dh
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?
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The(rmalization) mystery

• Experiment demands tth ? 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 tth as13/5 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.

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After thermalization
... matter is described by (relativistic)
hydrodynamics ! Requires lf ? L and small shear
viscosity h. HTL pert. theory
(nf3) Dimensionless quantity h/s. Classical
transp. th. h 1.5rTlf, s 4r ? h/s 0.4Tlf.
(Baym Arnold, Moore Yaffe)
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Azimuthal anisotropy v2
py
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h How small can it be?
D. Teaney
Boost invariant hydro with T0t0 1 requires h/s
0.1.
N4 SUSY Yang-Mills theory (g?1) h/s 1/4p
(Kovtun, Son, Starinets). Absolute lower bound on
h/s ?
h/s 1/4p implies lf (5 T)-1 0.3 d
QGP(TTc) sQGP
Challenge (31) dim. relativistic viscous fluid
dynamics
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First attempts
Challenge Calculate h/s for real QCD
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QCD equation of state
Challenge QCD e.o.s. with light domain wall
quarks
Challenge Devise method for determining n from
data
Challenge Identify the degrees of freedom as
function of T
Is the (s)QGP a gaseous, liquid, or solid plasma ?
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A possible method
BM K. Rajagopal, hep-ph/0502174
Eliminate T from e and s
Lower limit on n requires lower limit on s and
upper limit on e.
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Measuring e 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 e here we need an upper limit.
• New aspect at RHIC parton energy loss. dE/dx is
  telling us something important but what exactly?

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Entropy

• Two approaches
• Use inferred particle numbers at chemical
  freeze-out from statistical model fits of hadron
  yields
• 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 AuAu (6 central, 200
  GeV/NN) ? s (dS/dy)/(pR2t0) 33 3 fm-3

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Jet quenching in AuAu
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Jet quenching parton energy loss
Radiative energy loss
L
Scattering centers color charges
q
q
Density of scattering centers
g
Range of color force
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Energy loss at RHIC
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The Baier plot

• Plotted against e, is the same for a p 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.

Cold nuclear matter
Challenge Realistic calculation of gluon
radiation in medium
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Eikonal formalism
Kovner, Wiedemann
x?
Gluon radiation
x? 0
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Eikonal form. II
Challenge Compute ?Fi(x)Fi(0)? for x2 0 on
the lattice
Not unlike calculation of gluon structure
function, maybe moments are calculable using
euclidean techniques.
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Where does Eloss go?
STAR
pp
AuAu
Trigger jet
Away-side jet
Lost energy of away-side jet is redistributed to
rather large angles!
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Wakes in the QGP
J. Ruppert and B. Müller, Phys. Lett. B 618
(2005) 123
Mach cone requires collective mode with w(k) lt k

• Colorless sound
• Colored sound longitudinal gluons
• Transverse gluons

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Baryons vs. mesons
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Hadronization mechanisms
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Recombination wins
for a thermal source
Fragmentation dominates for a power-law tail
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Quark number scaling of v2
In the recombination regime, meson and baryon v2
can be obtained from the quark v2
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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.

Challenge Unified framework treating
recombination as special case of QCD
fragmentation in medium.
A. Majumder X.N. Wang, nucl-th/0506040
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Some other challenges

• Where is the QCD critical point in (m,T)?
• What is the nature of the QGP in Tc lt T lt 2Tc ?
• How well is QCD below Tc described by a weakly
  interacting resonance gas?
• Thermal photon spectral function r(m2,T).
• Are there collective modes with w(k) lt k ?
• Can lattice simulations help understand the
  dynamics of bulk (thermal) hadronization?

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Dont be afraid
Errors are the doors to discovery
James Joyce
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Back-up slides
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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 w(k).
k gQs
k Qs
Challenge Full (31) dim. simulation of
hard-soft dynamics
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Reco Thermal quarks
Relativistic formulation using hadron light-cone
frame
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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/Y
• LHIC program b-quarks and ?.
• RHIC data for J/Y are forthcoming (Runs 4 5).

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J/Y suppression ?
Vqq is screened at scale (gT)-1 ? heavy quark
bound states dissolve above some Td.
Color singlet free energy
Challenge Compute J/Y spectral function in
unquenched QCD
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C-Cbar kinetics
J/Y, ? can be ionized by thermal gluons. If
resonances persist above Tc, J/Y and ? can be
formed by recombination in the medium J/Y 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.