Parton Energy Loss
At Strong Coupling
Berndt Müller
Hard Probes 2010
Eilat, Israel: 10-15 October 2010
Friday, July 1, 2011
Overview

Reminder: Jet quenching at weak coupling
Micro-Primer: Strongly coupled AdS/CFT duality
Jet quenching in strongly coupled AdS/CFT
Phenomenological comparisons
Final thoughts

Some references:

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







Gubser, hep-th/0611272
Gubser, Gulotta, Pufu & Rocha, 0803.1470
Chesler, Jensen, Karch & Yaffe, 0810.1985
Marquet & Renk, 0908.0880
Casalderrey-Solana, Fernandez & Mateos, 0912.3717
Arnold & Vaman, 1008.4023
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Friday, July 1, 2011
Jet production & quenching
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Friday, July 1, 2011
Jet production & quenching
Itʼs NOT
about this
(the hard
scattering)
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Friday, July 1, 2011
Jet production & quenching
Itʼs NOT
about this
(the hard
scattering)
Itʼs ALL
about this
(medium
interaction)
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Friday, July 1, 2011
pQCD approach
Treat energetic parton dynamics
(radiation) perturbatively
Treat medium dynamics (gluon
content) non-perturbatively
Medium properties encoded in transport coefficients
�p2T �L
q̂ =
L
�∆E�L
ê =
L
Transverse momemtum
diffusion rate
Elastic energy loss rate
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Friday, July 1, 2011
Z-BDMPS formalism
Zakharovʼs path integral for in-medium gluon radiation
DGLAP splitting kernel
eikonal propagator of the parton-gluon dipole
A “typical” diagram
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Friday, July 1, 2011
pQCD scenarios
➧
S. Caron-Huot & C. Gale
Jet quenching scenarios landscape
LPM
effect
interference of vacuum
and medium radiation
QGP “brick” at T = 400 MeV
screened 1-gluon exchange
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Friday, July 1, 2011
pQCD scenarios
Assumes weakly coupled QGP
➧
S. Caron-Huot & C. Gale
Jet quenching scenarios landscape
LPM
effect
interference of vacuum
and medium radiation
QGP “brick” at T = 400 MeV
screened 1-gluon exchange
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Friday, July 1, 2011
Weak vs. strong coupling (P vs. NP)
gluon propagation:
P or NP
P = perturbative
(weakly coupled)
gluon
medium
structure:
P or NP
NP = non-perturbative
(strongly coupled)
quark
hard vertex:
always P
radiation vertex:
P or NP
quark propagation:
P or NP
pQCD only allows for NP medium structure (via qhat, ehat)
Rigorous AdS/CFT calculation treats all components NP
Hybrid approaches treat some aspects P and some NP
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Friday, July 1, 2011
Friday, July 1, 2011
Quark-gluon plasma
• Objects existing in higher dimensio
• 4d field theory lives on the bounda
Basic idea:
• Domain of utility: Large Nc , λ SY
Strong coupling
λ = g2 Nc >> 1
⇓
classical
gravity limit
Dynamics in 5d encodes dynamics i
black brane
5th dimension
• Objects existing in QFT: quarks, p
AdS5×S5 / N = 4 SYM duality
Our world (χ=0)
Black hole / brane (χ0)
10-dim. metric:
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Jets in N=4 SYM ?
Jets are not naturally formed at strong coupling !
Why?? “Democratic” splitting prevents formation of jets.
“democratic” splitting
Splitting time: ts = E/Q2, the final transverse size is: Lf ~ 1/Qf.
To discuss jet-like phenomena, we must select special (high E/Q2) initial
states or assume that strong coupling somehow only sets in after a parton
has reached virtuality Q2 ~ T2 !
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Friday, July 1, 2011
Heavy quark energy loss
Quark-gluon plasma
Deposited energy
and momentum
Heavy quark = endpoint
of a string attached to a
D7-brane at
Trailing string
(flux tube)
Black hole
χm = √λ / mQ << χ0
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Friday, July 1, 2011
Heavy quark = trailing string
v
χm
χh =
comoving field
Upper and lower parts
of the training string are
causally disconnected
radiated field
χ0 =
Energy radiated by quark (described by string below χh) thermalizes
almost instantly: medium response well described by hydrodynamics.
same formula as in QCD, but with
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Friday, July 1, 2011
pQCD vs. SC N=4 SYM
pQCD: Gluons are “liberated” by
(multiple) scattering in the medium
➥ radiation is governed by
transverse momentum diffusion:
Strongly coupled N=4 SYM:
Gluons are “liberated” in
(multiple) branching cascade;
➥ kept off-shell by thermal
force from the medium
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Friday, July 1, 2011
Dual picture
Parton cascade
holographic image of trailing string
Dynamics beyond 1/T is hydrodynamics !
envelope of the
parton cascade
hydro regime
parton cascade
hy
d ro
reg
im
e
r⊥3
r⊥
trailing string
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Friday, July 1, 2011
QGP structure
QGP energy density can be expressed
in terms of the parton structure function:
F2(x,Q2) describes the area density of gluons in the QGP which are encountered
by a fast traveling parton over the coherence length lc = 2E/Q2.
Weakly coupled QGP: most of the energy density is carried by partons with x ~ 1,
i.e. by quasi-particulate gluons.
Strongly coupled QGP: most of the energy density resides in partons with x ~ T/Q,
i.e. by “wee”, or field-like (but not necessarily coherent) gluons.
Whether these partons are considered as part of the jet, or as part of the QGP, is a
matter of interpretation (ref. frame, gauge, etc.).
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Friday, July 1, 2011
Light parton energy loss
χ= 0
χE
Light partons (gluons) can be
modeled as “doubled” strings
connected to the black hole
horizon, and not anchored to
a brane near the boundary.
Δx ≈
4E
α s N c q̂
χh
Total distance traveled by perturbation:
Compare with pQCD expression:
Splitting time:
dt = E/Q(t)2
virtuality due to
work on parton:
Q(t) ~ (T t)2
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Friday, July 1, 2011
Light parton energy loss
P. Chesler
“Gluon” string
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Friday, July 1, 2011
Light parton energy loss
P. Chesler
“Bragg” peak
dE
dt
t
“Gluon” string
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Friday, July 1, 2011
Light parton energy loss
P. Chesler
“Bragg” peak
dE
dt
t
“Gluon” string
Same phenomenon
in pQCD + hydro
Neufeld & BM
Qin, Majumder,
Song & Heinz
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Friday, July 1, 2011
pQCD vs. AdS/CFT
Jet fragmentation controlled by:
virtuality evolution Q2(t)
splitting functions P(z)
Vacuum
Virtuality evolution Q2(t) differs
both in vacuum and in medium.
collinear divergence (pQCD) vs.
“democratic” splitting (AdS/CFT)
Medium
AdS/CFT
pQCD
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Friday, July 1, 2011
Virtuality evolution
Example: E = 30 GeV, Q0 = 5 GeV, T0 = 300 MeV at t0 = 1 fm/c.
5
Q�t� �GeV�
4
3
AdS/CFT
2
pQCD
1
0
0
2
t �fm�c�
4
6
8
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Friday, July 1, 2011
Virtuality evolution
Example: E = 30 GeV, Q0 = 5 GeV, T0 = 300 MeV at t0 = 1 fm/c.
5
Q�t� �GeV�
4
3
AdS/CFT
2
pQCD
1
0
0
2
t �fm�c�
4
6
8
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Friday, July 1, 2011
Splitting functions
Include LPM effect: z(1-z)E/k⊥2 t > 1 and IR cut-off: k⊥2 > 0.5 GeV2
Effective fragmentation pattern at time t (without cascading).
Democratic splitting (αs = 1)
Collinear splitting (αs = 0.3)
140
120
t = 1.0 fm/c
D�z�
t = 0.3 fm/c
100
80
60
40
t = 0.1 fm/c
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0
0.0
0.2
0.4
0.6
z
Friday, July 1, 2011
0.8
1.0
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Phenomenology
Main difference between weak
and strong coupling (besides
overall strength of e-loss) is the
length dependence:
dE/dx ~ L (pQCD)
dE/dx ~ L2 (N=4 SYM)
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Friday, July 1, 2011
Phenomenology
Main difference between weak
and strong coupling (besides
overall strength of e-loss) is the
length dependence:
dE/dx ~ L (pQCD)
dE/dx ~ L2 (N=4 SYM)
Marquet & Renk
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Friday, July 1, 2011
Phenomenology
Main difference between weak
and strong coupling (besides
overall strength of e-loss) is the
length dependence:
dE/dx ~ L (pQCD)
dE/dx ~ L2 (N=4 SYM)
Marquet & Renk
IAA
Marquet & Renk
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Friday, July 1, 2011
Summary: Relevant questions

Are jets formed in QGP medium?


Is the QGP strongly coupled?


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Probably YES: jet quenching is stronger than expected from a
perturbative QGP (and shear viscosity is smaller)
This is not a problem for pQCD jet quenching theory
Is the parent parton strongly coupled after reaching the
medium virtuality?



YES ➠ Coupling is weak before virtuality reaches medium scale
We don’t know.
Study cone structure of in-medium radiation for triggered jets
Are the radiated gluons strongly coupled?


We don’t know.
Study cone structure and degree of thermalization of rad. energy
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Friday, July 1, 2011
What’s needed?

Establish length dependence of energy loss.
Establish energy dependence of energy loss.
Measure medium modification of angular and momentum
distribution of radiated energy.
Measure quark mass dependence of energy loss.

Many opportunities at RHIC and LHC:
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Tagged jets (energy, flavor)
Angle dependence
System size dependence
Fully reconstructed jets
A world-class jet detector at RHIC is needed
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Friday, July 1, 2011