11/13/08 William Horowitz Nuclear Seminar, The Ohio State University 1 LHC Predictions: Phys. Lett. B666:320, 2008 (arXiv:0706.2336) RHIC Predictions:

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


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)


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!


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)


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


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


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


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?


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)


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)


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)


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)


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)


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


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


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:


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)


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


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


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


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


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


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


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


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)


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


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)


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]



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


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



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


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



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


pQCD

AdS/CFT

pQCD

AdS/CFT


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


3511/13/08

William Horowitz

Backup Slides


3611/13/08

William Horowitz

Another AdS Test: Correlations

B Betz, M Gyulassy, J Noronha, and G Torrieri, arXiv:0807.4526


3711/13/08

William Horowitz


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


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


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


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


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


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)



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”


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


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


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


4711/13/08

William Horowitz

A Closer Look at ASW



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)


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


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)



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


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


5211/13/08

William Horowitz

Shameless self-promotion by the presenter


5311/13/08

William Horowitz


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


5411/13/08

William Horowitz

Outline

• Motivation for studying AdS/CFT

• Introduction to Heavy Ion Physics

• pQCD vs. AdS Drag: Expectations, Results, Limitations

• Conclusions

Documents

11/13/08 William Horowitz Nuclear Seminar, The Ohio State University 1 LHC Predictions: Phys. Lett. B666:320, 2008 (arXiv:0706.2336) RHIC Predictions: