8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 1 pQCD vs. AdS/CFT Tested by Heavy Quark Energy Loss William Horowitz Columbia University Frankfurt

Nuclear Theory/RIKEN Seminar

18/31/07

William Horowitz

pQCD vs. AdS/CFT Tested by Heavy Quark Energy Loss

William HorowitzColumbia University

Frankfurt Institute for Advanced Studies (FIAS)August 31, 2007

With many thanks to Miklos Gyulassy, Simon Wicks, and Ivan Vitev

arXiv:0706.2336 (LHC predictions)


28/31/07

William Horowitz

QCD Calculations

Lattice QCD pQCD

• All momenta• Euclidean correlators

• Any quantity• Small coupling

Previously only two tools:


38/31/07

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

3+1 SYM

z = 0


48/31/07

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)t

xQ, m

v

D7 Probe Brane

D3 Black Brane(horizon)

3+1D Brane Boundary

Q.M. SSYM

=> C.M. SNG

Black Holez = 0

zh = T

zm = 2m / 1/2


58/31/07

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


68/31/07

William Horowitz

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


78/31/07

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)


88/31/07

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 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


98/31/07

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


108/31/07

William Horowitz

Quantitative AdS/CFT 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!


118/31/07

William Horowitz

– Use LHC’s large pT reach and identification of c and b to distinguish between pQCD, AdS/CFT• 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


128/31/07

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)


138/31/07

William Horowitz

– 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 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


148/31/07

William Horowitz

An Enhanced 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)


158/31/07

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




168/31/07

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: (|)D3 Black Brane

D7 Probe Brane Q

Worldsheet boundary Spacelikeif > crit

TrailingString

“Brachistochrone”

“z”

x5


178/31/07

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



188/31/07

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


198/31/07

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


208/31/07

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

WH, M. Gyulassy, to be published


218/31/07

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

• Universality of pQCD and AdS/CFT Dependencies?


228/31/07

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


238/31/07

William Horowitz

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


248/31/07

William Horowitz

Backups


258/31/07

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


268/31/07

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


278/31/07

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


288/31/07

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


298/31/07

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)


308/31/07

William Horowitz

Introduction to Jargon

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:


318/31/07

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

Documents

8/31/07 William Horowitz Nuclear Theory/RIKEN Seminar 1 pQCD vs. AdS/CFT Tested by Heavy Quark Energy Loss William Horowitz Columbia University Frankfurt