10/28/08 william horowitz nuclear seminar, mcgill university 1 lhc predictions: phys. lett....

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


210/28/08

William Horowitz

Outline

• Motivation for studying AdS/CFT

• Introduction to Heavy Ion Physics

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

• Conclusions


310/28/08

William Horowitz

Motivation


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


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


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


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


810/28/08

William Horowitz

Connection to Experimenta.k.a. the Reality Check for Theory


910/28/08

William Horowitz

Introduction to Heavy Ion Physics


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)


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)


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


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


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:


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)


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


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


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!


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


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


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


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


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)


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


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)


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]



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


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



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


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



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


pQCD

AdS/CFT

pQCD

AdS/CFT


3210/28/08

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


3310/28/08

William Horowitz

Backups


3410/28/08

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


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


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


3710/28/08

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


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


3910/28/08

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)



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”


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


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


4310/28/08

William Horowitz

T Renk and K Eskola, Phys. Rev. C 75, 054910 (2007)

WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation


4410/28/08

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)


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


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)



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


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


4910/28/08

William Horowitz

Shameless self-promotion by the presenter


5010/28/08

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

10/28/08 william horowitz nuclear seminar, mcgill university 1 lhc predictions: phys. lett....

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