Falsifying AdS/CFT Drag or pQCD Heavy
Quark Energy Loss with A+A at RHIC and LHC
William Horowitz
Columbia University
Frankfurt Institute for Advanced Studies (FIAS)
January 10, 2008
arXiv:0706.2336 (LHC predictions)
arXiv:0710.0703 (RHIC predictions)
With many thanks to Miklos Gyulassy,
and Simon Wicks
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Outline
• Motivation for studying AdS/CFT
• Introduction to Jet Physics
• AdS Drag: Expectations, Results,
Limitations
• Conclusions
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Motivation
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Limited Toolbox for QCD Calculations
Previously only two:
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Lattice QCD
pQCD
• All momenta
• Euclidean correlators
• Any quantity
• Small coupling
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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
3+1 SYM

z=0
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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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Connection to Experiment
a.k.a. the Reality Check for Theory
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Introduction to Jet Physics
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Why High-pT Jets?
• Compare unmodified p+p collisions to
A+A:
pT
pT
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
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High-pT Observables
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, OSU
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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pQCD vs. AdS Drag:
Expectations, Results, Limitations
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pQCD Energy Loss Mechanisms
• Radiative bremsstrahlung
– Reduced from Bethe-Heitler limit by inmedium rescattering/interference:
• Landau-Pomeranchuk-Migdal (LPM) effect
• Elastic (collisional)
– Original thought: El << Rad
– But El ~ Rad at RHIC/LHC
WHDG (Wicks, Horowitz, Djordjevic, Gyulassy), Nucl.Phys.A784:426-442,2007, and refs. therein
– Importance under debate
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AdS/CFT Drag
• Model heavy quark jet energy loss by
embedding in AdS space
dpT/dt = - m pT
• AdS Result:
dpT/dt ~ -(T2/Mq) pT
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Energy Loss Comparison
D7 Probe Brane
t

– AdS/CFT Drag:
zm = 2pm / l1/2
Q, m
v
x
dpT/dt ~ -(T2/Mq) pT
zh = pT
z=0
3+1D Brane
Boundary
D3 Black Brane
(horizon)
Black Hole
– Compare to Bethe-Heitler
dpT/dt ~ -(T3/Mq2) pT
– Compare to 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
– Naïve
LHC Prediction
Unfortunately,
Large
Significant
suppression
expectations
rise large
inZoo:
Rleads
born
suppression
What
(pTto
)out
for
flattening
a in
Mess!
pQCD
fullpQCD
numerical
Rad+El
similar
calculation:
to AdS/CFT
AA
– Let’s
Use ofgorealistic
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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But There’s a Catch
– 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
– gcrit ~ Mq/(lT)
– Ambiguous 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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D7 Probe Brane
Q
Worldsheet boundary
Spacelike if g > gcrit
x5
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
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Nuclear Seminar, OSU
LHC
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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
• Year 1 of LHC could show qualitative differences
between energy loss mechanisms:
– dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST
• Ratio of charm to bottom RAA, Rcb, will be an
important observable
– Ratio is: flat in ST; approaches 1 from below in pQCD E-loss
– A measurement of this ratio NOT going to 1 will be a clear sign of
new physics: pQCD predicts ~ 2-3 times increase in Rcb by 30 GeV—
this can be observed in year 1 at LHC
• Measurement at RHIC will be possible
– AdS/CFT calculations applicable to higher momenta than at LHC
due to lower medium temperature
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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 (cont’d)
• Additional c, b PID Goodies:
– Adil Vitev in-medium fragmentation results in a much
more rapid rise to 1 for RcAA/RbAA with the possibility of
breaching 1 and asymptotically approaching 1 from above
– Surface emission models (although already unlikely as per
v2(pT) data) predict flat in pT c, b RAA, with a ratio of 1
– Moderately suppressed radiative only energy loss shows a
dip in the ratio at low pT; convolved loss is monotonic.
Caution: in this regime, approximations are violated
– Mach cone may be due to radiated gluons: from pQCD the
away-side dip should widen with increasing parton mass
• Need for p+A control
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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
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Quantitative AdS/CFT with Jets
• 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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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
1/10/08
• 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
1/10/08
WH, S. Wicks,
M. Gyulassy,
Djordjevic, in preparation
Nuclear
Seminar,M.
OSU
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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)
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A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005)
Nuclear Seminar, OSU
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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
1/10/08
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)
1/10/08
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005)
Nuclear Seminar, OSU
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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
1/10/08
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
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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)
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