William Horowitz
The Ohio State University
May 21, 2009
With many thanks to Brian Cole, Yuri Kovchegov, and Ulrich Heinz
5/21/09 Energy Loss at RHIC and LHC
William Horowitz
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• Introduction
• pQCD
• AdS/CFT
5/21/09
• Conclusions
Energy Loss at RHIC and LHC
William Horowitz
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Heavy ion collision
Heavy ion jet physics p
T f
William Horowitz
3 Energy Loss at RHIC and LHC

T
• Compare unmodified p+p collisions to
A+A: p
T p
T
2D Transverse direction
Longitudinal
(beam pipe) direction
Figures from http://www.star.bnl.gov/central/focus/highPt/
• Use suppression pattern to either:
– Learn about medium (requires detailed understanding of energy loss): jet tomography
– Learn about energy loss
William Horowitz
4 5/21/09 Energy Loss at RHIC and LHC

T
Naïvely: if medium has no effect, then R
AA
= 1
Common variables used are transverse momentum, p
T
, and angle with respect to the reaction plane, f
Fourier expand R
AA
: f p
T
5/21/09 Energy Loss at RHIC and LHC
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5/21/09 Energy Loss at RHIC and LHC
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(circa 2005)
Y. Akiba for the PHENIX collaboration, hep-ex/0510008
– Consistency:
R
AA
( h )~R
AA
( p )
– Null Control:
R
AA
( g )~1
– GLV Prediction: Theory~Data for reasonable fixed L~5 fm and dN g
/dy~dN p
/dy
William Horowitz
7 5/21/09 Energy Loss at RHIC and LHC

T
– v
2 too small p 0 v
2
– NPE supp. too large
WHDG
NPE v
2
C. Vale, QM09 Plenary (analysis by R. Wei)
STAR, Phys. Rev. Lett. 98, 192301 (2007)
Pert. at LHC energies?
5/21/09
PHENIX, Phys. Rev. Lett. 98, 172301 (2007)
Energy Loss at RHIC and LHC
William Horowitz
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WHDG, Nucl.Phys.A784:426-442,2007 Bass et al., Phys.Rev.C79:024901,2009
– Inconsistent medium properties
5/21/09
– Distinguish between models
Energy Loss at RHIC and LHC
Bass et al.
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• Vary input param.
• Find “best” value
PHENIX, PRC77:064907,2008
Energy Loss at RHIC and LHC
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5/21/09
• Difficult at R
AA
– Many assumptions
• Prod. spectra, FF, geometry, etc.
• Focus on “Brick”
– Fixed L, T, E jet
• Compare WHDG Rad to ASW-SH
– WHDG Rad: DGLV opacity expansion
• GLV + massive quarks, gluons
– ASW-SH: opacity expansion
William Horowitz
11 Energy Loss at RHIC and LHC

• Examine ASW-SH = GLV claim
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• Warm-up for WHDG Rad vs. ASW-MS
Energy Loss at RHIC and LHC
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• Implemented formulae very different
– But, massless DGLV integrand same form
(Modulo detail of scattering center distribution)
– But, var. have very diff. physical meaning (!)
• Strong cutoff dependence (!)
• Massive gluon effect (!)
– Pun intended
William Horowitz
13 Energy Loss at RHIC and LHC

5/21/09
• dN g
/dx
– Single inclusive radiated gluon spectrum
• P( e )
– Poisson convolution
– Model multiple emission
• Additional assumptions
– Convolve dN g
• E f
= (1 – e )E i
/dx to find P( e )
• pdf
William Horowitz
14 Energy Loss at RHIC and LHC

5/21/09
• ASW-SH code no good for R
AA
– To be fair, hasn’t been used
• R
AA cutoff dep. likely => large th. err.
– Must be overcome for tomography
– Strong a s dependence, too
• Large gluon mass effect
– Higher order diagrams likely important
• Not to be confused with higher orders of opacity
William Horowitz
15 Energy Loss at RHIC and LHC

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T
5/21/09
• Why study AdS E-loss models?
– Many calculations vastly simpler
• Complicated in unusual ways
– Data difficult to reconcile with pQCD
– pQCD quasiparticle picture leads to dominant q ~ m ~ .5 GeV mom. transfers
=> Nonperturbatively large a s
• Use data to learn about E-loss mechanism, plasma properties
– Domains of self-consistency crucial for understanding
William Horowitz
Energy Loss at RHIC and LHC 17

– Langevin Diffusion
• Collisional energy loss for heavy quarks
• Restricted to low p
T
• pQCD vs. AdS/CFT computation of D, the diffusion coefficient
Moore and Teaney, Phys.Rev.C71:064904,2005
Casalderrey-Solana and Teaney, Phys.Rev.D74:085012,2006; JHEP 0704:039,2007
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– ASW/LRW model
• Radiative energy loss model for all parton species
• pQCD vs. AdS/CFT computation of
• Debate over its predicted magnitude
BDMPS, Nucl.Phys.B484:265-282,1997
Armesto, Salgado, and Wiedemann, Phys. Rev. D69 (2004) 114003
Liu, Ragagopal, Wiedemann, PRL 97:182301,2006; JHEP 0703:066,2007
Energy Loss at RHIC and LHC
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String Drag calculation
– Embed string rep. quark/gluon in AdS geom.
– Includes all E-loss modes (difficult to interpret)
– Gluons and light quarks
Gubser, Gulotta, Pufu, Rocha, JHEP 0810:052, 2008
Chesler, Jensen, Karch, Yaffe, arXiv:0810.1985 [hep-th]
– Empty space HQ calculation
Kharzeev, arXiv:0806.0358 [hep-ph]
– Previous HQ: thermalized QGP plasma, temp. T,
Gubser, Phys.Rev.D74:126005,2006
Herzog, Karch, Kovtun, Kozcaz, Yaffe, JHEP 0607:013, 2006
William Horowitz
19 Energy Loss at RHIC and LHC

D7 Probe Brane t v x z = 0
– AdS/CFT Drag: dp
T
/dt ~ -(T 2 /M q
) p
T z m
= l
1/2 /2 p m z h
= 1/ p
T z = 
Q, m
3+1D Brane
Boundary
D3 Black Brane
(horizon)
Black Hole
– Similar to Bethe-Heitler dp
T
/dt ~ -(T 3 /M q
2 ) p
T
– Very different from LPM dp
T
/dt ~ -LT 3 log(p
T
/M q
)
Energy Loss at RHIC and LHC
William Horowitz
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c
AA
T
b
AA
T
• Individual c and b R
AA
(p
T
) predictions:
WH and M. Gyulassy, Phys. Lett. B 666, 320 (2008)
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– Taking the ratio cancels most normalization differences seen previously
– pQCD ratio asymptotically approaches 1, and more slowly so for increased quenching (until quenching saturates)
– AdS/CFT ratio is flat and many times smaller than pQCD at only moderate p
– Distinguish rad and el contributions?
T
William Horowitz
Energy Loss at RHIC and LHC 21

5/21/09
• How universal are th. HQ drag results?
– Examine different theories
– Investigate alternate geometries
• Other AdS geometries
– Bjorken expanding hydro
– Shock metric
• Warm-up to Bj. hydro
• Can represent both hot and cold nuclear matter
William Horowitz
22 Energy Loss at RHIC and LHC

Constant T Thermal Black Brane
DIS
Shock Geometries
Nucleus as Shock
Embedded String in Shock
J Friess, et al., PRD75:106003, 2007
Albacete, Kovchegov, Taliotis,
JHEP 0807, 074 (2008)
Bjorken-Expanding Medium
Before z x v shock
Q
After z x
Q v shock
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5/21/09
• Parameterize string worldsheet
– X m
( t , s )
• Plug into Nambu-Goto action
• Varying S
NG yields EOM for X m
• Canonical momentum flow (in t , s )
William Horowitz
24 Energy Loss at RHIC and LHC

5/21/09
• Find string solutions in HQ rest frame
– v
HQ
= 0
• Assume static case (not new)
– Shock wave exists for all time
– String dragged for all time
• X m
= (t, x(z), 0,0, z)
• Simple analytic solutions:
– x(z) = x
0
, x
0
± m ½ z 3 /3
William Horowitz
25 Energy Loss at RHIC and LHC

z = 0
• Three t-ind. solutions (static gauge):
X m
= (t, x(z), 0,0, z)
– x(z) = x
0
, x
0
± m ½ z 3 /3
Q z =  v shock x
0
- m ½ z 3 /3 x
0
+ m ½ z 3 /3 x
0 x
• Constant solution unstable
• Time-reversed negative x solution unphysical
• Sim. to x ~ z 3 /3, z << 1, for const. T BH geom.
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26 5/21/09 Energy Loss at RHIC and LHC

x(z) = m ½ z 3 /3 =>
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Relate m to nuclear properties
– Use AdS dictionary
• Metric in Fefferman-Graham form: m ~ T
--
/N c
2
– T’
00
~ N c
2 L 4
• N c
2 gluons per nucleon in shock
• L is typical mom. scale; L -1 typical dist. scale
William Horowitz
27 Energy Loss at RHIC and LHC

1/
L
• HQ Rest Frame • Shock Rest Frame
L v sh
M q v q
= -v sh i v q
= 0 i v sh
= 0
– Change coords, boost T mn into HQ rest frame:
• T
--
~ N c
2 L 4 g 2 ~ N c
2 L 4 (p’/M) 2
• p’ ~ g M: HQ mom. in rest frame of shock
M q
– Boost mom. loss into shock rest frame
– p 0 t
= 0:
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• This leads to
5/21/09
–Recall for BH:
–Shock gives exactly the same drag as BH for L = p T
• We’ve generalized the BH solution to both cold and hot nuclear matter E-loss
Energy Loss at RHIC and LHC
William Horowitz
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• Local speed of light (in HQ rest frame)
– Demand reality of point-particle action
• Solve for v = 0 for finite mass HQ
– z = z
M
= l ½ /2 p M q
5/21/09
– Same speed limit as for BH metric when L = p T
Energy Loss at RHIC and LHC
William Horowitz
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5/21/09
– Use data to test E-loss mechanism
• R c
AA
(p
T
)/R b
AA
(p
T
) wonderful tool
– Calculated HQ drag in shock geometry
• For L = p T, drag and speed limit identical to BH
• Generalizes HQ drag to hot and cold nuclear matter
– Unlike BH, quark mass unaffected by shock
• Quark always heavy from strong coupling dressing?
• BH thermal adjustment from plasma screening IR?
– Future work:
• Time-dependent shock treatment
• AdS E-loss in Bjorken expanding medium
Energy Loss at RHIC and LHC
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5/21/09 Energy Loss at RHIC and LHC
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