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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Good Signs for pQCD at RHIC:
(circa 2005)
Y. Akiba for the PHENIX collaboration,
hep-ex/0510008
– 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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Trouble for wQGP Picture
- too
h/s too small
• veHydro
large
2 too small
A.
H. Feng,
and J. Jia,
C71:034909
(2005)
M. Drees,
Djorjevic,
M. Gyulassy,
R.Phys.
Vogt,Rev.
S. Wicks,
Phys. Lett.
(first
byD.E.Teaney,
Shuryak,
Phys.
Rev.
C66:027902
(2002))
Rev.
C68,
034913 (2003)
B632:81-86
(2006) Phys.
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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 stronglycoupled QCD in SUGRA
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Ideal Hydro?
Hydro merely
• pQCD: h/s ~ 1
propagates initial
• AdS: universal lower bound
for allits results
conditions;
infinitely coupled systems
~ 1/4p
are h/s
highly
dependent
on them
• AdS success?
T. Hirano, U. W. Heinz, D. Kharzeev, R. Lacy, Y. Nara, Phys. Lett.
B636:299-304 (2006)
•Glauber initial state =>
ideal (ST) hydro
•CGC initial state =>
viscous (pQCD) hydro
Must understand initial state better before reaching a conclusion:
A. Adil, M. Gyulassy, T. Hirano, Phys. Rev. D73:074006 (2006)
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Simultaneous p, e- Suppression
• pQCD is not falsified:
Naïve
pQCD => large mass, small loss
–•
Elastic
loss?
-R
•
But
p,
h
R
~
e
– Uncertainty in
AAc, b
AA!
contributions
– In-medium
fragmentation?
– Resonances?
H. Van Hees, V. Greco, and R. Rapp, Phys. Rev. C73, 034913 (2006)
A. Adil and I. Vitev, hep-ph/0611109
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
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Simultaneous RAA, v2 Description
– Energy loss translates
spatial anisotropy of
medium to jets
WH, Acta Phys. Hung. A27:221-225
PHENIX, Phys. Rev. Lett. 98, 172301 (2007)
• RAA and v2 are thus anticorrelated
• First seen for pions, no
nonperturbative model
reproduces both RAA and
v2
• Observed for e-, too
• No known solution to the
puzzle
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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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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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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:
erad ~ a3 L2 log(pT/Mq)/pT
• String theory drag momentum loss:
eST ~ 1 - Exp(-m L),
m = plT2/2Mq
S. Gubser, Phys.Rev.D74:126005 (2006)
– Independent of pT and strongly dependent on Mq!
– T2 dependence in exponent makes for a very sensitive probe
– Expect: eQCD
0 vs. eAdS indep of pT!!
• dRAA(pT)/dpT > 0 => pQCD ; dRAA(pT)/dpT < 0 => ST
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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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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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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
RcAA(pT)/RbAA(pT) ~ 1 - a3 n(pT) L2 log(Mb/Mc) ( /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
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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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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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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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Backups: LHC p Predictions
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Suppression of AWS
• AWS pQCD-based controlling parameter
nonperturbatively large to fit RHIC data
must be
-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)Workshop
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LHC p Predictions
WH, S. Wicks, M. Gyulassy, M. Djordjevic,
in preparation
• 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 AWSbased energy loss (next slide)
• We wish to understand the
origin of this difference
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Comparison of LHC p Predictions
(a)
(b)
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. C38:461474 (2005)
Curves of ASW-based energy loss are flat in pT
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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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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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Backup Slides
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RHIC e-
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RHIC c, b RAA(pT)
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RHIC RcAA(pT)/RbAA(pT)
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n(pT)
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Hydro Initial State
Hirano and Nara(’04), Hirano et al.(’06)
Kuhlman et al.(’06), Drescher et al.(’06)
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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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Langevin Scheme
– Langevin equations (assumes gv ~ 1 to neglect
radiative effects):
– Relate drag coef. to diffusion coef.:
– IIB Calculation:
ST here
• Use of Langevin requires relaxation time be large
compared to the inverse temperature:
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Plugging in Numbers
– Langevin pT reach:
• 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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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:
erad ~ a3
L2 log(pT/Mq)/pT
– String theory drag momentum loss:
eST ~ 1 - Exp(-m L),
m = plT2/2m
S. Gubser, Phys.Rev.D74:126005 (2006)
– Independent of pT and strongly dependent on m!!
– T2 dependence makes for a very sensitive probe
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