1. 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)
November 30, 2007
arXiv:  (LHC predictions)
arXiv: (RHIC predictions)
With many thanks to Miklos Gyulassy,
and Simon Wicks
Nuclear Theory Seminar, Texas A&M

2. QCD Calculations Previously only two tools: Lattice QCD pQCD
All momenta
Euclidean correlators
Any quantity
Small coupling
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3. Nuclear Theory Seminar, Texas A&M
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
Nuclear Theory Seminar, Texas A&M

4. 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
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5. 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 strongly-coupled QCD in SUGRA
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6. Connection to Experiment
a.k.a. the Reality Check for Theory
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7. Nuclear Theory Seminar, Texas A&M
pQCD Success at RHIC:
(circa 2005)
Y. Akiba for the PHENIX collaboration, hep-ex/
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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8. Trouble for wQGP Picture
v2 too large
A. Drees, H. Feng, and J. Jia, Phys. Rev. C71: (2005)
(first by E. Shuryak, Phys. Rev. C66: (2002))
D. Teaney, Phys. Rev. C68, (2003)
Hydro h/s too small
wQGP not ruled out, but what if we try strong coupling?
e- RAA too small
M. Djorjevic, M. Gyulassy, R. Vogt, S. Wicks, Phys. Lett. B632:81-86 (2006)
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9. Qualitative AdS/CFT Successes:
h/sAdS/CFT ~ 1/4p << 1 ~ h/spQCD
e- RAA ~ p, h RAA; e- RAA(f)
sstrong=(3/4) sweak, similar to Lattice
Mach wave-like structures
J. P. Blaizot, E. Iancu, U. Kraemmer, A. Rebhan, hep-ph/
AdS/CFT
PHENIX, Phys. Rev. Lett. 98, (2007)
S. S. Gubser, S. S. Pufu, and A. Yarom, arXiv:
T. Hirano and M. Gyulassy, Nucl. Phys. A69:71-94 (2006)
Nuclear Theory Seminar, Texas A&M

10. 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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11. Energy Loss Dependencet x
Q, m v
D7 Probe Brane
D3 Black Brane
(horizon)
3+1D Brane
Boundary
Black Hole
z = 0
zh = pT
zm = 2pm / l1/2
AdS/CFT Drag:
dpT/dt ~ -(T2/Mq) pT
Compare to Bethe-Heitler
dpT/dt ~ -(T3/Mq2) pT
Compare to LPM
dpT/dt ~ -LT3 log(pT/Mq)
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12. Looking for a Robust, Detectable Signal
Use LHC’s large pT reach and identification of c and b to distinguish between pQCD, AdS/CFT
RAA ~ (1-e(pT))n(pT), where pf = (1-e)pi (i.e. e = 1-pf/pi)
Asymptotic pQCD momentum loss:
String theory drag momentum loss:
Independent of pT and strongly dependent on Mq!
T2 dependence in exponent makes for a very sensitive probe
Expect: epQCD vs. eAdS indep of pT!!
dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST
erad ~ as L2 log(pT/Mq)/pT
eST ~ 1 - Exp(-m L), m = pl1/2 T2/2Mq
S. Gubser, Phys.Rev.D74: (2006); C. Herzog et al. JHEP 0607:013,2006
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13. Nuclear Theory Seminar, Texas A&M
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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14. LHC c, b RAA pT Dependence
WH, M. Gyulassy, arXiv:
Naïve expectations born out in full numerical calculation:
dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST
LHC Prediction Zoo: What a Mess!
Let’s go through step by step
Significant rise in RAA(pT) for pQCD Rad+El
Unfortunately, large suppression pQCD similar to AdS/CFT
Large suppression leads to flattening
Use of realistic geometry and Bjorken expansion allows saturation below .2
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15. Nuclear Theory Seminar, Texas A&M
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
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
RcbpQCD(pT) ~ 1 - as n(pT) L2 log(Mb/Mc) ( /pT)
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16. LHC RcAA(pT)/RbAA(pT) Prediction
Recall the Zoo:
WH, M. Gyulassy, arXiv: [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)
AdS/CFT ratio is flat and many times smaller than pQCD at only moderate pT
WH, M. Gyulassy, arXiv: [nucl-th]
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17. But There’s a Catch Speed limit estimate for applicability of AdS/CFT
drag computation
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(t0, x=y=0): “(”
largest gcrit for smallest T = Tc: “]”
D7 Probe Brane Q
“z” x5
Worldsheet boundary Spacelike if g > gcrit
Trailing
String
“Brachistochrone”
D3 Black Brane
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18. LHC RcAA(pT)/RbAA(pT) Prediction (with speed limits)
WH, M. Gyulassy, arXiv: [nucl-th]
T(t0): (O), corrections unlikely for smaller momenta
Tc: (|), corrections likely for higher momenta
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19. Nuclear Theory Seminar, Texas A&M
Measurement at RHIC
Future detector upgrades will allow for identified c and b quark measurements
RHIC production spectrum significantly harder than LHC
y=0
RHIC
LHC
NOT slowly varying
No longer expect
pQCD dRAA/dpT > 0
Large n requires corrections to naïve
Rcb ~ Mc/Mb
Nuclear Theory Seminar, Texas A&M

20. RHIC c, b RAA pT Dependence
WH, M. Gyulassy, arXiv: [nucl-th]
Large increase in n(pT) overcomes reduction in E-loss and makes pQCD dRAA/dpT < 0, as well
Nuclear Theory Seminar, Texas A&M

21. Nuclear Theory Seminar, Texas A&M
RHIC Rcb Ratio
pQCD
pQCD
AdS/CFT
AdS/CFT
WH, M. Gyulassy, arXiv: [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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22. Nuclear Theory Seminar, Texas A&M
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 partonic
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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23. 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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24. Nuclear Theory Seminar, Texas A&M
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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25. Nuclear Theory Seminar, Texas A&M
Backups
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26. Nuclear Theory Seminar, Texas A&M
LHC p Predictions
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 AWS-based energy loss (next slide)
We wish to understand the origin of this difference
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
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27. Nuclear Theory Seminar, Texas A&M
Asymptopia at the LHC
Asymptotic pocket formulae:
DErad/E ~ a3 Log(E/m2L)/E
DEel/E ~ a2 Log((E T)1/2/mg)/E
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
Nuclear Theory Seminar, Texas A&M

28. Nuclear Theory Seminar, Texas A&M
Langevin Model
Langevin equations (assumes gv ~ 1 to neglect radiative effects):
Relate drag coef. to diffusion coef.:
IIB Calculation:
Use of Langevin requires relaxation time be large compared to the inverse temperature:
AdS/CFT here
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29. But There’s a Catch (II)
Limited experimental pT reach?
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
ALICE Physics Performance Report, Vol. II
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30. Nuclear Theory Seminar, Texas A&M
K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005)
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38: (2005)
K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005)
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31. Introduction to Jargon
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 pT f
Common to Fourier expand RAA:
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32. 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: ,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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33. Nuclear Theory Seminar, Texas A&M
Pion RAA
Is it a good measurement for tomography?
Yes: small experimental error
Claim: we should not be so immediately dis-missive of the pion RAA as a tomographic tool
Maybe not: some models appear “fragile”
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34. 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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35. Different Models have Different Sensitivities to the Pion RAA
GLV:
s < 2
Higher Twist:
DGLV+El+Geom:
AWS:
s ~ 3
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
Nuclear Theory Seminar, Texas A&M

36. Nuclear Theory Seminar, Texas A&M
T Renk and K Eskola, Phys. Rev. C 75, (2007)
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
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37. Nuclear Theory Seminar, Texas A&M
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)
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38: (2005)
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38. 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
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/
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39. Nuclear Theory Seminar, Texas A&M
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: (2005)
Nuclear Theory Seminar, Texas A&M