testing ads/cft drag and pqcd heavy quark energy loss
DESCRIPTION
Testing AdS/CFT Drag and pQCD Heavy Quark Energy Loss. William Horowitz The Ohio State University Columbia University Frankfurt Institute for Advanced Studies (FIAS) October 28, 2008. LHC Predictions: Phys. Lett. B666:320, 2008 (arXiv:0706.2336) - PowerPoint PPT PresentationTRANSCRIPT
Nuclear Seminar, McGill University
110/28/08
William Horowitz
LHC Predictions: Phys. Lett. B666:320, 2008 (arXiv:0706.2336)RHIC Predictions: J. Phys. G35:044025, 2008 (arXiv:0710.0703)
Testing AdS/CFT Drag and pQCD Heavy Quark Energy Loss
William HorowitzThe Ohio State University
Columbia UniversityFrankfurt Institute for Advanced Studies (FIAS)
October 28, 2008
With many thanks to Miklos Gyulassy and Simon Wicks
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210/28/08
William Horowitz
Outline
• Motivation for studying AdS/CFT
• Introduction to Heavy Ion Physics
• pQCD vs. AdS Drag: Expectations, Results, Limitations
• Conclusions
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310/28/08
William Horowitz
Motivation
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410/28/08
William Horowitz
Limited Toolbox for QCD Calculations
Lattice QCD pQCD
• All momenta• Euclidean correlators
• Any quantity• Small coupling (large momenta)
Previously only two, restricted methods:
Two 10 Tflops QCDOC Computers: RBRC and DOE
Nuclear Seminar, McGill University
510/28/08
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
Bosonic part of IIB low energy effective action
Geometry of bosonic part of 10D supergravity, near horizon limit
J Maldacena, Adv.Theor.Math.Phys.2:231-252,1998
Nuclear Seminar, McGill University
610/28/08
William Horowitz
Regime of Applicability– 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)
Q.M. SSYM
=> C.M. SNG
J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D75:106003, 2007
Nuclear Seminar, McGill University
710/28/08
William Horowitz
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
strongly-coupled QCD in SUGRA
Nuclear Seminar, McGill University
810/28/08
William Horowitz
Connection to Experimenta.k.a. the Reality Check for Theory
Nuclear Seminar, McGill University
910/28/08
William Horowitz
Introduction to Heavy Ion Physics
Nuclear Seminar, McGill University
1010/28/08
William Horowitz
Geometry of a HI Collision
• Hydro propagates IC– Results depend strongly on initial conditions
• Viscosity reduces eventual momentum anisotropy
T Ludlum and L McLerran, Phys. Today 56N10:48 (2003)
M Kaneta, Results from the Relativistic Heavy Ion Collider (Part II)
Nuclear Seminar, McGill University
1110/28/08
William Horowitz
– Hydro /s small ~ .1• QGP fluid near-perfect
liquid
– Naïve pQCD => /s ~ 1• New estimates ~ .1
Z Xu, C Greiner, and H Stoecker, PRL101:082302 (2008)
– Lowest order AdS result: /s = 1/4• Universality?
Perfect Fluidity:AdS + Hydro’s Most Famous
Success
D. Teaney, Phys. Rev. C68, 034913 (2003)P Kovtun, D Son, and A Starinets, Phys.Rev.Lett.94:111601 (2005)P Kats and P Petrov, arXiv:0712.0743M Brigante et al., Phys. Rev. D77:126006 (2008)
Nuclear Seminar, McGill University
1210/28/08
William Horowitz
IC, Viscosity, and Hydro
– Sharper IC (CGC) => viscosity– Softer IC (Glauber) => “perfect”
T Hirano, et al., Phys. Lett. B636:299-304, 2006
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1310/28/08
William Horowitz
• Compare unmodified p+p collisions to A+A:
• Use suppression pattern to either:– Learn about medium (requires detailed
understanding of energy loss): jet tomography
– Learn about energy loss
Why High-pT Jets?
pTpT
Figures from http://www.star.bnl.gov/central/focus/highPt/
Longitudinal(beam pipe) direction
2D Transverse directions
Nuclear Seminar, McGill University
1410/28/08
William Horowitz
Jet Physics Terminology
pT
Naïvely: 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:
Nuclear Seminar, McGill University
1510/28/08
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)
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1610/28/08
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 strong coupling?
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
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1710/28/08
William Horowitz
• Mach wave-like structures• sstrong=(3/4) sweak, similar to Lattice• /sAdS/CFT ~ 1/4 << 1 ~ /spQCD• 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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1810/28/08
William Horowitz
AdS/CFT Energy Loss Models• 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!
Nuclear Seminar, McGill University
1910/28/08
William Horowitz
AdS/CFT Drag• Model heavy quark jet energy loss
by embedding string in AdS space
dpT/dt = - pT
= T2/2Mq
J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D75:106003, 2007
Nuclear Seminar, McGill University
2010/28/08
William Horowitz
Energy Loss Comparison
– AdS/CFT Drag:dpT/dt ~ -(T2/Mq) pT
– Similar to Bethe-HeitlerdpT/dt ~ -(T3/Mq
2) pT
– Very different from LPMdpT/dt ~ -LT3 log(pT/Mq)
tx
Q, m v
D7 Probe Brane
D3 Black Brane(horizon)
3+1D Brane Boundary
Black Holez = 0
zh = T
zm = 2m / 1/2
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2110/28/08
William Horowitz
RAA Approximation
– Above a few GeV, quark production spectrum is approximately power law:• dN/dpT ~ 1/pT
(n+1), where n(pT) has some momentum dependence
– We can approximate RAA(pT):
• RAA ~ (1-(pT))n(pT),
where pf = (1-)pi (i.e. = 1-pf/pi)
y=0
RHIC
LHC
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2210/28/08
William Horowitz
– Use LHC’s large pT reach and identification of c and b to distinguish between pQCD, AdS/CFT• 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
Nuclear Seminar, McGill University
2310/28/08
William Horowitz
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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2410/28/08
William Horowitz
– LHC Prediction Zoo: What a Mess!– Let’s go through step by step
– Unfortunately, large suppression pQCD similar to AdS/CFT– 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 met in full numerical calculation: dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST
LHC c, b RAA pT Dependence
WH, M. Gyulassy, arXiv:0706.2336
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2510/28/08
William Horowitz
• 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
An Enhanced Signal
RcbpQCD(pT) 1 - s n(pT) L2 log(Mb/Mc) ( /pT)
Nuclear Seminar, McGill University
2610/28/08
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, arXiv:0706.2336 [nucl-th]
WH, M. Gyulassy, arXiv:0706.2336 [nucl-th]
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2710/28/08
William Horowitz
– Speed limit estimate for applicability of AdS drag• < crit = (1 + 2Mq/1/2 T)2
~ 4Mq2/(T2)
– Limited by Mcharm ~ 1.2 GeV
• Similar to BH LPM– crit ~ Mq/(T)
– No Single T for QGP• smallest crit for largest T
T = T(0, x=y=0): “(”
• largest crit for smallest T
T = Tc: “]”
Not So Fast!
D3 Black Brane
D7 Probe Brane Q
Worldsheet boundary Spacelikeif > crit
TrailingString
“Brachistochrone”
“z”
x5
Nuclear Seminar, McGill University
2810/28/08
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, arXiv:0706.2336 [nucl-th]
Nuclear Seminar, McGill University
2910/28/08
William Horowitz
Measurement at RHIC– Future detector upgrades will allow for
identified c and b quark measurements
y=0
RHIC
LHC
• • NOT slowly varying
– No longer expect pQCD dRAA/dpT > 0
• Large n requires corrections to naïve
Rcb ~ Mc/Mb
– RHIC production spectrum significantly harder than LHC
Nuclear Seminar, McGill University
3010/28/08
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, arXiv:0710.0703 [nucl-th]
Nuclear Seminar, McGill University
3110/28/08
William Horowitz
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
WH, M. Gyulassy, arXiv:0710.0703 [nucl-th]
pQCD
AdS/CFT
pQCD
AdS/CFT
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3210/28/08
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Conclusions
• Previous AdS qualitative successes inconclusive• AdS/CFT Drag observables calculated• Generic differences (pQCD vs. AdS/CFT Drag)
seen in RAA
– Masked by extreme pQCD
• Enhancement from ratio of c to b RAA
– Discovery potential in Year 1 LHC Run
• Understanding regions of self-consistency crucial
• RHIC measurement possible
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3310/28/08
William Horowitz
Backups
Nuclear Seminar, McGill University
3410/28/08
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
Nuclear Seminar, McGill University
3510/28/08
William Horowitz
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
Nuclear Seminar, McGill University
3610/28/08
William Horowitz
But There’s a Catch (II)• Limited experimental pT reach?
– 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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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
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3810/28/08
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
Nuclear Seminar, McGill University
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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)
Nuclear Seminar, McGill University
4010/28/08
William Horowitz
Pion RAA
• Is it a good measurement for tomography?
– Yes: small experimental error
• Claim: we should not be so immediately dis-missive of the pion RAA as a tomographic tool
– Maybe not: some models appear “fragile”
Nuclear Seminar, McGill University
4110/28/08
William Horowitz
Fragility: A Poor Descriptor
• All energy loss models with a formation time saturate at some Rmin
AA > 0
• The questions asked should be quantitative : – Where is Rdata
AA compared to RminAA?
– How much can one change a model’s controlling parameter so that it still agrees with a measurement within error?
– Define sensitivity, s = min. param/max. param that is consistent with data within error
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4210/28/08
William Horowitz
Different Models have Different Sensitivities to the Pion RAA
• GLV: s < 2
• Higher Twist:s < 2
• DGLV+El+Geom:s < 2
• AWS:s ~ 3 WH, S. Wicks, M. Gyulassy, M. Djordjevic, in
preparation
Nuclear Seminar, McGill University
4310/28/08
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T Renk and K Eskola, Phys. Rev. C 75, 054910 (2007)
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
Nuclear Seminar, McGill University
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William Horowitz
A Closer Look at ASW
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)
The lack of sensitivity needs to be more closely examined because (a) unrealistic geometry (hard cylinders) and no expansion and (b) no expansion shown against older data (whose error bars have subsequently shrunk
(a) (b)
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4510/28/08
William Horowitz
– Surface Emission: one phrase explanation of fragility• All models become surface emitting with infinite E
loss
– Surface Bias occurs in all energy loss models• Expansion + Realistic geometry => model probes a
large portion of medium
Surface Bias vs. Surface Emission
A. Majumder, HP2006 S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
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4610/28/08
William Horowitz
A Closer Look at ASW
– Difficult to draw conclusions on inherent surface bias in AWS from this for three reasons: • No Bjorken expansion• Glue and light quark
contributions not disentangled
• Plotted against Linput (complicated mapping from Linput to physical distance)
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461-474 (2005)
Nuclear Seminar, McGill University
4710/28/08
William Horowitz
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
Nuclear Seminar, McGill University
4810/28/08
William Horowitz
Conclusions• AdS/CFT Drag observables calculated• Generic differences (pQCD vs.
AdS/CFT Drag) seen in RAA
– Masked by extreme pQCD
• Enhancement from ratio of c to b RAA
– Discovery potential in Year 1 LHC Run
• Understanding regions of self-consistency crucial
• RHIC measurement possible
Nuclear Seminar, McGill University
4910/28/08
William Horowitz
Shameless self-promotion by the presenter
Nuclear Seminar, McGill University
5010/28/08
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