1. The LHC to Test pQCD vs. AdS/CFT Heavy Quark Energy Loss
William Horowitz
Columbia University
FIAS
April 26, 2007
With many thanks to Miklos Gyulassy.
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2. Good Signs for pQCD 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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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))
e- too small
M. Djorjevic, M. Gyulassy, R. Vogt, S. Wicks, Phys. Lett. B632:81-86 (2006)
D. Teaney, Phys. Rev. C68, (2003)
Hydro h/s too small
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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 Maldecena conjecture is true
Then a tool exists to calculate strongly-coupled QCD in SUGRA
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5. Ideal Hydro?
Hydro merely propagates initial conditions; its results are highly dependent on them
pQCD: h/s ~ 1
AdS: universal lower bound for all infinitely coupled systems h/s ~ 1/4p
AdS success?
Glauber initial state =>
ideal (ST) hydro
CGC initial state =>
viscous (pQCD) hydro
T. Hirano, U. W. Heinz, D. Kharzeev, R. Lacy, Y. Nara, Phys. Lett. B636: (2006)
Must understand initial state better before reaching a conclusion:
A. Adil, M. Gyulassy, T. Hirano, Phys. Rev. D73: (2006)
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6. 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)
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7. Simultaneous RAA, v2 Description
Energy loss translates spatial anisotropy of medium to jets
RAA and v2 are thus anti-correlated
First seen for pions, no nonperturbative model reproduces both RAA and v2
Observed for e-, too
No known solution to the puzzle
PHENIX, Phys. Rev. Lett. 98, (2007)
WH, Acta Phys. Hung. A27:
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8. Strings, Jets, and the LHC
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
Considerable debate over its magnitude
ST drag calculation
Equation for infinitely massive quark moving with constant v through infinitely coupled SYM at uniform T
not yet used to calculate observables: let’s do it!
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9. 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); aSYM ~ .05 => D/2pT~3
LHC medium density predictions vary by factor of 2
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10. Looking for a Robust, Detectable Signal
Use large LHC 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: eQCD vs. eAdS indep of pT!!
dRAA(pT)/dpT > 0 => pQCD ; dRAA(pT)/dpT < 0 => ST
erad ~ a3 L2 log(pT/Mq)/pT
eST ~ 1 - Exp(-m L), m = plT2/2Mq
S. Gubser, Phys.Rev.D74: (2006)
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11. Models
AdS/CFT Drag
“Obvious”: as = aSYM, TSYM = TQCD
D/2pT = 3 inspired: as = .05, t0 = 1
Hydro inspired: as = .3, t0 = .6
“Alternative”: l = 5.5, TSYM = TQCD/31/4
WHDG convolved radiative and collisional energy loss
as = .3, t0 = .2
WHDG radiative energy loss (similar to ASW)
= 40, 100
All use realistic, nonuniform medium with Bjorken expansion
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12. LHC c, b RAA pT Dependence
Full numerical calculation shows ST RAA decreases with pT (as compared to strong increase for pQCD)
Saturation, or fragility, occurs at a much smaller RAA due to realistic modeling of the medium
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13. 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
Ratio starts below 1, independent of pT
RcAA(pT)/RbAA(pT) ~ 1 - a3 n(pT) L2 log(Mb/Mc) ( /pT)
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14. LHC RcAA(pT)/RbAA(pT) Prediction
Recall the previous plot:
Taking the ratio cancels most normalization differences seen previously
pQCD ratio asymptotically approaches 1, and more slowly so for increased quenching (until quenching saturates)
ST ratio is flat and many times smaller than pQCD at only moderate pT
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15. Conclusions
PID and large pT reach will give the LHC a unique position to make discoveries in the heavy quark sector
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 will be an important observable
Ratio is: flat in ST; asymptotically approaching 1 from below in pQCD
While future AdS/CFT calculations could well alter the ST predictions shown here, it is highly unlikely that a pQCD mechanism can be found that allows mass effects to persist out to momenta orders of magnitude larger than Mq
A measurement of this ratio NOT going to 1 will be a clear sign of new physics: pQCD predicts ~ 3 times increase in this ratio by 30 GeV—this can be observed in year 1 at the LHC
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16. Conclusions (cont’d) Additional LHC 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 p v2(pT) data) predict flat in pT c, b RAA, with a ratio of 1
Mach cone may be due to radiated gluons: from pQCD the away-side dip should widen with increasing parton mass
Moderately suppressed radiative only energy loss shows a dip in the ratio at low pT; convolved loss is monotonic
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17. Backups: LHC p Predictions
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18. Suppression of AWS
AWS pQCD-based controlling parameter must be nonperturbatively large to fit RHIC data
-pQCD gives = c e3/4, where c ~ 2; c ~ 8-20 required for RHIC data
-Needed because radiative only energy loss (and > 1? R = (1/2) L3)
K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005)
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19. 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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20. 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
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21. 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
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22. Conclusions
LHC RAA(pT) data will distinguish between energy loss models
GLV Rad+El+Geom predicts significant rise in pT
ASW type models predict flat pT dependence
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23. Backup Slides
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24. RHIC e-
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25. RHIC c, b RAA(pT)
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26. RHIC RcAA(pT)/RbAA(pT)
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27. n(pT)
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28. Hydro Initial State Hirano and Nara(’04), Hirano et al.(’06)‏
Kuhlman et al.(’06), Drescher et al.(’06)‏
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29. 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 gives l ~ 10
Taking aSYM ~ .05 => l ~ 1.8 (keep in mind for later)
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30. Langevin Scheme
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:
ST here
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31. Plugging in Numbers Langevin pT reach: D/(2pT) = 4/l1/2 from ST:
gv(8 GeV e- from c) ~ 11
D/(2pT) = 4/l1/2 from ST:
aSYM = aS = .3 => D/(2pT) ~ 1
Oversuppresses RAA
aSYM ~ .05 required for D/(2pT) ~ 3
Mass constraint, (for T = 350 MeV)
aSYM = .3 this gives ~ .6 GeV
aSYM = .05 this gives ~ .25 GeV
Both charm and bottom satisfy this condition
Not entirely unreasonable
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36. Strings, Jet Physics, and the LHC: Looking for a Signal
Use large LHC pT reach and identification of c and b to distinguish
RAA ~ (1-e(pT))n(pT), pf = (1-e)pi
Asymptotic pQCD momentum loss:
String theory drag momentum loss:
Independent of pT and strongly dependent on m!!
T2 dependence makes for a very sensitive probe
erad ~ a3 L2 log(pT/Mq)/pT
eST ~ 1 - Exp(-m L), m = plT2/2m
S. Gubser, Phys.Rev.D74: (2006)
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