pQCD vs. AdS/CFT Tested by Heavy
Quark Energy Loss
William Horowitz
Columbia University
Frankfurt Institute for Advanced Studies (FIAS)
August 31, 2007
arXiv:0706.2336 (LHC predictions)
With many thanks to Miklos Gyulassy,
Simon Wicks, and Ivan Vitev
8/31/07
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William Horowitz
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QCD Calculations
Previously only two tools:
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Lattice QCD
pQCD
• All momenta
• Euclidean correlators
• Any quantity
• Small coupling
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Maldacena Conjecture
Large Nc limit of d-dimensional conformal field
theory dual to string theory on the product of
d+1-dimensional Anti-de Sitter space with a
compact manifold
3+1 SYM

z=0
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Regime of Applicability
– 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
D7 Probe Brane
Classical supergravity (SUGRA)
t

zm = 2pm / l1/2
Q.M. SSYM
=> C.M. SNG
v
Q, m
3+1D Brane
Boundary
D3 Black Brane
(horizon)
zh = pT
z=0
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x
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Black Hole
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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 stronglycoupled QCD in SUGRA
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Connection to Experiment
a.k.a. the Reality Check for Theory
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pQCD Success 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
Hydro
h/s
too small
e-2Rtoo
too
•v
wQGP
notsmall
ruled
out, but what if we try
AA large
strong coupling?
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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Qualitative AdS/CFT Successes:
-R1~
sMach
=(3/4)
wave-like
s
structures
,
similar
• h/s
e-strong
RAA
~
p,
h
R
;
e
)to Lattice
~
1/4p
<<
weak
AA
AA(fh/s
AdS/CFT
pQCD
AdS/CFT
J. P. Blaizot,
S. S. Gubser,
E. Iancu,
S. S.U.
Pufu,
Kraemmer,
and A. Yarom,
A. Rebhan,
arXiv:0706.0213
hep-ph/0611393
T. Hirano and M. Gyulassy, Nucl. Phys. A69:71-94 (2006)
PHENIX, Phys. Rev. Lett. 98, 172301 (2007)
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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!
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Looking for a Robust, Detectable Signal
– Use LHC’s large pT reach and 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:
erad ~ as L2 log(pT/Mq)/pT
• String theory drag momentum loss:
eST ~ 1 - Exp(-m L),
m = pl1/2 T2/2Mq
S. Gubser, Phys.Rev.D74:126005 (2006); C. Herzog et al. JHEP 0607:013,2006
– Independent of pT and strongly dependent on Mq!
– T2 dependence in exponent makes for a very sensitive probe
– Expect: epQCD
0 vs. eAdS indep of pT!!
• dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST
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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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LHC c, b RAA pT Dependence
WH, M. Gyulassy, nucl-th/0706.2336
– Naïve
LHC Prediction
Unfortunately,
Large
Significant
suppression
expectations
rise large
inZoo:
Rleads
born
suppression
What
(pTto
)out
for
flattening
a in
Mess!
pQCD
fullpQCD
numerical
Rad+El
similar
calculation:
to AdS/CFT
AA
– Let’s
Use ofgorealistic
through
dRAA
geometry
step
(pT)/dp
by step
> 0 Bjorken
=> pQCD;
expansion
dRAA(pTallows
)/dpT <
saturation
0 => ST below .2
Tand
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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
RcbpQCD(pT) ~ 1 - as 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. Simple analytic approx.
of uniform medium gives
RcbpQCD(pT) ~ nbMc/ncMb ~ Mc/Mb ~ .27
– Ratio starts below 1; independent of pT
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LHC RcAA(pT)/RbAA(pT) Prediction
• Recall the Zoo:
WH, M. Gyulassy, nucl-th/0706.2336
– Taking the ratio cancels most normalization differences seen previously
– pQCD ratio asymptotically approaches 1, and more slowly so for increased
quenching (until quenching saturates)
WH, M.times
Gyulassy,
nucl-th/0706.2336
– AdS/CFT ratio is flat and many
smaller
than pQCD at only moderate pT
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But There’s a Catch
– 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: (|)
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D7 Probe Brane
Q
Worldsheet boundary
Spacelike if g > gcrit
x5
Trailing
String
“Brachistochrone”
D3 Black Brane
“z”
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LHC RcAA(pT)/RbAA(pT) Prediction
(with speed limits)
WH, M. Gyulassy, nucl-th/0706.2336
– T(t0): (O), corrections unlikely for smaller momenta
– Tc: (|), corrections likely for higher momenta
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Measurement at RHIC
– Future detector upgrades will allow for identified c
and b quark measurements
– RHIC production spectrum significantly
harder than LHC
•
• NOT slowly varying
y=0
RHIC
– No longer expect
pQCD dRAA/dpT > 0
• Large n requires
corrections to naïve
Rcb ~ Mc/Mb
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LHC
William Horowitz
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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
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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
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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?
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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
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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
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Backups
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LHC p Predictions
WH, S. Wicks, M. Gyulassy, M. Djordjevic,
in preparation
8/31/07
• 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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Asymptopia at the LHC
Asymptotic pocket formulae:
DErad/E ~ a3 Log(E/m2L)/E
DEel/E ~ a2 Log((E T)1/2/mg)/E
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WH, Nuclear
S. Wicks,Theory/RIKEN
M. Gyulassy, M.Seminar
Djordjevic, in preparation
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Langevin Model
– Langevin equations (assumes gv ~ 1 to neglect
radiative effects):
– Relate drag coef. to diffusion coef.:
– IIB Calculation:
AdS/CFT here
• Use of Langevin requires relaxation time be large
compared to the inverse temperature:
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But There’s a Catch (II)
• Limited experimental pT reach?
ALICE Physics Performance Report, Vol. II
– 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
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K. J. Eskola, H. Honkanen, C. A. Salgado, and U.
A. Wiedemann, Nucl. Phys. A747:511:529 (2005)
K. J. Eskola, H. Honkanen, C. A. Salgado, and
U. A. Wiedemann, Nucl. Phys. A747:511:529
(2005)
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A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005)
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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
Common to Fourier expand RAA:
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pT
f
William Horowitz
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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.A784:426-442,2007
1D Hubble flow => r(t) ~ 1/t
=> T(t) ~ 1/t1/3
M. Gyulassy and L. McLerran, Nucl.Phys.A750:30-63,2005
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