1. Testing AdS/CFT at LHC William Horowitz The Ohio State University
February 6, 2009
With many thanks to Yuri Kovchegov and Ulrich Heinz
High-pT Physics at LHC

2. First, a Perturbative Detour
High-pT Physics at LHC

3. pQCD Success in High-pT at RHIC:
(circa 2005)
Y. Akiba for the PHENIX collaboration, hep-ex/
Consistency: RAA(h)~RAA(p)
Null Control: RAA(g)~1
GLV Calculation: Theory~Data for reasonable fixed L~5 fm and dNg/dy~dNp/dy
Assuming pQCD E-loss, let’s clear up some myths
High-pT Physics at LHC

4. Surface Emission: Red Herring?
If you believe in pQCD E-loss, observed jets come from deep in the medium
HT, AMY, ASW
WHDG
BDMPS + Hydro
S. A. Bass, et al., arXiv: [nucl-th].
S. Wicks, et al., Nucl. Phys. A784,
426 (2007)
T. Renk and K. J. Eskola,
PoS LHC07, 032 (2007)
High-pT Physics at LHC

5. Fragility is Fragile
Linear-linear plot of RAA(qhat) is the incorrect way to think about the problem
PHENIX,
Phys. Rev. C77, (2008)
K. J. Eskola, et al., Nucl. Phys. A747, 511 (2005)
High-pT Physics at LHC

6. Fragility is Fragile (cont’d)
If you believe in pQCD E-loss, RAA is NOT a fragile probe of the medium
Linear on a log-log plot
Double => halve RAA
Similar results for WHDG,
GLV, AMY, ZOWW, etc.
PHENIX,
Phys. Rev. C77, (2008)
High-pT Physics at LHC

7. Quantitative Extraction
PHENIX, PRC77,
(2008)
Model params to within ~20%
Experimental error only!!
Sys. theor. err. could be quite large
Running coupling uncertainties
Smaller at LHC?
Multi-gluon correlations?
Larger at LHC?
Handling of geometry …
See also TECHQM wiki:
S. Wicks, et al., Nucl. Phys. A783, 493 (2007)
High-pT Physics at LHC

8. Trouble for High-pT wQGP Picture
v2 too small
NPE supp. too large
p0 v2
M Tannenbaum, High-pT Physics at LHC ‘09
NPE v2
STAR, Phys. Rev. Lett. 98, (2007)
Pert. at LHC energies?
PHENIX, Phys. Rev. Lett. 98, (2007)
High-pT Physics at LHC

9. Back to the Future Fifth Dimension
High-pT Physics at LHC

10. Motivation for High-pT AdS
Why study AdS E-loss models?
Many calculations vastly simpler
Complicated in unusual ways
Data difficult to reconcile with pQCD
pQCD quasiparticle picture leads to dominant q ~ m ~ .5 GeV mom. transfers
=> Nonperturbatively large as
Use data to learn about E-loss mechanism, plasma properties
Domains of self-consistency crucial for understanding
High-pT Physics at LHC

11. 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
High-pT Physics at LHC

12. AdS/CFT Energy Loss Models
Langevin Diffusion
Collisional energy loss for heavy quarks
Restricted to low pT
pQCD vs. AdS/CFT computation of D, the diffusion coefficient
ASW/LRW model
Radiative energy loss model for all parton species
pQCD vs. AdS/CFT computation of
Debate over its predicted magnitude
Heavy Quark Drag calculation
Embed string representing HQ into AdS geometry
Includes all E-loss modes
Empty space calculation:
Previously: thermalized QGP plasma, temp. T, gcrit<~Mq/T
Moore and Teaney, Phys.Rev.C71:064904,2005
Casalderrey-Solana and Teaney, Phys.Rev.D74:085012,2006; JHEP 0704:039,2007
BDMPS, Nucl.Phys.B484: ,1997
Armesto, Salgado, and Wiedemann, Phys. Rev. D69 (2004)
Liu, Ragagopal, Wiedemann, PRL 97:182301,2006; JHEP 0703:066,2007
Kharzeev, arXiv: [hep-ph]
Gubser, Phys.Rev.D74:126005,2006
Herzog, Karch, Kovtun, Kozcaz, Yaffe, JHEP 0607:013,2006
High-pT Physics at LHC

13. Energy Loss Comparison
D7 Probe Brane t
z = 0 x v
AdS/CFT Drag:
dpT/dt ~ -(T2/Mq) pT
Q, m
zm = l1/2/2pm
3+1D Brane
Boundary
D3 Black Brane
(horizon)
zh = 1/pT
Black Hole
z = ¥
Similar to Bethe-Heitler
dpT/dt ~ -(T3/Mq2) pT
Very different from LPM
dpT/dt ~ -LT3 log(pT/Mq)
High-pT Physics at LHC

14. 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
We can approximate RAA(pT):
RAA ~ (1-e(pT))n(pT),
where pf = (1-e)pi (i.e. e = 1-pf/pi)
y=0
RHIC
LHC
High-pT Physics at LHC

15. 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:
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
High-pT Physics at LHC

16. 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)
High-pT Physics at LHC

17. LHC c, b RAA pT Dependence
WH and M. Gyulassy,
Phys. Lett. B 666, 320 (2008)
Naïve expectations met in full numerical calculation:
dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST
Significant rise in RAA(pT) for pQCD Rad+El
Large suppression leads to flattening
Use of realistic geometry and Bjorken expansion allows saturation below .2
LHC Prediction Zoo: What a Mess!
Let’s go through step by step
Unfortunately, large suppression pQCD similar to AdS/CFT
High-pT Physics at LHC

18. 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)
High-pT Physics at LHC

19. LHC RcAA(pT)/RbAA(pT) Prediction
Recall the Zoo:
WH and M. Gyulassy, Phys. Lett. B 666, 320 (2008)
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
Distinguish rad and el contributions?
WH and M. Gyulassy, Phys. Lett. B 666, 320 (2008)
High-pT Physics at LHC

20. Additional Discerning Power
Consider ratio for ALICE pT reach
mc = mb = 0
Adil-Vitev in-medium fragmentation rapidly approaches, and then broaches, 1
Does not include partonic E-loss, which will be nonnegligable as ratio goes to unity
Higgs (non)mechanism => Rc/Rb ~ 1 ind. of pT
High-pT Physics at LHC

21. Worldsheet boundary Spacelike if g > gcrit
Not So Fast!
D7 Probe Brane Q
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)
No single T for QGP
Worldsheet boundary Spacelike if g > gcrit z
Trailing
String
“Brachistochrone” x
D3 Black Brane
High-pT Physics at LHC

22. LHC RcAA(pT)/RbAA(pT) Prediction (with speed limits)
WH and M. Gyulassy, Phys. Lett. B 666, 320 (2008)
T(t0): (, highest T—corrections unlikely for smaller momenta
Tc: ], lowest T—corrections likely for higher momenta
High-pT Physics at LHC

23. Derivation of BH Speed Limit I
Constant HQ velocity
Assume const. v kept by F.v
Critical field strength Ec = M2/l½
E > Ec: Schwinger pair prod.
Limits g < gc ~ T2/lM2
Alleviated by allowing var. v
Drag similar to const. v
Minkowski Boundary
z = 0
F.v = dp/dt E Q v
zM = l½ / 2pM D7
dp/dt
J. Casalderrey-Solana and D. Teaney, JHEP 0704, 039 (2007) D3
zh = 1/pT
Herzog, Karch, Kovtun, Kozcaz, Yaffe, JHEP 0607:013 (2006)
z = ¥
High-pT Physics at LHC

24. Derivation of BH Speed Limit II
Local speed of light
BH Metric => varies with depth z
v(z)2 < 1 – (z/zh)4
HQ located at zM = l½/2pM
Limits g < gc ~ T2/lM2
Same limit as from const. v
Mass a strange beast
Mtherm < Mrest
Mrest ¹ Mkin
Note that M >> T
Minkowski Boundary
z = 0
F.v = dp/dt E Q v
zM = l½ / 2pM D7
S. S. Gubser, Nucl. Phys. B 790, 175 (2008)
dp/dt D3
zh = 1/pT
z = ¥
High-pT Physics at LHC

25. Universality and Applicability
How universal are drag results?
Examine different theories
Investigate alternate geometries
When does the calculation break down?
Depends on the geometry used
High-pT Physics at LHC

26. New Geometries Constant T Thermal Black Brane Shock Geometries
Nucleus as Shock
J Friess, et al., PRD75:106003, 2007
DIS
Embedded String in Shock
Before
After
Albacete, Kovchegov, Taliotis,
JHEP 0807, 074 (2008) Q
vshock x z
vshock x z Q
Bjorken-Expanding Medium
High-pT Physics at LHC

27. Shocking Motivation Warm-up for full Bjorken metric
R. A. Janik and R. B. Peschanski, Phys. Rev. D 73, (2006)
No local speed of light limit!
Metric yields
-1 < v < 1
In principle, applicable to all quark masses for all momenta
Subtlety in exchange of limits?
High-pT Physics at LHC

28. Standard Method of Attack
Parameterize string worldsheet
Xm(t, s)
Plug into Nambu-Goto action
Varying SNG yields EOM for Xm
Canonical momentum flow (in t, s)
High-pT Physics at LHC

29. Shock Geometry Results
Three t-ind. solutions (static gauge):
Xm = (t, x(z), 0,0, z)
x(z) = c, ± m ½ z3/3
Constant solution unstable
Time-reversed negative x solution unphysical
Sim. to x ~ z3/3, z << 1, for const. T BH geom. Q
z = 0
vshock
- m ½ z3/3
+ m ½ z3/3 c x
z = ¥
High-pT Physics at LHC

30. HQ Momentum Loss in the Shock
x(z) = m ½ z3/3 =>
Relate m to nuclear properties
Use AdS dictionary: m ~ T--/Nc2
T-- = (boosted den. of scatterers) x (mom.)
T-- = Nc2 (L3 p+/L) x (p+)
Nc2 gluons per nucleon in shock
L is typical mom. scale; L-1 typical dist. scale
p+: mom. of shock gluons as seen by HQ
p: mom. of HQ as seen by shock
=> m = L2p+2
High-pT Physics at LHC

31. HQ Drag in the Shock HQ Rest Frame Shock Rest Frame Recall for BH:Mq L
vsh
vq = -vsh Mq
1/L
vq = 0 i i
vsh = 0
Recall for BH:
Shock gives exactly the same drag as BH for L = p T
High-pT Physics at LHC

32. Conclusions and Outlook for
the LHC Experiment:
Use data to test E-loss mechanism
RcAA(pT)/RbAA(pT) wonderful tool
p+Pb and Direct-g Pb+Pb critical null controls
the AdS Drag:
Applicability and universality crucial
Both investigated in shock geom.
Shock geometry reproduces BH momentum loss
Unrestricted in momentum reach
Variable velocity case nontrivial
Future work
Time-dependent shock treatment
AdS E-loss in Bjorken expanding medium
High-pT Physics at LHC

33. Backup Slides
High-pT Physics at LHC

34. 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
High-pT Physics at LHC

35. 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
High-pT Physics at LHC

36. 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
High-pT Physics at LHC

37. Simultaneous p, e- Suppression
pQCD is not falsified:
Elastic loss?
Uncertainty in c, b contributions
In-medium fragmentation?
Resonances?
A. Adil and I. Vitev, hep-ph/
Naïve pQCD => large mass, small loss
But p, h RAA ~ e- RAA!
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/
H. Van Hees, V. Greco, and R. Rapp, Phys. Rev. C73, (2006)
High-pT Physics at LHC

38. Zooming In Factor ~2-3 increase in ratio for pQCD
Possible distinction for Rad only vs. Rad+El at low-pT
High-pT Physics at LHC

39. Additional Discerning Power
Consider ratio for ALICE pT reach
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
High-pT Physics at LHC

40. Consider ratio for ALICE pT reach
High-pT Physics at LHC

41. 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
High-pT Physics at LHC

42. Comparison of LHC p Predictions
(b)
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)
Curves of ASW-based energy loss are flat in pT
High-pT Physics at LHC

43. Why ASW is Flat
Flat in pT curves result from extreme suppression at the LHC
When probability leakage P(e > 1) is large, the (renormalized or not) distribution becomes insensitive to the details of energy loss
Enormous suppression due to:
Already (nonperturbatively) large suppression at RHIC for ASW
Extrapolation to LHC assumes 7 times RHIC medium densities (using EKRT)
Note: even if LHC is only ~ 2-3 times RHIC, still an immoderate ~ 30-45
As seen on the previous slide, Vitev predicted a similar rise in RAA(pT) as we do
Vitev used only radiative loss, Prad(e), but assumed fixed path
WHDG similar because elastic and path fluctuations compensate
High-pT Physics at LHC

44. Elastic Can’t be Neglected!
M. Mustafa, Phys. Rev. C72: (2005) S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/
High-pT Physics at LHC

45. Elastic Remains Important
High-pT Physics at LHC

46. A Closer Look at PQM
Difficult to draw conclusions on inherent surface bias in PQM 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)
High-pT Physics at LHC

47. Direct g: A+A IS Well Understood
PHENIX, Phys. Rev. Lett. 94, (2005)
High-pT Physics at LHC

48. More Geometry pT dependence of surface bias
Nontrivial a posteriori fixed length dependence
(not surface emission!)
S. A. Bass, et al., arXiv: [nucl-th].
S. Wicks, WH, M. Djordjevic and M. Gyulassy, Nucl. Phys. A784, 426 (2007)
High-pT Physics at LHC