1. CERN Physics Department
What we may learn from AdS/CFT about the phenomenology of Heavy Ion Collisions
Urs Achim Wiedemann
CERN Physics Department
TH Unit
Durham,
19 December 2007
based on work in collaboration with
Qudsia Ejaz, Thomas Faulkner, Hong Liu, Krishna Rajagopal

2. Beyond the Standard Model
How does collectivity emerge from elementary interactions?

3. Beyond the Standard Model
How does collectivity emerge from elementary interactions?
14 TeV
ATLAS
CMS
LHCb
ALICE
Heavy 5.5 TeV
ALICE
CMS
ATLAS
Beyond the Standard Model

4. Beyond the Standard Model
String theory
The Standard Model
How does collectivity emerge from elementary interactions?
Novel techniques for thermal QFTs
Topic of this talk
Beyond the Standard Model
String inspired model building

5. Why do we need collider energies
Question:
Why do we need collider energies
to test properties of dense QCD matter
which arise on typical scales ?

6. Answer 1: Large quantitative gains
Increasing the center of mass energy implies
Denser initial system, higher initial temperature
Longer lifetime
Bigger spatial extension
Stronger collective phenomena
A large body of experimental data from RHIC supports this argument.

7. Answer 2: Qualitatively novel access to properties of dense matter
For a detailed experimentation with dense QCD matter, one ideally wants to do DIS on the QGP.
… and we can by using auto-generated probes at high
Large allows us to embed well-controlled large- processes (hard probes) in dense nuclear matter.
Q: How sensitive are hard probes?

8. Bjorken’s original estimate and its correction
Bjorken 1982: consider jet in p+p collision, hard parton interacts with
underlying event collisional energy loss
(Bjorken realized later that this estimate was numerically erroneous.)
Bjorken conjectured monojet phenomenon in proton-proton
Today we know (th): radiative energy loss dominates
Baier Dokshitzer Mueller Peigne Schiff 1995
p+p:
Negligible !
Monojet phenomenon!
A+A:
observed at RHIC,

9. High pT Hadron Spectra Centrality dependence: 0-5% 70-90% L large
L small

10. Centrality dependence: Au+Au vs. d+Au
Final state suppression
Initial state enhancement
partonic energy loss

11. “DIS on QGP”

12. Parton Propagation in an External Color Field
High-energy scattering determined by eikonal Wilson line
During scattering, transverse coordinates are frozen, color rotates
lala

13. Example: virtual photoabsorption cross section
Incoming virtual photon to O(g0)
Outgoing from target
Target average:
For total cross section, square
Model:
Exponent of real quantity
Saturation
scale
A.H.Mueller …
lala

14. Example: gluon production in q+A
Incoming free quark wave function dressed to O(g)
Outgoing from target
Number of produced gluons
Target average involves adjoint Wilson loop:
Bertsch Gunion spectrum +
Brownian Motion
Kovner Wiedemann, PRD 64 (2001)
Kovchegov Mueller 1998
lala

15. The medium-modified Final State Parton Shower
Wiedemann, NPB 588 (2000) 303
Radiation off produced parton
Target average includes Brownian motion:
BDMPS transport coefficient
Expectation value of light-like Wilson line

16. The medium-modified Final State Parton Shower
Medium characterized by
transport coefficient:
Wang, Gyulassy (1994); Baier, Dokshitzer, Mueller, Peigne, Schiff (1996); Zakharov (1997);
Wiedemann (2000); Gyulassy, Levai, Vitev (2000); Wang ...
Salgado,Wiedemann PRD68: (2003)
energy loss of leading parton
pt-broadening of shower

17. Quenching parameter from HI phenomenology
Eskola, Honkanen, Salgado, Wiedemann
Nucl Phys A747 (2005) 511
Can we understand the order or magnitude of this fit parameter from 1st principles of a thermal QFT?

19. Static q-qbar potential

20. Static quark-antiquark potential E(L)
The T-dependence of E(L) has been
studied in lattice QCD.
Bielefeld Group, hep-lat/
time
transverse distance L
Ltime
Consider thermal expectation value
of static Wilson loop in fundamental
representation. For
we define a static quark-antiquark
potential
Lattice results support the argument of
Matsui and Satz 1986 that quarkonium
‘melts’ due to color screening above
the QCD phase transition.
Exponent of imaginary quantity

21. J/Psi: a q-qbar pair moving through the medium produced in heavy ion collisions
BUT: Connecting lattice QCD
to heavy ion phenomenology
requires model-dependent
input
- formation time?
- formation mechanism?
- collective motion of ‘medium’
Can one get insight from 1st principles of a thermal QFT on some of these so-far model-dependent inputs?
Within reach in HICs at the LHC

22. Quarkonium dissociation at finite pt
Wilson loops defining a static quark-antiquark potential
at relative rapidity (or velocity ) with respect to the medium.
Not calculable in lattice QCD but of phenomenological interest.

23. AdS/CFT

24. String Theory Calculations of Properties of Matter
AdS/CFT correspondence relates
Strong coupling problems Classical Problem in a curved
in non-abelian QFT higher-dimensional space
Maldacena, 1997
String coupling and string tension
T’Hooft coupling
Translation into field theoretic quantities
Black hole horizon
Curvature radius
Finite T Lattice QCD is difficult to apply to
problems involving real-time dynamics
(moving QQbar pair, light-like Wilson loops, …)
hydrodynamic properties (Problem of analytical continuation to
if lowest Matsubara frequency in imaginary time formalism is ) ….

25. Wilson loops from AdS/CFT
AdS/CFT - Recipe
Finite temperature N=4 SYM dual to AdS5 Schwarzschild black hole:
Translation into field theoretic quantities:
Hawking temperature is QGP temperature
String tension
determines t’Hooft coupling
Maldacena (1998)
Rey and Lee (1998)
Black hole horizon
Our (3+1)-dim world
Wilson loop C in our world
horizon
: area of string world sheet with boundary C.
Curvature radius

26. Finding S(C) Wilson loop can be considered
Not more difficult than finding the catenary
Wilson loop can be considered
as the space-time trajectory of a
quark-antiquark pair.
Key: open string connecting the
quark pair can venture into the
radial 5th dimension.
Finding S(C): finding the shape
of the string hanging from the
spatial infinity of a black hole.

27. Calculating the loop in boosted metric
AdS BH metric boosted in x3-direction:
Parameterization of two-dimensional world-sheet bounded by C:
Boundary condition:
Nambu-Goto action:
Our task: find catenary

28. Time-like vs. space-like world sheet
Time-like world sheet:
e.o.m.
action
length
Lagrangian
Hamiltonian
Space-like world sheet:

29. Quenching parameter
Space-like world sheet

30. Results for quenching parameter
determine subtraction term S0
(via single string drag solution)
Herzog, Karch, Kovtun, Kozcaz, Yaffe
hep-th/
S. Gubser, hep-th/
consider ordered limit:
expand S(C) for small L:
Liu, Rajagopal, Wiedemann,
hep-ph/
What if the medium is moving with rapidity at angle w.r.t. jet trajectory?
Liu, Rajagopal, Wiedemann, hep-ph/

31. N=4 SYM Numerology Is this comparison meaningful?
In QGP of QCD, parton energy loss described perturbatively up to
non-perturbative quenching parameter.
We calculate quenching parameter in N=4 SYM (not necessarily a
calculation of full energy loss of SYM)
If we relate N=4 SYM to QCD by fixing
for T = 300 MeV
for T = 400 MeV
This is close to values from experimental fits.
Is this comparison meaningful?

32. Comment on: Is comparison meaningful?
N=4 SYM theory
conformal
Physics near vacuum and at very high energy is very different from that of QCD
no asmptotic freedom
no confinement
superymmetric
no chiral condensate
no dynamical quarks, 6 scalar
and 4 Weyl fermionic fields in
adjoint representation

33. At finite temperature: Is comparions meaningful?
conformal
no asmptotic freedom
no confinement
superymmetric (badly broken)
no chiral condensate
no dynamical quarks, 6 scalar
and 4 Weyl fermionic fields in
adjoint representation
N=4 SYM theory at finite T
QCD at T ~ few x Tc
near conformal (lattice)
not intrinsic properties of
QGP at strong coupling
not present
may be taken care of by
proper normalization

34. Quenching parameter for other theories
General CFTs with gravity dual: (large N and strong coupling)
Liu, Rajagopal, Wiedemann, hep-ph/
a central charge
s entropy
Near conformal theories: corrections small
Buchel, hep-th/
Finite coupling and Nc corrections: hard
Armesto, Edelstein, Mas hep-ph/
R-charge chemical potentials:
Avramis, Sfetsos;
Armesto, Edelstein, Mas;
Lin, Matsuo; …
Corrections small when chemical potentials small

35. Static q-qbar potential
Time-like world sheet

36. Screening length shows velocity scaling
The screening length of the static q-qbar potential scales with velocity
This indicates that the q-qbar dissociation temperatures scales like
For any quark mass, there is a maximal velocity
beyond which there is no potential between the pair.

37. D3-D7-brane construction of mesons
9+1-dim Minkowski space, N D3-branes and Nf D7-branes
D3:
D7:
Position of D7-brane, e.g. x8=L, x9 = 0.
Low-lying meson
spectrum in
gauge theory
Fluctuations
of x8, x9
on D7-branes
Mass spectrum of these mesonic excitations analyzed
Kruczenski, Mateos, Myers, Winters;
Babington, Erdmenger, Evans, Guralnik, Kirsch; …

38. D7-brane embedding at finite temperature
9+1-dim Minkowski space, N D3-branes and Nf D7-branes
D3:
D7:
Position of D7-brane, e.g. x8=L, x9 = 0.
Low-lying meson
spectrum in
gauge theory
Fluctuations
of x8, x9
on D7-branes
Mass spectrum of these mesonic excitations analyzed
Kruczenski, Mateos, Myers, Winters;
Babington, Erdmenger, Evans, Guralnik, Kirsch; …

39. Meson dispersion relation at finite temperature
Mesons at arbitrary high momentum propagate with finite limiting velocity v0, which can be very small. For very large quark mass, we are consistent with result for static quark potential
Ejaz, Faulkner, Liu, Rajagopal, Wiedemann; arXiv:

40. THE END of this talk
Many chapters on comparing AdS/CFT to QCD written already
In thermal sector:
- Shear viscosity in QCD
diffusion constants
thermal spectral functions
quenching
drag
quark-antiquark static potential …
Policastro, Son, Starinets, PRL 87, (2001)…
Policastro, Son, Starinets, hep-th/ , …
Teaney, hep-th/ , …
Liu, Rajagopal, Wiedemann hep-ph/ PRL, ….
Herzog et al hep-th/ ; Gubser hep-th/
Casalderrey-Solana, Teaney hep-ph/
Liu, Rajagopal, Wiedemann hep-ph/ ; …
‘Comparison’ neither straightforward nor obviously far-fetched
- rich testing ground for understanding non-perturbative properties of
non-abelian thermal gauge field theories
Many chapters to be written …

41. BACK-UP
Let me now turn to the properties of the bulk matter produced in a nucleus-nucleus collision.

42. Quark-antiquark static potential

43. Quark-antiquark static potential - angular dep.

44. Space-like World Sheet
Lagrangian
Hamiltonian
Space-like world sheet for:
e.o.m.
action
length

45. Energy Loss in a Strongly Expanding Medium
In A-A collisions, the density of scattering centers is time-dependent:
Salgado, Wiedemann PRL 89, (2002)
= 1.5, 1.0, 0.5, 0
Dynamical Scaling Law:
same spectrum obtained for
equivalent static transport coefficient:
In a nucleus-nucleus collision, the medium expands strongly and the density decreases in time. For example, for a 1-dimensional Bjorken expansion, this expansion parameter alpha equals one. If transverse expansion matters, alpha is larger than one. Now, remarkably, calculations of parton energy loss in such an expanding medium show a scaling law. The radiated gluon energy for different expansion scenarios can be mapped onto a single curve if rescaled in terms of this linear line-averaged transport coefficient.
In practice, this means that you can analyzed effects of parton energy loss in heavy ion collisions as if the medium were static. At the end of the analysis, one simply translates the extracted static average transport coefficient into the corresponding dynamical one.
Calculations for a static medium
apply to expanding systems
Rescaled spectrum