1. GOING WITH THE FLOW What the data from RHIC have taught us so far
Berndt Mueller (Duke University)
大阪大学 , 14 October 2005

2. The quest for simplicityN* D N K h r p h’ X a0 W f0 a1 S*
Hadronic resonance gas
Before 1975, nuclear matter at high energy density was considered a real mess !
QCD predicts that hot matter becomes simple – the QGP (not necessarily weakly interacting!).
Characteristic features: deconfinement and chiral symmetry restoration (i.e. quarks lose their dynamically generated mass).
Quark-gluon plasma u d _ s g

3. The QCD phase diagram B Plasma T Quark- Gluon RHIC Tc Hadronic matter
Critical endpoint ?
Plasma
Nuclei
Chiral symmetry
broken
restored
Colour
superconductor
Neutron stars T
1st order line ?
Quark-
Gluon
RHIC Tc

4. QCD equation of state Free massless particle limits 20%
Tc = 175  10 MeV
Lattice gauge theory provides a model independent answer (for mB=0).

5. The space-time picture
Thermal freeze-out
Hadronization
Equilibration

6. The path to the Q-G plasma…
…Is Hexagonal and 2.4 Miles Long
The Relativistic Heavy Ion Collider at Brookhaven National Laboratory
STAR

7. Charged particle tracks from a central Au+Au collision
RHIC data collection
RHIC has had runs with:
Au+Au at 200, 130, 62 and 19.6 GeV
Cu+Cu at 200, 62 GeV
d+Au at 200 GeV
p+p at 200, 130 GeV
Charged particle tracks from a central Au+Au collision

8. Frequently asked questions
How do we know that we have produced equilibrated matter, not just a huge bunch of particles ?
What makes this matter special ?
How do we measure its properties ?
Which evidence do we have that quarks are deconfined for a brief moment (about s) ?
Which evidence do we have for temporary chiral symmetry restoration ?
What do we still need to learn ?
Translation: When can RHIC be closed down ?

9. FAQ #1 How do we know that we produced equilibrated matter,
not just a bunch of particles ?
Answer:
Particles are thermally distributed and flow collectively !

10. Chemical equilibrium
Chemical equilibrium fits work, except where they should not (resonances with large rescattering).
RHIC 200 GeV
Tch = 160  10 MeV
µB = 24  5 MeV
STAR Preliminary
Central Au-Au √s=200 GeV

11. The “elliptic” flow (v2)
Coordinate space:
initial asymmetry
Momentum space:
final asymmetry py
Pressure gradient
collective flow px x y
Two-particle correlations
dN/d(1- 2) 1 + 2v22cos(2[1- 2])

12. FAQ #2 What makes this matter special ? Answer:
It flows astonishingly smoothly !
“The least viscous non-superfluid ever seen”

13. v2 requires low viscosity
Relativistic viscous fluid dynamics:
Shear viscosity h tends to smear out the effects of sharp gradients
pQCD:
Dimensionless quantity

14. Viscosity must be ultra-low
v2 data comparison with (2D) relativistic hydrodynamics results suggests h/s  0.1
Recent excitement:
D. Teaney
Quantum lower bound on h/s :
h/s = 1/4p (Kovtun, Son, Starinets)
Realized in strongly coupled (g1) N = 4 SUSY YM theory, also in QCD ?
h/s = 1/4p implies lf ≈ (5 T)-1 ≈ 0.3 d
QGP(T≈Tc) = sQGP

15. An sQGP liquid?
For realistic gE, perturbative quasiparticles are short-lived:
Similar relationship for quarks: G/m* ≈ 1.3
Suggestive scenario:
As T  Tc+0, G/m* increases, QGP quasiparticles (gluons, quarks, plasmons, plasminos) become broad and short-lived.
As T  Tc-0, G/m* increases, hadrons (mesons, baryons) become broad and short-lived resonances.

16. Schematic scenario HG QGP sHad  sQGP liquid Tc T Hagedorn ????
Hadrons exchange quarks rapidly and become short-lived resonances
Quarks and gluons collide frequently and form short-lived “resonances”
Hagedorn
???? T

17. FAQ #3 How do we unambiguously measure its properties ? Answer:
With hard QCD probes,
such as jets, photons, or heavy quarks

18. Parton energy loss (aka: jet quenching)
High-energy parton loses energy by
rescattering in dense, hot medium. q
Radiative energy loss: L
Scattering centers = color charges q q
Density of scattering centers g
Scattering power of the QCD medium:
Range of color force

19. Deviation from binary NN collision scaling:
Pions vs. photons
Deviation from binary NN collision scaling:
Photons
Hadrons

20. Larger than expected from perturbation theory ?
Energy loss at RHIC
Data are described by a very large loss parameter for central collisions:
(Dainese, Loizides, Paic, hep-ph/ )
Larger than expected from perturbation theory ?
Pion gas
QGP
Cold nuclear matter
RHIC data
sQGP
R. Baier
pT = 4.5 – 10 GeV/c

21. Test case: RAA for charm
Heavy quarks (c, b) should lose less energy by gluon radiation, but…
…experiment (STAR, PHENIX) observe strong suppression up to RAA ~ 0.2 observed in most central events.
Is collisional energy loss much larger than expected?
New plots without grid ans w/o d+Au in centrality 2 3. Shaded region reflecting d_Nbin

22. FAQ #4 Which evidence do we have that quarks are deconfined
for a brief moment (about s) ?
Answer:
Baryons and mesons are formed
from independently flowing quarks

23. Baryons vs. mesons
What makes baryons different from mesons ?

24. Hadronization mechanisms
Meson
Meson
Fragmentation
Recombination
Baryon
from dense system

25. Recombination always wins …
… for a thermal source
Baryons compete with mesons
Fragmentation still wins for a power law tail

26. Recombination - fragmentation
Teff = 350 MeV blue-shifted temperature T = 180 MeV
pQCD spectrum shifted by 2.2 GeV
R.J. Fries, BM, C. Nonaka, S.A. Bass
Baryon enhancement

27. Hadron v2 reflects quark flow !
Recombination model suggests that hadronic flow reflects partonic flow (n = number of valence quarks):
Provides measurement of partonic v2 !

28. FAQ #5 Which evidence do we have for temporary
chiral symmetry restoration ?

29. Strangeness at RHIC (sss) (qss) (qqs) QCD mass disappears Mass (MeV)
Flavor

30. FAQ #6: What do we still need to (or want to) learn ?
Number of degrees of freedom:
via energy density – entropy relation.
Color screening:
via dissolution of heavy quark bound states (J/Y).
Chiral symmetry restoration:
modification of hadron masses via e+e- spectroscopy.
Quantitative determination of transport properties:
viscosity, stopping power, sound velocity, etc.
What exactly is the “s”QGP ?

31. Challenge: Devise method for determining n from data
QCD equation of state
20%
Challenge: Devise method for determining n from data

32. n from e and s Eliminate T from e and s :
BM & K. Rajagopal, hep-ph/
Eliminate T from e and s :
Lower limit on n requires lower limit on s and upper limit on e.

33. 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.
dS/dy = 5100 ± 400 for Au+Au (6% central, 200 GeV/NN)
Yields: s = (dS/dy)/(pR2t0) = 33 ± 3 fm-3
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.

34. Where does Eloss go? p+p Au+Au
Away-side jet
Trigger jet
Lost energy of away-side jet is redistributed to rather large angles!

35. Wakes in the QGP pQCD (HTL) dispersion relation Mach cone requires
J. Ruppert and B. Müller, Phys. Lett. B 618 (2005) 123
pQCD (HTL) dispersion relation
Mach cone requires
collective mode with w(k) < k:
Colorless sound
Colored sound = longitudinal gluons
Transverse gluons

36. Collective modes in medium
Longitudinal (sound) modes
“Colored” sound
Normal sound
Transverse modes
Mach cone structures from a space-like longitudinal plasmon branch:
J. Ruppert & B. Müller, Phys. Lett. B 618 (2005) 123
Mach cone from sonic boom:
H. Stoecker
J. Casalderrey-Solana & E. Shuryak
Cherenkov-like gluon radiation into a space-like transverse gluon branch:
I. Dremin
A. Majumder, X.-N. Wang, hep-ph/

37. Jet-Medium Interactions
Renk & Ruppert. hep-ph/
Angular distribution and size of off-jet axis peak depends on:
Energy fraction in collective mode
Propagation velocity
Collective flow pattern
Note: f = 0.9 is a very large collective fraction requiring an extremely efficient energy transfer mechanism!

38. Outlook
The “discovery phase” of RHIC has already uncovered several surprises: near-ideal liquid flow, valence quark number scaling of v2; very large partonic energy loss.
Several important observables are still waiting to be explored. Run-4 and -5 data (just coming out!) are beginning to provide some of the needed information.
The RHIC data are posing many well defined theoretical challenges, such as:
Structure of QCD matter near Tc ?
Thermalization mechanisms in gauge theories ?
Transport coefficients in gauge theories ?
A new window of calculable hadronization ?

39. Special thanks to… Steffen Bass Chiho Nonaka Jörg Ruppert
Thorsten Renk
Rainer Fries
Yuki Asakawa