Testing AdS/CFT Drag and pQCD
Heavy Quark Energy Loss
William Horowitz
The Ohio State University
Columbia University
Frankfurt Institute for Advanced Studies (FIAS)
October 28, 2008
LHC Predictions: Phys. Lett. B666:320, 2008 (arXiv:0706.2336)
RHIC Predictions: J. Phys. G35:044025, 2008 (arXiv:0710.0703)
With many thanks to Miklos Gyulassy and Simon Wicks
10/28/08
Nuclear Seminar, McGill University
William Horowitz
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Outline
• Motivation for studying AdS/CFT
• Introduction to Heavy Ion Physics
• pQCD vs. AdS Drag: Expectations,
Results, Limitations
• Conclusions
10/28/08
Nuclear Seminar, McGill University
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Motivation
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Limited Toolbox for QCD Calculations
Previously only two, restricted methods:
Lattice QCD
Two 10 Tflops QCDOC Computers: RBRC and DOE
• All momenta
• Euclidean correlators
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Nuclear Seminar, McGill University
pQCD
• Any quantity
• Small coupling
(large momenta)
William Horowitz
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Maldacena Conjecture
Large Nc limit of d-dimensional conformal field theory
dual to string theory on the product of d+1-dimensional
Anti-de Sitter space with a compact manifold
J Maldacena, Adv.Theor.Math.Phys.2:231-252,1998
Bosonic part of IIB low energy
effective action
Geometry of bosonic part of 10D supergravity, near horizon limit
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Nuclear Seminar, McGill University
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Regime of Applicability
– Large Nc, constant ‘t Hooft coupling (
)
Small quantum corrections
– Large ‘t Hooft coupling
Small string vibration corrections
– Only tractable case is both limits at once
Classical supergravity (SUGRA)
Q.M. SSYM
=> C.M. SNG
J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D75:106003, 2007
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Strong Coupling Calculation
• The supergravity double conjecture:
QCD  SYM  IIB
– IF super Yang-Mills (SYM) is not too
different from QCD, &
– IF Maldacena conjecture is true
– Then a tool exists to calculate stronglycoupled QCD in SUGRA
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Nuclear Seminar, McGill University
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Connection to Experiment
a.k.a. the Reality Check for Theory
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Introduction to
Heavy Ion Physics
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Geometry of a HI Collision
M Kaneta, Results from the
Relativistic Heavy Ion Collider (Part II)
• Hydro propagates IC
T Ludlum and L McLerran, Phys. Today 56N10:48 (2003)
– Results depend strongly on initial conditions
• Viscosity reduces eventual momentum
anisotropy
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Perfect Fluidity:
AdS + Hydro’s Most Famous Success
– Hydro h/s small ~ .1
• QGP fluid near-perfect
liquid
– Naïve pQCD => h/s ~ 1
• New estimates ~ .1
Z Xu, C Greiner, and H Stoecker, PRL101:082302 (2008)
– Lowest order AdS result:
h/s = 1/4p
• Universality?
P Kovtun, D Son, and A Starinets, Phys.Rev.Lett.94:111601 (2005)
P Kats and P Petrov, arXiv:0712.0743
M Brigante et al., Phys. Rev. D77:126006 (2008)
10/28/08
D. Teaney, Phys. Rev. C68, 034913 (2003)
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IC, Viscosity, and Hydro
T Hirano, et al., Phys. Lett. B636:299-304, 2006
– Sharper IC (CGC) => viscosity
– Softer IC (Glauber) => “perfect”
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Nuclear Seminar, McGill University
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Why High-pT Jets?
• Compare unmodified p+p collisions to
A+A:
pT
pT
2D Transverse directions
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
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Jet Physics Terminology
Naïvely: if medium has no effect, then RAA = 1
Common variables used are transverse
momentum, pT, and angle with respect to the
reaction plane, f
Common to Fourier expand RAA:
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Nuclear Seminar, McGill University
pT
f
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pQCD Success at RHIC:
(circa 2005)
Y. Akiba for the PHENIX collaboration,
hep-ex/0510008
– Consistency:
RAA(h)~RAA(p)
– Null Control:
RAA(g)~1
– GLV Prediction: Theory~Data for reasonable
fixed L~5 fm and dNg/dy~dNp/dy
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Trouble for wQGP Picture
Hydro
h/s
too small
e-2Rtoo
too
•v
wQGP
notsmall
ruled
out, but what if we try
AA large
strong coupling?
A.
H. Feng,
and J. Jia,
C71:034909
(2005)
M. Drees,
Djorjevic,
M. Gyulassy,
R.Phys.
Vogt,Rev.
S. Wicks,
Phys. Lett.
(first
byD.E.Teaney,
Shuryak,
Phys.
Rev.
C66:027902
(2002))
Rev.
C68,
034913 (2003)
B632:81-86
(2006) Phys.
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Qualitative AdS/CFT Successes:
-R1~
sMach
=(3/4)
wave-like
s
structures
,
similar
• h/s
e-strong
RAA
~
p,
h
R
;
e
)to Lattice
~
1/4p
<<
weak
AA
AA(fh/s
AdS/CFT
pQCD
AdS/CFT
J. P. Blaizot,
S. S. Gubser,
E. Iancu,
S. S.U.
Pufu,
Kraemmer,
and A. Yarom,
A. Rebhan,
arXiv:0706.0213
hep-ph/0611393
T. Hirano and M. Gyulassy, Nucl. Phys. A69:71-94 (2006)
PHENIX, Phys. Rev. Lett. 98, 172301 (2007)
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AdS/CFT Energy Loss Models
• Langevin model
– Collisional energy loss for heavy quarks
– Restricted to low pT
– pQCD vs. AdS/CFT computation of D, the diffusion
coefficient
• ASW model
– Radiative energy loss model for all parton species
– pQCD vs. AdS/CFT computation of
– Debate over its predicted magnitude
• ST drag calculation
– Drag coefficient for a massive quark moving through a
strongly coupled SYM plasma at uniform T
– not yet used to calculate observables: let’s do it!
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AdS/CFT Drag
• Model heavy quark jet energy loss by
embedding string in AdS space
dpT/dt = - m pT
m = pl1/2 T2/2Mq
J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D75:106003, 2007
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Energy Loss Comparison
D7 Probe Brane
t

– AdS/CFT Drag:
zm = 2pm / l1/2
Q, m
dpT/dt ~ -(T2/Mq) pT
zh = pT
z=0
v
x
3+1D Brane
Boundary
D3 Black Brane
(horizon)
Black Hole
– Similar to Bethe-Heitler
dpT/dt ~ -(T3/Mq2) pT
– Very different from LPM
dpT/dt ~ -LT3 log(pT/Mq)
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RAA Approximation
– Above a few GeV, quark production
spectrum is approximately power law:
• dN/dpT ~ 1/pT(n+1), where n(pT) has some
momentum dependence
y=0
RHIC
– We can approximate RAA(pT):
• RAA ~ (1-e(pT))n(pT),
where pf = (1-e)pi (i.e. e = 1-pf/pi)
LHC
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Looking for a Robust, Detectable Signal
– Use LHC’s large pT reach and identification of c
and b to distinguish between pQCD, AdS/CFT
• Asymptotic pQCD momentum loss:
erad ~ as L2 log(pT/Mq)/pT
• String theory drag momentum loss:
eST ~ 1 - Exp(-m L),
m = pl1/2 T2/2Mq
S. Gubser, Phys.Rev.D74:126005 (2006); C. Herzog et al. JHEP 0607:013,2006
– Independent of pT and strongly dependent on Mq!
– T2 dependence in exponent makes for a very sensitive probe
– Expect: epQCD
0 vs. eAdS indep of pT!!
• dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST
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Model Inputs
– AdS/CFT Drag: nontrivial mapping of QCD to SYM
• “Obvious”: as = aSYM = const., TSYM = TQCD
– D 2pT = 3 inspired: as = .05
– pQCD/Hydro inspired: as = .3 (D 2pT ~ 1)
• “Alternative”: l = 5.5, TSYM = TQCD/31/4
• Start loss at thermalization time t0; end loss at Tc
– WHDG convolved radiative and elastic energy loss
• as = .3
– WHDG radiative energy loss (similar to ASW)
•
= 40, 100
– Use realistic, diffuse medium with Bjorken expansion
– PHOBOS (dNg/dy = 1750); KLN model of CGC (dNg/dy = 2900)
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LHC c, b RAA pT Dependence
WH, M. Gyulassy, arXiv:0706.2336
– Significant
NaïvePrediction
LHC
Unfortunately,
Large
suppression
expectations
rise large
inZoo:
Rleads
met
suppression
What
(pTin
to
) for
full
flattening
a Mess!
pQCD
numerical
pQCD
Rad+El
similar
calculation:
to AdS/CFT
AA
– Use
Let’sofgorealistic
through
dRAA
geometry
step
(pT)/dp
by step
> 0 Bjorken
=> pQCD;
expansion
dRAA(pTallows
)/dpT <
saturation
0 => ST below .2
Tand
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An Enhanced Signal
• But what about the interplay between
mass and momentum?
– Take ratio of c to b RAA(pT)
• pQCD: Mass effects die out with increasing pT
RcbpQCD(pT) ~ 1 - as n(pT) L2 log(Mb/Mc) ( /pT)
– Ratio starts below 1, asymptotically approaches 1.
Approach is slower for higher quenching
• ST: drag independent of pT, inversely
proportional to mass. Simple analytic approx.
of uniform medium gives
RcbpQCD(pT) ~ nbMc/ncMb ~ Mc/Mb ~ .27
– Ratio starts below 1; independent of pT
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LHC RcAA(pT)/RbAA(pT) Prediction
• Recall the Zoo:
WH, M. Gyulassy, arXiv:0706.2336 [nucl-th]
– Taking the ratio cancels most normalization differences seen previously
– pQCD ratio asymptotically approaches 1, and more slowly so for increased
quenching (until quenching saturates)
WH, M.times
Gyulassy,
arXiv:0706.2336
– AdS/CFT ratio is flat and many
smaller
than[nucl-th]
pQCD at only moderate pT
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Not So Fast!
– Speed limit estimate for
applicability of AdS drag
• g < gcrit = (1 + 2Mq/l1/2 T)2
~ 4Mq2/(l T2)
– Limited by Mcharm ~ 1.2 GeV
• Similar to BH
LPM
D7 Probe Brane
Worldsheet boundary
Spacelike if g > gcrit
x5
– gcrit ~ Mq/(lT)
– No Single T for QGP
• smallest gcrit for largest T
T = T(t0, x=y=0): “(”
• largest gcrit for smallest T
T = Tc: “]”
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Q
Nuclear Seminar, McGill University
Trailing
String
“Brachistochrone”
D3 Black Brane
“z”
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LHC RcAA(pT)/RbAA(pT) Prediction
(with speed limits)
WH, M. Gyulassy, arXiv:0706.2336 [nucl-th]
– T(t0): (O), corrections unlikely for smaller momenta
– Tc: (|), corrections likely for higher momenta
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Measurement at RHIC
– Future detector upgrades will allow for identified c
and b quark measurements
– RHIC production spectrum significantly
harder than LHC
•
• NOT slowly varying
y=0
RHIC
– No longer expect
pQCD dRAA/dpT > 0
• Large n requires
corrections to naïve
Rcb ~ Mc/Mb
10/28/08
Nuclear Seminar, McGill University
LHC
William Horowitz
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RHIC c, b RAA pT Dependence
WH, M. Gyulassy, arXiv:0710.0703 [nucl-th]
• Large increase in n(pT) overcomes reduction in
E-loss and makes pQCD dRAA/dpT < 0, as well
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RHIC Rcb Ratio
pQCD
pQCD
AdS/CFT
AdS/CFT
WH, M. Gyulassy, arXiv:0710.0703 [nucl-th]
• Wider distribution of AdS/CFT curves due to large n:
increased sensitivity to input parameters
• Advantage of RHIC: lower T => higher AdS speed limits
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Conclusions
• Previous AdS qualitative successes inconclusive
• AdS/CFT Drag observables calculated
• Generic differences (pQCD vs. AdS/CFT Drag)
seen in RAA
– Masked by extreme pQCD
• Enhancement from ratio of c to b RAA
– Discovery potential in Year 1 LHC Run
• Understanding regions of self-consistency crucial
• RHIC measurement possible
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Nuclear Seminar, McGill University
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Backups
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Geometry of a HI Collision
Medium density and jet production
are wide, smooth distributions
Use of unrealistic geometries strongly
bias results
S. Wicks, WH, M. Djordjevic, M. Gyulassy,
Nucl.Phys.A784:426-442,2007
1D Hubble flow => r(t) ~ 1/t
=> T(t) ~ 1/t1/3
M. Gyulassy and L. McLerran, Nucl.Phys.A750:30-63,2005
10/28/08
Nuclear Seminar, McGill University
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Langevin Model
– Langevin equations (assumes gv ~ 1 to neglect
radiative effects):
– Relate drag coef. to diffusion coef.:
– IIB Calculation:
AdS/CFT here
• Use of Langevin requires relaxation time be large
compared to the inverse temperature:
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But There’s a Catch (II)
• Limited experimental pT reach?
ALICE Physics Performance Report, Vol. II
– ATLAS and CMS do not seem to be limited in this
way (claims of year 1 pT reach of ~100 GeV) but
systematic studies have not yet been performed
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LHC p Predictions
WH, S. Wicks, M. Gyulassy, M. Djordjevic,
in preparation
10/28/08
• Our predictions show a
significant increase in RAA as a
function of pT
• This rise is robust over the
range of predicted dNg/dy for
the LHC that we used
• This should be compared to
the flat in pT curves of AWSbased energy loss (next slide)
• We wish to understand the
origin of this difference
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Asymptopia at the LHC
Asymptotic pocket formulae:
DErad/E ~ a3 Log(E/m2L)/E
DEel/E ~ a2 Log((E T)1/2/mg)/E
10/28/08
WH,
S. Wicks,
M. Gyulassy,
Djordjevic, in preparation
Nuclear
Seminar,
McGillM.University
William Horowitz
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K. J. Eskola, H. Honkanen, C. A. Salgado, and U.
A. Wiedemann, Nucl. Phys. A747:511:529 (2005)
K. J. Eskola, H. Honkanen, C. A. Salgado, and
U. A. Wiedemann, Nucl. Phys. A747:511:529
(2005)
10/28/08
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005)
Nuclear Seminar, McGill University
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Pion RAA
• Is it a good measurement for tomography?
– Yes: small experimental error
– Maybe not: some models
appear “fragile”
• Claim: we should not be so immediately dismissive of the pion RAA as a tomographic tool
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Fragility:
A Poor Descriptor
• All energy loss models with a formation time
saturate at some RminAA > 0
• The questions asked should be quantitative :
– Where is RdataAA compared to RminAA?
– How much can one change a model’s controlling
parameter so that it still agrees with a measurement
within error?
– Define sensitivity, s = min. param/max. param that
is consistent with data within error
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Different Models have Different
Sensitivities to the Pion RAA
• GLV:
s<2
• Higher Twist:
s<2
• DGLV+El+Geom:
s<2
• AWS:
s~3
10/28/08
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
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T Renk and K Eskola, Phys. Rev. C 75, 054910 (2007)
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
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A Closer Look at ASW
The lack of sensitivity needs to be more closely examined
because (a) unrealistic geometry (hard cylinders) and no
expansion and (b) no expansion shown against older data (whose
error bars have subsequently shrunk
(a)
(b)
K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann,
Nucl. Phys. A747:511:529 (2005)
10/28/08
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005)
Nuclear Seminar, McGill University
William Horowitz
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Surface Bias vs. Surface Emission
– Surface Emission: one phrase explanation of fragility
• All models become surface emitting with infinite E loss
– Surface Bias occurs in all energy loss models
• Expansion + Realistic geometry => model probes a large
portion of medium
A. Majumder, HP2006
10/28/08
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
Nuclear Seminar, McGill University
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A Closer Look at ASW
– Difficult to draw conclusions on
inherent surface bias in AWS
from this for three reasons:
• No Bjorken expansion
• Glue and light quark contributions
not disentangled
• Plotted against Linput (complicated
mapping from Linput to physical
distance)
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005)
10/28/08
Nuclear Seminar, McGill University
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Additional Discerning Power
– Adil-Vitev in-medium fragmentation rapidly approaches, and then broaches, 1
» Does not include partonic energy loss, which will be nonnegligable as ratio goes to unity
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Conclusions
• AdS/CFT Drag observables calculated
• Generic differences (pQCD vs.
AdS/CFT Drag) seen in RAA
– Masked by extreme pQCD
• Enhancement from ratio of c to b RAA
– Discovery potential in Year 1 LHC Run
• Understanding regions of selfconsistency crucial
• RHIC measurement possible
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Shameless self-promotion by the presenter
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Geometry of a HI Collision
Medium density and jet production
are wide, smooth distributions
Use of unrealistic geometries strongly
bias results
S. Wicks, WH, M. Djordjevic, M. Gyulassy,
Nucl.Phys.A784:426-442,2007
1D Hubble flow => r(t) ~ 1/t
=> T(t) ~ 1/t1/3
M. Gyulassy and L. McLerran, Nucl.Phys.A750:30-63,2005
10/28/08
Nuclear Seminar, McGill University
William Horowitz
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