1. pQCD vs. AdS/CFT Tested by Heavy Quark Energy Loss
William Horowitz
Columbia University
Frankfurt Institute for Advanced Studies (FIAS)
June 26, 2007
arXiv:  (LHC predictions)
With many thanks to Miklos Gyulassy,
Simon Wicks, Jorge Casalderrey-Solana, and Urs Wiedemann.
SQM 2007

2. pQCD Success at RHIC: (circa 2005) Consistency: RAA(h)~RAA(p)
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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3. 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…
e- RAA too small
M. Djorjevic, M. Gyulassy, R. Vogt, S. Wicks, Phys. Lett. B632:81-86 (2006)
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4. Strong Coupling 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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5. Qualitative AdS/CFT Successes:
e- RAA ~ p, h RAA; e- RAA(f)
Mach wave-like structures
h/sAdS/CFT ~ 1/4p << 1 ~ h/spQCD
sstrong=(3/4) sweak, similar to Lattice
J. P. Blaizot, E. Iancu, U. Kraemmer, A. Rebhan, hep-ph/
AdS/CFT
PHENIX, Phys. Rev. Lett. 98, (2007)
J. J. Friess, S. S. Gubser, G. Michalogiorgakis, S. S. Pufu, Phys. Rev. D75: (2007)
T. Hirano and M. Gyulassy, Nucl. Phys. A69:71-94 (2006)
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6. AdS/CFT vs. pQCD 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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7. Looking for a Robust, Detectable Signal
Use LHC’s large pT reach and identification of c and b to distinguish
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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8. 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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9. LHC c, b RAA pT Dependence
WH, M. Gyulassy, nucl-th/
LHC Prediction Zoo: What a Mess!
Let’s go through step by step
Naïve expectations born out in full numerical calculation:
dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST
Large suppression leads to flattening
Use of realistic geometry and Bjorken expansion allows saturation below .2
Significant rise in RAA(pT) for pQCD Rad+El
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10. A Cleaner 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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11. 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/
SQM 2007

12. But There’s a Catch Speed limit estimate for applicability of AdS/CFT
D7 Probe Brane
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
Ambiguous T for QGP
smallest gcrit for largest
T = T(t0, x=y=0): (O)
largest gcrit for smallest T = Tc: (|) Q
“z” x5
Induced horizon
Appears if g > gcrit
Trailing
String
“Brachistochrone”
Black D3 Brane
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13. 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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14. Identified c and b at RHIC
Index of power law production spectrum:
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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15. 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
SQM 2007

16. 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
SQM 2007

17. 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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18. Conclusions (cont’d) Additional c, b PID Goodies: Need for p+A control
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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19. Backups
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20. 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
SQM 2007

21. 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
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22. n(pT)
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23. 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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24. But There’s a Catch (II)
Limited experimental pT reach?
ALICE Physics Performance Report, Vol. II
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25. Zoom In Factor ~2-3 increase in ratio for pQCD
Possible distinction for Rad only vs. Rad+El at low-pT
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26. Regimes of Applicability
String Regime
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)
RHIC/LHC Regime
Mapping QCD Nc to SYM is easy, but coupling is hard
aS runs whereas aSYM does not: aSYM is something of an unknown constant
Taking aSYM = aS = .3 (D/2pT ~ 1); D/2pT ~ 3 => aSYM ~ .05
SQM 2007