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 2, 2007
arXiv:  (LHC predictions)
arXiv: (RHIC predictions)
With many thanks to Miklos Gyulassy,
Simon Wicks, and Ivan Vitev
Heavy Quark Workshop, LBNL

2. Shameless Web Self Promotion
Hello Online Viewers!
Scary!
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3. Heavy Quark Workshop, LBNL
pQCD Success at RHIC:
(circa 2005)
Y. Akiba for the PHENIX collaboration, nucl-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
Heavy Quark Workshop, LBNL

4. 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)
Heavy Quark Workshop, LBNL

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
Heavy Quark Workshop, LBNL

6. 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)
Heavy Quark Workshop, LBNL

7. 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!
Heavy Quark Workshop, LBNL

8. Energy Loss Comparison
ST Drag
dpT/dt = -(pl1/2 T2/2Mq)pT
Compare to Bethe-Heitler
dpT/dt ~ -(T3/Mq2) pT
Compare to LPM
dpT/dt ~ -LT3 log(pT/Mq)
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9. Looking for a Robust, Detectable Signal
Use future detectors’ 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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10. Model Inputs for LHC Predictions
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)
Heavy Quark Workshop, LBNL

11. LHC c, b RAA pT Dependence
WH, M. Gyulassy, nucl-th/
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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12. Heavy Quark Workshop, LBNL
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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13. LHC RcAA(pT)/RbAA(pT) Prediction
Recall the Zoo:
WH, M. Gyulassy, 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, nucl-th/
Heavy Quark Workshop, LBNL

14. 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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15. LHC RcAA(pT)/RbAA(pT) Prediction (with speed limits)
WH, M. Gyulassy, nucl-th/
T(t0): (O), corrections unlikely for smaller momenta
Tc: (|), corrections likely for higher momenta
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16. Heavy Quark Workshop, LBNL
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
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17. RHIC c, b RAA pT Dependence
WH, M. Gyulassy, to be published
Large increase in n(pT) overcomes reduction in E-loss and makes pQCD dRAA/dpT < 0, as well
Heavy Quark Workshop, LBNL

18. Heavy Quark Workshop, LBNL
RHIC Rcb Ratio
pQCD
pQCD
AdS/CFT
AdS/CFT
WH, M. Gyulassy, to be published
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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19. Heavy Quark Workshop, LBNL
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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20. 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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21. Heavy Quark Workshop, LBNL
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+p baseline and p+A control
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22. Heavy Quark Workshop, LBNL
Backups
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23. Heavy Quark Workshop, LBNL
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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24. Heavy Quark Workshop, LBNL
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
Heavy Quark Workshop, LBNL

25. Heavy Quark Workshop, LBNL
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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26. 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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27. Heavy Quark Workshop, LBNL
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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28. 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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29. 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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30. QCD Calculations Previously only two tools: Lattice QCD pQCD
All momenta
Euclidean correlators
Any quantity
Small coupling
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31. Heavy Quark Workshop, LBNL
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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32. 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)
D7 Probe Brane t x v
Q, m
3+1D Brane
Boundary
zm = 2pm / l1/2
Q.M. SSYM
=> C.M. SNG
D3 Black Brane
(horizon)
zh = pT
Black Hole
z = 0
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