1. Probing AdS/CFT with Heavy Quarks
William Horowitz
Columbia University
Frankfurt Institute for Advanced Studies (FIAS)
October 26, 2007
arXiv:  (LHC predictions)
arXiv: (RHIC predictions)
With many thanks to Miklos Gyulassy,
Simon Wicks, and Ivan Vitev
AdS Strings Intersect with Nuclear Beams at Columbia

2. AdS Strings Intersect with Nuclear Beams at Columbia
Introduction
AdS/CFT looks promising, pQCD also has its successes
Desire a robust probe that can cleanly falsify one or both formalisms:
Try Heavy Quarks!
AdS Strings Intersect with Nuclear Beams at Columbia

3. 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!
AdS Strings Intersect with Nuclear Beams at Columbia

4. 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
AdS Strings Intersect with Nuclear Beams at Columbia

5. 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)
AdS Strings Intersect with Nuclear Beams at Columbia

6. 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
AdS Strings Intersect with Nuclear Beams at Columbia

7. AdS Strings Intersect with Nuclear Beams at Columbia
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)
AdS Strings Intersect with Nuclear Beams at Columbia

8. 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/
AdS Strings Intersect with Nuclear Beams at Columbia

9. 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
Worldsheet boundary Spacelike if g > gcrit
Trailing
String
“Brachistochrone”
D3 Black Brane
AdS Strings Intersect with Nuclear Beams at Columbia

10. 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
AdS Strings Intersect with Nuclear Beams at Columbia

11. AdS Strings Intersect with Nuclear Beams at Columbia
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
AdS Strings Intersect with Nuclear Beams at Columbia

12. 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
AdS Strings Intersect with Nuclear Beams at Columbia

13. AdS Strings Intersect with Nuclear Beams at Columbia
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
AdS Strings Intersect with Nuclear Beams at Columbia

14. AdS Strings Intersect with Nuclear Beams at Columbia
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
Universality of pQCD and AdS/CFT Dependencies?
AdS Strings Intersect with Nuclear Beams at Columbia

15. 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
AdS Strings Intersect with Nuclear Beams at Columbia

16. AdS Strings Intersect with Nuclear Beams at Columbia
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
AdS Strings Intersect with Nuclear Beams at Columbia

17. AdS Strings Intersect with Nuclear Beams at Columbia
Backups
AdS Strings Intersect with Nuclear Beams at Columbia

18. AdS Strings Intersect with Nuclear Beams at Columbia
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
AdS Strings Intersect with Nuclear Beams at Columbia

19. AdS Strings Intersect with Nuclear Beams at Columbia
Asymptopia at the LHC
Asymptotic pocket formulae:
DErad/E ~ a3 Log(E/m2L)/E
DEel/E ~ a2 Log((E T)1/2/mg)/E
AdS Strings Intersect with Nuclear Beams at Columbia
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation

20. AdS Strings Intersect with Nuclear Beams at Columbia
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
AdS Strings Intersect with Nuclear Beams at Columbia

21. 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
AdS Strings Intersect with Nuclear Beams at Columbia

22. AdS Strings Intersect with Nuclear Beams at Columbia
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)
AdS Strings Intersect with Nuclear Beams at Columbia

23. 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:
AdS Strings Intersect with Nuclear Beams at Columbia

24. 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
AdS Strings Intersect with Nuclear Beams at Columbia

25. AdS Strings Intersect with Nuclear Beams at Columbia
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
AdS Strings Intersect with Nuclear Beams at Columbia

26. 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)
AdS Strings Intersect with Nuclear Beams at Columbia

27. 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)
AdS Strings Intersect with Nuclear Beams at Columbia

28. h/s Sensitive to Initial Conditions
Diffuse BGK IC
=> Ideal Hydro,
h/s ~ 1/4p
Sharp CGC IC
=> Viscous Hydro
Currently no exp. constraint on IC
T. Hirano, U. Heinz, D. Kharzeev, R. Lacey, Y. Nara, Phys. Lett. B636: ,2006
AdS Strings Intersect with Nuclear Beams at Columbia