SQM 2007

16/26/07

William Horowitz

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

William HorowitzColumbia University

Frankfurt Institute for Advanced Studies (FIAS)June 26, 2007

With many thanks to Miklos Gyulassy, Simon Wicks, Jorge Casalderrey-Solana, and Urs

Wiedemann.

arXiv:0706.2336 (LHC predictions)

SQM 2007

26/26/07

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)

SQM 2007

36/26/07

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…

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

SQM 2007

46/26/07

William Horowitz

Strong Coupling• 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

SQM 2007

56/26/07

William Horowitz

• sstrong=(3/4) sweak, similar to Lattice• /sAdS/CFT ~ 1/4 << 1 ~ /spQCD• e- RAA ~ , RAA; e- RAA()• Mach wave-like structures

T. Hirano and M. Gyulassy, Nucl. Phys. A69:71-94 (2006)

Qualitative AdS/CFT Successes:

PHENIX, Phys. Rev. Lett. 98, 172301 (2007)

J. J. Friess, S. S. Gubser, G. Michalogiorgakis, S. S. Pufu, Phys. Rev. D75:106003 (2007)J. P. Blaizot, E. Iancu, U. Kraemmer, A. Rebhan, hep-ph/0611393

AdS/CFT

SQM 2007

66/26/07

William Horowitz

AdS/CFT vs. pQCD 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!

SQM 2007

76/26/07

William Horowitz

– Use LHC’s large pT reach and identification of c and b to distinguish• 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

SQM 2007

86/26/07

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)

SQM 2007

96/26/07

William Horowitz

– 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

SQM 2007

106/26/07

William Horowitz

A Cleaner 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)

SQM 2007

116/26/07

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

WH, M. Gyulassy, nucl-th/0706.2336

WH, M. Gyulassy, nucl-th/0706.2336

SQM 2007

126/26/07

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: (|)Black D3 Brane

D7 Probe Brane Q

Induced horizonAppearsif > crit

TrailingString

“Brachistochrone”

“z”

x5

SQM 2007

136/26/07

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

WH, M. Gyulassy, nucl-th/0706.2336

SQM 2007

146/26/07

William Horowitz

Identified c and b at RHIC– Index of power law production spectrum:

y=0

RHIC

LHC

• • NOT slowly varying

– No longer expect pQCD dRAA/dpT > 0

• Large n requires corrections to naïve

Rcb ~ Mc/Mb

SQM 2007

156/26/07

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

SQM 2007

166/26/07

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

SQM 2007

176/26/07

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

SQM 2007

186/26/07

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

SQM 2007

196/26/07

William Horowitz

Backups

SQM 2007

206/26/07

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

SQM 2007

216/26/07

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

SQM 2007

226/26/07

William Horowitz

n(pT)

SQM 2007

236/26/07

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

SQM 2007

246/26/07

William Horowitz

But There’s a Catch (II)• Limited experimental pT reach?

ALICE Physics Performance Report, Vol. II

SQM 2007

256/26/07

William Horowitz

Zoom In

– Factor ~2-3 increase in ratio for pQCD

– Possible distinction for Rad only vs. Rad+El at low-pT

SQM 2007

266/26/07

William Horowitz

Regimes of Applicability• String Regime

– 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)

• RHIC/LHC Regime– Mapping QCD Nc to SYM is easy, but coupling is hard

S runs whereas SYM does not: SYM is something of an unknown constant

Taking SYM = S = .3 (D/2T ~ 1); D/2T ~ 3 => SYM ~ .05