Falsifying AdS/CFT Drag or pQCD Heavy Quark Energy Loss with A+A at RHIC and LHC
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Transcript of Falsifying AdS/CFT Drag or pQCD Heavy Quark Energy Loss with A+A at RHIC and LHC
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Heavy Quark Workshop, LBNL
111/02/07
William Horowitz
Falsifying AdS/CFT Drag or pQCD Heavy Quark Energy Loss with A+A at RHIC and
LHC
William HorowitzColumbia University
Frankfurt Institute for Advanced Studies (FIAS)November 2, 2007
With many thanks to Miklos Gyulassy, Simon Wicks, and Ivan Vitev
arXiv:0706.2336 (LHC predictions)arXiv:0710.0703 (RHIC predictions)
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Heavy Quark Workshop, LBNL
211/02/07
William Horowitz
Shameless Web Self Promotion
Scary!
Hello Online Viewers!
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Heavy Quark Workshop, LBNL
311/02/07
William Horowitz
pQCD Success at RHIC:
ā Consistency: RAA()~RAA()
ā Null Control: RAA()~1
ā GLV Prediction: Theory~Data for reasonable fixed L~5 fm and dNg/dy~dN/dy
Y. Akiba for the PHENIX collaboration, nucl-ex/0510008
(circa 2005)
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Heavy Quark Workshop, LBNL
411/02/07
William Horowitz
ā¢ e- RAA too small
M. Djorjevic, M. Gyulassy, R. Vogt, S. Wicks, Phys. Lett. B632:81-86 (2006)
ā¢ wQGP not ruled out, but what if we try strong coupling?
D. Teaney, Phys. Rev. C68, 034913 (2003)
ā¢ Hydro /s too small ā¢ v2 too large
A. Drees, H. Feng, and J. Jia, Phys. Rev. C71:034909 (2005)(first by E. Shuryak, Phys. Rev. C66:027902 (2002))
Trouble for wQGP Picture
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Heavy Quark Workshop, LBNL
511/02/07
William Horowitz
Strong Coupling Calculation
ā¢ The supergravity double conjecture:
QCD SYM IIB
ā IF super Yang-Mills (SYM) is not too different from QCD, &
ā IF Maldacena conjecture is trueā Then a tool exists to calculate
strongly-coupled QCD in SUGRA
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Heavy Quark Workshop, LBNL
611/02/07
William Horowitz
ā¢ Mach wave-like structuresā¢ sstrong=(3/4) sweak, similar to Latticeā¢ /sAdS/CFT ~ 1/4 << 1 ~ /spQCDā¢ e- RAA ~ , RAA; e- RAA()
T. Hirano and M. Gyulassy, Nucl. Phys. A69:71-94 (2006)
Qualitative AdS/CFT Successes:
PHENIX, Phys. Rev. Lett. 98, 172301 (2007)
J. P. Blaizot, E. Iancu, U. Kraemmer, A. Rebhan, hep-ph/0611393
AdS/CFT
S. S. Gubser, S. S. Pufu, and A. Yarom, arXiv:0706.0213
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Heavy Quark Workshop, LBNL
711/02/07
William Horowitz
Quantitative AdS/CFT with Jetsā¢ Langevin model
ā Collisional energy loss for heavy quarksā Restricted to low pT
ā pQCD vs. AdS/CFT computation of D, the diffusion coefficient
ā¢ ASW modelā Radiative energy loss model for all parton speciesā pQCD vs. AdS/CFT computation ofā Debate over its predicted magnitude
ā¢ ST drag calculationā Drag coefficient for a massive quark moving through
a strongly coupled SYM plasma at uniform Tā not yet used to calculate observables: letās do it!
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Heavy Quark Workshop, LBNL
811/02/07
William Horowitz
Energy Loss Comparison
ā ST DragdpT/dt = -(T2/2Mq)pT
ā Compare to Bethe-HeitlerdpT/dt ~ -(T3/Mq
2) pT
ā Compare to LPMdpT/dt ~ -LT3 log(pT/Mq)
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Heavy Quark Workshop, LBNL
911/02/07
William Horowitz
ā Use future detectorsā identification of c and b to distinguish between pQCD, AdS/CFTā¢ RAA ~ (1-(pT))n(pT), where pf = (1-)pi (i.e. = 1-pf/pi)ā¢ Asymptotic pQCD momentum loss:
ā¢ String theory drag momentum loss:
ā Independent of pT and strongly dependent on Mq!ā T2 dependence in exponent makes for a very sensitive probe
ā Expect: pQCD 0 vs. AdS indep of pT!!ā¢ dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST
rad s L2 log(pT/Mq)/pT
Looking for a Robust, Detectable Signal
ST 1 - Exp(- L), = T2/2Mq
S. Gubser, Phys.Rev.D74:126005 (2006); C. Herzog et al. JHEP 0607:013,2006
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Heavy Quark Workshop, LBNL
1011/02/07
William Horowitz
Model Inputs for LHC Predictionsā AdS/CFT Drag: nontrivial mapping of QCD to SYM
ā¢ āObviousā: s = SYM = const., TSYM = TQCD
ā D/2T = 3 inspired: s = .05ā pQCD/Hydro inspired: s = .3 (D/2T ~ 1)
ā¢ āAlternativeā: = 5.5, TSYM = TQCD/31/4
ā¢ Start loss at thermalization time 0; end loss at Tc
ā WHDG convolved radiative and elastic energy lossā¢ s = .3
ā WHDG radiative energy loss (similar to ASW)ā¢ = 40, 100
ā Use realistic, diffuse medium with Bjorken expansion
ā PHOBOS (dNg/dy = 1750); KLN model of CGC (dNg/dy = 2900)
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Heavy Quark Workshop, LBNL
1111/02/07
William Horowitz
ā Unfortunately, large suppression pQCD similar to AdS/CFTā Large suppression leads to flatteningā Use of realistic geometry and Bjorken expansion allows saturation below .2ā Significant rise in RAA(pT) for pQCD Rad+Elā NaĆÆve expectations born out in full numerical calculation: dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST
LHC c, b RAA pT Dependence
ā LHC Prediction Zoo: What a Mess!ā Letās go through step by step
WH, M. Gyulassy, nucl-th/0706.2336
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Heavy Quark Workshop, LBNL
1211/02/07
William Horowitz
An Enhanced Signalā¢ But what about the interplay
between mass and momentum?ā Take ratio of c to b RAA(pT)
ā¢ pQCD: Mass effects die out with increasing pT
ā Ratio starts below 1, asymptotically approaches 1. Approach is slower for higher quenching
ā¢ ST: drag independent of pT, inversely proportional to mass. Simple analytic approx. of uniform medium gives
RcbpQCD(pT) ~ nbMc/ncMb ~ Mc/Mb ~ .27ā Ratio starts below 1; independent of pT
RcbpQCD(pT) 1 - s n(pT) L2 log(Mb/Mc) ( /pT)
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Heavy Quark Workshop, LBNL
1311/02/07
William Horowitz
LHC RcAA(pT)/Rb
AA(pT) Prediction
ā¢ Recall the Zoo:
ā Taking the ratio cancels most normalization differences seen previouslyā pQCD ratio asymptotically approaches 1, and more slowly so for
increased quenching (until quenching saturates)ā AdS/CFT ratio is flat and many times smaller than pQCD at only
moderate pT
WH, M. Gyulassy, nucl-th/0706.2336
WH, M. Gyulassy, nucl-th/0706.2336
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Heavy Quark Workshop, LBNL
1411/02/07
William Horowitz
ā Speed limit estimate for applicability of AdS/CFT drag computationā¢ < crit = (1 + 2Mq/1/2 T)2
~ 4Mq2/(T2)
ā Limited by Mcharm ~ 1.2 GeV
ā¢ Similar to BH LPMā crit ~ Mq/(T)
ā Ambiguous T for QGPā¢ smallest crit for largest
T = T(0, x=y=0): ā(āā¢ largest crit for smallest T = Tc:
ā]ā
But Thereās a Catch
D3 Black Brane
D7 Probe Brane Q
Worldsheet boundary Spacelikeif > crit
TrailingString
āBrachistochroneā
āzā
x5
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Heavy Quark Workshop, LBNL
1511/02/07
William Horowitz
LHC RcAA(pT)/Rb
AA(pT) Prediction(with speed limits)
ā T(0): (O), corrections unlikely for smaller momenta
ā Tc: (|), corrections likely for higher momenta
WH, M. Gyulassy, nucl-th/0706.2336
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Heavy Quark Workshop, LBNL
1611/02/07
William Horowitz
Measurement at RHICā Future detector upgrades will allow for
identified c and b quark measurements
y=0
RHIC
LHC
ā¢ ā¢ NOT slowly varying
ā No longer expect pQCD dRAA/dpT > 0
ā¢ Large n requires corrections to naĆÆve
Rcb ~ Mc/Mb
ā RHIC production spectrum significantly harder than LHC
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Heavy Quark Workshop, LBNL
1711/02/07
William Horowitz
RHIC c, b RAA pT Dependence
ā¢ Large increase in n(pT) overcomes reduction in E-loss and makes pQCD dRAA/dpT < 0, as well
WH, M. Gyulassy, to be published
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Heavy Quark Workshop, LBNL
1811/02/07
William Horowitz
RHIC Rcb Ratio
ā¢ Wider distribution of AdS/CFT curves due to large n: increased sensitivity to input parameters
ā¢ Advantage of RHIC: lower T => higher AdS speed limits
WH, M. Gyulassy, to be published
pQCD
AdS/CFT
pQCD
AdS/CFT
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Heavy Quark Workshop, LBNL
1911/02/07
William Horowitz
Conclusionsā¢ Year 1 of LHC could show qualitative differences
between energy loss mechanisms:ā dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST
ā¢ Ratio of charm to bottom RAA, Rcb, will be an important observable
ā Ratio is: flat in ST; approaches 1 from below in pQCD partonic E-lossā 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 GeVāthis can be observed in year 1 at LHC
ā¢ Measurement at RHIC will be possibleā AdS/CFT calculations applicable to higher momenta than at
LHC due to lower medium temperature
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Heavy Quark Workshop, LBNL
2011/02/07
William Horowitz
Additional Discerning Power
ā Adil-Vitev in-medium fragmentation rapidly approaches, and then broaches, 1Ā» Does not include partonic energy loss, which will be nonnegligable as ratio goes to unity
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Heavy Quark Workshop, LBNL
2111/02/07
William Horowitz
Conclusions (contād)ā¢ Additional c, b PID Goodies:
ā Adil Vitev in-medium fragmentation results in a much more rapid rise to 1 for Rc
AA/RbAA with the
possibility of breaching 1 and asymptotically approaching 1 from above
ā Surface emission models (although already unlikely as per v2(pT) data) predict flat in pT c, b RAA, with a ratio of 1
ā 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
ā Mach cone may be due to radiated gluons: from pQCD the away-side dip should widen with increasing parton mass
ā¢ Need for p+p baseline and p+A control
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Heavy Quark Workshop, LBNL
2211/02/07
William Horowitz
Backups
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Heavy Quark Workshop, LBNL
2311/02/07
William Horowitz
LHC Predictions
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
ā¢ Our predictions show a significant increase in RAA as a function of pT
ā¢ This rise is robust over the range of predicted dNg/dy for the LHC that we used
ā¢ This should be compared to the flat in pT curves of AWS-based energy loss (next slide)
ā¢ We wish to understand the origin of this difference
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Heavy Quark Workshop, LBNL
2411/02/07
William HorowitzWH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
Asymptopia at the LHCAsymptotic pocket formulae:Erad/E 3 Log(E/2L)/EEel/E 2 Log((E T)1/2/mg)/E
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Heavy Quark Workshop, LBNL
2511/02/07
William Horowitz
Langevin Modelā Langevin equations (assumes v ~ 1 to
neglect radiative effects):
ā Relate drag coef. to diffusion coef.:ā IIB Calculation:
ā¢ Use of Langevin requires relaxation time be large compared to the inverse temperature:
AdS/CFT here
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Heavy Quark Workshop, LBNL
2611/02/07
William Horowitz
But Thereās a Catch (II)ā¢ Limited experimental pT reach?
ā 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
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Heavy Quark Workshop, LBNL
2711/02/07
William Horowitz
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. C38:461-474 (2005)
K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann, Nucl. Phys. A747:511:529 (2005)
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Heavy Quark Workshop, LBNL
2811/02/07
William Horowitz
Introduction to Jargon
pT
NaĆÆvely: if medium has no effect, then RAA = 1
Common variables used are transverse momentum, pT, and angle with respect to the reaction plane,
Common to Fourier expand RAA:
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Heavy Quark Workshop, LBNL
2911/02/07
William Horowitz
Geometry of a HI Collision
Medium density and jet production are wide, smooth distributions
Use of unrealistic geometries strongly bias results
M. Gyulassy and L. McLerran, Nucl.Phys.A750:30-63,2005
1D Hubble flow => () ~ 1/=> T() ~ 1/1/3
S. Wicks, WH, M. Djordjevic, M. Gyulassy, Nucl.Phys.A784:426-442,2007
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Heavy Quark Workshop, LBNL
3011/02/07
William Horowitz
QCD Calculations
Lattice QCD pQCD
ā¢ All momentaā¢ Euclidean correlators
ā¢ Any quantityā¢ Small coupling
Previously only two tools:
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Heavy Quark Workshop, LBNL
3111/02/07
William Horowitz
Maldacena ConjectureLarge 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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Heavy Quark Workshop, LBNL
3211/02/07
William Horowitz
Regime of Applicabilityā Large Nc, constant āt Hooft coupling
( )Small quantum corrections
ā Large āt Hooft couplingSmall string vibration corrections
ā Only tractable case is both limits at onceClassical supergravity (SUGRA)t
xQ, m
v
D7 Probe Brane
D3 Black Brane(horizon)
3+1D Brane Boundary
Q.M. SSYM
=> C.M. SNG
Black Holez = 0
zh = T
zm = 2m / 1/2