Nuclear Seminar, The Ohio State University
111/13/08
William Horowitz
LHC Predictions: Phys. Lett. B666:320, 2008 (arXiv:0706.2336)RHIC Predictions: J. Phys. G35:044025, 2008 (arXiv:0710.0703)
Testing String Theory with Jets
William HorowitzThe Ohio State University
Columbia UniversityFrankfurt Institute for Advanced Studies (FIAS)
November 13, 2008
With many thanks to Miklos Gyulassy
Nuclear Seminar, The Ohio State University
211/13/08
William Horowitz
A Little History: QCD as Theory of Strong Force
– 1935: Yukawa proposes pion as nuclear mediator– 1947: Powell, et al., definitively distinguishes from – 1947-: Particle zoo => 1962: Gell-Mann’s Eightfold Way => 1964: -
found at BNL– 1965: Nambu and Hahn propose color to solve Pauli problem– 1969-73: Feynman’s partons—weakly-coupled point-like subnuclear
particles– 1973: Coleman and Gross—Asymptotic freedom unique to nonabelian
QFTs– 1975: Jets—quarks (’75) and gluons (’79)
– 1992: SU(Nc = 3)
V. E. Barnes et al., OBSERVATION OF A HYPERON WITHSTRANGENESS -3, Phys. Rev. Lett. 12, 204 (1964)
m = 1686 +/- 12 MeV/c2
C. M. G. Lattes, H. Muirhead, G. P. S. Occhialini, and C. F. Powell,PROCESSES INVOLVING CHARGED MESONS, Nature 159, 694(1947).
D. Decamp et al. (ALEPH), Phys. Lett. B284, 151 (1992)
Two and three jet events: R. Brandelik et al. (TASSO), Phys. Lett. B86, 243 (1979)
Nuclear Seminar, The Ohio State University
311/13/08
William Horowitz
Traditional Toolbox for QCD
Lattice QCD pQCD
Previously only two methods:
Two 10 Tflops QCDOC Computers: RBRC and DOE Diagrams!
Nuclear Seminar, The Ohio State University
411/13/08
William Horowitz
Lattice QCD
Traditional Tools (cont’d)• Successful
• But limited
pQCD
• All momenta• Euclidean correlators
• Any quantity• Small coupling (large momenta)
de Florian, Sassot, Stratmann, Phys.Rev.D75:114010,2007
Davies et al. (HPQCD), PRL 92, 022001 (2004)
Nuclear Seminar, The Ohio State University
511/13/08
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
J Maldacena, Adv.Theor.Math.Phys.2:231-252,1998
Geometry of bosonic part of 10D supergravity, near horizon limit
TPlasma = THawking
Nuclear Seminar, The Ohio State University
611/13/08
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, The Ohio State University
711/13/08
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, The Ohio State University
811/13/08
William Horowitz
Testing String Theory
Kallosh and Linde, JCAP 0704:017,2007:Too small to be detected
Huovinen et al., Phys. Lett. B503 (2001) 58
Adapted from P Sorensen, WWND ‘08, arXiv:0808.0503
=> 1/4?
Nuclear Seminar, The Ohio State University
911/13/08
William Horowitz
What’s All the Fuss About?
…data [from RHIC] appear to be more accurately described using string theory methods than with more traditional approaches.
Hold yer horses!Let’s look at the details
Brian Greene (TV)
Will Horowitz (OSU)
Nuclear Seminar, The Ohio State University
1011/13/08
William Horowitz
QGP Creation– Robust prediction of QCD phase transition
Lattice:
Walecka: Hagedorn:
J. D. Walecka, Theoretical Nuclear and Subnuclear Physics, 2nd ed.S. C. Frautschi, Phys. Rev. D3, 2821 (1971)
Karsh et al., Phys. Rev. D62, 034021 (2000), Nucl. Phys. A698, 199 (2002), PoS LAT2005, 193 (2006)
M. Cheng et al., Phys. Rev. D77, 014511 (2008)
Nuclear Seminar, The Ohio State University
1111/13/08
William Horowitz
Probing the QGP• Low momentum (low-pT) particles
– Collective dynamics of the bulk• Statistical Models: temperature• Hydrodynamics: spectra, elliptic flow• HBT (Hanbury-Brown Twiss): freeze-out
surface
• High momentum (high-pT) particles– Parton jets, vacuum fragmentation
• Learn about medium (jet tomography)• Learn about energy loss mechanism (pQCD,
ST)
Nuclear Seminar, The Ohio State University
1211/13/08
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, The Ohio State University
1311/13/08
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, The Ohio State University
1411/13/08
William Horowitz
IC, Viscosity, and Hydro
• Sharper IC (CGC) => viscosity• Softer IC (Glauber) => “perfect”• Test IC with fluctuations?• Control over hadronization?
T Hirano, et al., Phys. Lett. B636:299-304, 2006
P Sorensen, WWND ‘08, arXiv:0808.0503
Nuclear Seminar, The Ohio State University
1511/13/08
William Horowitz
• IC smaller effect• Vacuum fragmentation well
controlled • Compare unmodified p+p collisions
to A+A:
Why High-pT Jets?
pTpT
Figures from http://www.star.bnl.gov/central/focus/highPt/
Longitudinal(beam pipe) direction
2D Transverse directions
Nuclear Seminar, The Ohio State University
1611/13/08
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,
Convenient to Fourier expand RAA:
Nuclear Seminar, The Ohio State University
1711/13/08
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)
Nuclear Seminar, The Ohio State University
1811/13/08
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
Nuclear Seminar, The Ohio State University
1911/13/08
William Horowitz
PHENIX, Phys.Rev.Lett.101:082301,2008
• 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
Naïve AdS/CFT
S. S. Gubser, S. S. Pufu, and A. Yarom, arXiv:0706.0213
Nuclear Seminar, The Ohio State University
2011/13/08
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!
Moore and Teaney, Phys.Rev.C71:064904,2005Casalderrey-Solana and Teaney, Phys.Rev.D74:085012,2006; JHEP 0704:039,2007
BDMPS, Nucl.Phys.B484:265-282,1997Armesto, Salgado, and Wiedemann, Phys. Rev. D69 (2004) 114003Liu, Ragagopal, Wiedemann, PRL 97:182301,2006; JHEP 0703:066,2007
Gubser, Phys.Rev.D74:126005,2006Herzog, Karch, Kovtun, Kozcaz, Yaffe, JHEP 0607:013,2006
Nuclear Seminar, The Ohio State University
2111/13/08
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, The Ohio State University
2211/13/08
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
Nuclear Seminar, The Ohio State University
2311/13/08
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
Nuclear Seminar, The Ohio State University
2411/13/08
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, The Ohio State University
2511/13/08
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)
Nuclear Seminar, The Ohio State University
2611/13/08
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
Nuclear Seminar, The Ohio State University
2711/13/08
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, The Ohio State University
2811/13/08
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]
Nuclear Seminar, The Ohio State University
2911/13/08
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, The Ohio State University
3011/13/08
William Horowitz
LHC RcAA(pT)/Rb
AA(pT) Prediction(with speed limits)
– T(0): (, corrections unlikely for smaller momenta
– Tc: ], corrections likely for higher momenta
WH, M. Gyulassy, arXiv:0706.2336 [nucl-th]
Nuclear Seminar, The Ohio State University
3111/13/08
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, The Ohio State University
3211/13/08
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, The Ohio State University
3311/13/08
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
Nuclear Seminar, The Ohio State University
3411/13/08
William Horowitz
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
Nuclear Seminar, The Ohio State University
3511/13/08
William Horowitz
Backup Slides
Nuclear Seminar, The Ohio State University
3611/13/08
William Horowitz
Another AdS Test: Correlations
B Betz, M Gyulassy, J Noronha, and G Torrieri, arXiv:0807.4526
Nuclear Seminar, The Ohio State University
3711/13/08
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, The Ohio State University
3811/13/08
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, The Ohio State University
3911/13/08
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
Nuclear Seminar, The Ohio State University
4011/13/08
William Horowitz
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
Nuclear Seminar, The Ohio State University
4111/13/08
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, The Ohio State University
4211/13/08
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)
Nuclear Seminar, The Ohio State University
4311/13/08
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, The Ohio State University
4411/13/08
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
Nuclear Seminar, The Ohio State University
4511/13/08
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, The Ohio State University
4611/13/08
William Horowitz
T Renk and K Eskola, Phys. Rev. C 75, 054910 (2007)
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
Nuclear Seminar, The Ohio State University
4711/13/08
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)
Nuclear Seminar, The Ohio State University
4811/13/08
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
Nuclear Seminar, The Ohio State University
4911/13/08
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, The Ohio State University
5011/13/08
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, The Ohio State University
5111/13/08
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, The Ohio State University
5211/13/08
William Horowitz
Shameless self-promotion by the presenter
Nuclear Seminar, The Ohio State University
5311/13/08
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, The Ohio State University
5411/13/08
William Horowitz
Outline
• Motivation for studying AdS/CFT
• Introduction to Heavy Ion Physics
• pQCD vs. AdS Drag: Expectations, Results, Limitations
• Conclusions