pQCD vs. AdS/CFT Tested by Heavy Quark Energy Loss
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Transcript of pQCD vs. AdS/CFT Tested by Heavy Quark Energy Loss
SQM 2007
16/26/07
William Horowitz
pQCD vs. AdS/CFT Tested by Heavy Quark Energy Loss
William HorowitzColumbia University
Frankfurt Institute for Advanced Studies (FIAS)June 26, 2007
With many thanks to Miklos Gyulassy, Simon Wicks, Jorge Casalderrey-Solana, and Urs
Wiedemann.
arXiv:0706.2336 (LHC predictions)
SQM 2007
26/26/07
William Horowitz
pQCD Success at RHIC:
– Consistency: RAA()~RAA()
– Null Control: RAA()~1
– GLV Prediction: Theory~Data for reasonable fixed L~5 fm and dNg/dy~dN/dy
Y. Akiba for the PHENIX collaboration, hep-ex/0510008
(circa 2005)
SQM 2007
36/26/07
William Horowitz
• e- RAA too small
M. Djorjevic, M. Gyulassy, R. Vogt, S. Wicks, Phys. Lett. B632:81-86 (2006)
• wQGP not ruled out, but what if we try…
D. Teaney, Phys. Rev. C68, 034913 (2003)
• Hydro /s too small • 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
SQM 2007
46/26/07
William Horowitz
Strong Coupling• 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
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• sstrong=(3/4) sweak, similar to Lattice• /sAdS/CFT ~ 1/4 << 1 ~ /spQCD• e- RAA ~ , RAA; e- RAA()• Mach wave-like structures
T. Hirano and M. Gyulassy, Nucl. Phys. A69:71-94 (2006)
Qualitative AdS/CFT Successes:
PHENIX, Phys. Rev. Lett. 98, 172301 (2007)
J. J. Friess, S. S. Gubser, G. Michalogiorgakis, S. S. Pufu, Phys. Rev. D75:106003 (2007)J. P. Blaizot, E. Iancu, U. Kraemmer, A. Rebhan, hep-ph/0611393
AdS/CFT
SQM 2007
66/26/07
William Horowitz
AdS/CFT vs. pQCD 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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76/26/07
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– Use LHC’s large pT reach and identification of c and b to distinguish• RAA ~ (1-(pT))n(pT), where pf = (1-)pi (i.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: pQCD 0 vs. AdS indep of pT!!• 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
SQM 2007
86/26/07
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Model Inputs– AdS/CFT Drag: nontrivial mapping of QCD to SYM
• “Obvious”: s = SYM = const., TSYM = TQCD
– D/2T = 3 inspired: s = .05– pQCD/Hydro inspired: s = .3 (D/2T ~ 1)
• “Alternative”: = 5.5, TSYM = TQCD/31/4
• Start loss at thermalization time 0; end loss at Tc
– WHDG convolved radiative and elastic energy loss• s = .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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96/26/07
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– Large suppression leads to flattening– Use of realistic geometry and Bjorken expansion allows saturation below .2– Significant rise in RAA(pT) for pQCD Rad+El– Naïve expectations born out in full numerical calculation: dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST
LHC c, b RAA pT Dependence
– LHC Prediction Zoo: What a Mess!– Let’s go through step by step
WH, M. Gyulassy, nucl-th/0706.2336
SQM 2007
106/26/07
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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
– 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 - s n(pT) L2 log(Mb/Mc) ( /pT)
SQM 2007
116/26/07
William Horowitz
LHC RcAA(pT)/Rb
AA(pT) Prediction
• Recall the Zoo:
– 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
WH, M. Gyulassy, nucl-th/0706.2336
WH, M. Gyulassy, nucl-th/0706.2336
SQM 2007
126/26/07
William Horowitz
But There’s a Catch
– Speed limit estimate for applicability of AdS/CFT drag computation• < crit = (1 + 2Mq/1/2 T)2
~ 4Mq2/(T2)
– Limited by Mcharm ~ 1.2 GeV
– Ambiguous T for QGP• smallest crit for largest
T = T(0, x=y=0): (O)
• largest crit for smallest T = Tc: (|)Black D3 Brane
D7 Probe Brane Q
Induced horizonAppearsif > crit
TrailingString
“Brachistochrone”
“z”
x5
SQM 2007
136/26/07
William Horowitz
LHC RcAA(pT)/Rb
AA(pT) Prediction(with speed limits)
– T(0): (O), corrections unlikely for smaller momenta
– Tc: (|), corrections likely for higher momenta
WH, M. Gyulassy, nucl-th/0706.2336
SQM 2007
146/26/07
William Horowitz
Identified c and b at RHIC– Index of power law production spectrum:
y=0
RHIC
LHC
• • NOT slowly varying
– No longer expect pQCD dRAA/dpT > 0
• Large n requires corrections to naïve
Rcb ~ Mc/Mb
SQM 2007
156/26/07
William Horowitz
RHIC c, b RAA pT Dependence
• Large increase in n(pT) overcomes reduction in E-loss and makes pQCD dRAA/dpT < 0, as well
WH, M. Gyulassy, to be published
SQM 2007
166/26/07
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RHIC Rcb Ratio
• Wider distribution of AdS/CFT curves due to large n: increased sensitivity to input parameters
• Advantage of RHIC: lower T => higher AdS speed limits
pQCD
AdS/CFT
pQCD
AdS/CFT
WH, M. Gyulassy, to be published
SQM 2007
176/26/07
William Horowitz
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
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186/26/07
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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 Rc
AA/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
SQM 2007
196/26/07
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Backups
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206/26/07
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LHC 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 AWS-based energy loss (next slide)
• We wish to understand the origin of this difference
SQM 2007
216/26/07
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
SQM 2007
226/26/07
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n(pT)
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236/26/07
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Langevin Model– Langevin equations (assumes v ~ 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:
AdS/CFT here
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246/26/07
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But There’s a Catch (II)• Limited experimental pT reach?
ALICE Physics Performance Report, Vol. II
SQM 2007
256/26/07
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Zoom In
– Factor ~2-3 increase in ratio for pQCD
– Possible distinction for Rad only vs. Rad+El at low-pT
SQM 2007
266/26/07
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Regimes of Applicability• String Regime
– Large Nc, constant ‘t Hooft coupling ( )Small quantum corrections
– Large ‘t Hooft couplingSmall string vibration corrections
– Only tractable case is both limits at onceClassical supergravity (SUGRA)
• RHIC/LHC Regime– Mapping QCD Nc to SYM is easy, but coupling is hard
S runs whereas SYM does not: SYM is something of an unknown constant
Taking SYM = S = .3 (D/2T ~ 1); D/2T ~ 3 => SYM ~ .05