21/05/07 william horowitz cern heavy ion forum 1 possible string theoretic deviations from pqcd in...

CERN Heavy Ion Forum

121/05/07

William Horowitz

Possible String Theoretic Deviations from pQCD in Heavy

Quark Energy Loss at LHC

William HorowitzColumbia University

Frankfurt Institute for Advanced Studies (FIAS)May 21, 2007

With many thanks to Miklos Gyulassy.


221/05/07

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)


321/05/07

William Horowitz

• 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

D. Teaney, Phys. Rev. C68, 034913 (2003)

• Hydro /s too small • e- RAA too small

M. Djorjevic, M. Gyulassy, R. Vogt, S. Wicks, Phys. Lett. B632:81-86 (2006)


421/05/07

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


521/05/07

William Horowitz

• sstrong=(3/4) sweak, similar to Lattice

• /sAdS/CFT ~ 1/4 << 1 ~ /spQCD

• e- RAA ~ , RAA; e- RAA()

• Mach wave-like structures• Give up on pQCD?

Qualitative AdS/CFT Successes:


621/05/07

William Horowitz

• pQCD elastic: /s ~ 1– pQCD r+e PC: /s ~ .1?

• AdS: universal lower bound for all infinitely coupled systems /s ~ 1/4

Ideal Hydro?

T. Hirano, U. W. Heinz, D. Kharzeev, R. Lacy, Y. Nara, Phys. Lett. B636:299-304 (2006)

Hydro merely propagates initial conditions; its results are highly dependent on them

•Glauber initial state =>ideal (ST) hydro•CGC initial state =>viscous (pQCD) hydro

Must understand initial state better before reaching a conclusion:A. Adil, M. Gyulassy, T. Hirano, Phys. Rev. D73:074006 (2006)


721/05/07

William Horowitz

Simultaneous , e- Suppression

• pQCD is not falsified:– Elastic loss?– Uncertainty in c, b

contributions– In-medium

fragmentation?– Resonances?

S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076A. Adil and I. Vitev, hep-ph/0611109

H. Van Hees, V. Greco, and R. Rapp, Phys. Rev. C73, 034913 (2006)

• Naïve pQCD => large mass, small loss

• But , RAA ~ e- RAA!


821/05/07

William Horowitz

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

Simultaneous RAA, v2 Description

– Energy loss translates spatial anisotropy of medium to jets• RAA and v2 are thus anti-

correlated• First seen for pions, no

nonperturbative model reproduces both RAA and v2

• Observed for e-, too• No known solution to

the puzzle

WH, Acta Phys. Hung. A27:221-225

GREL 40-50%

MPC 30%


921/05/07

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– Equation for infinitely massive quark moving with

constant v through infinitely coupled SYM at uniform T

– not yet used to calculate observables: let’s do it!


1021/05/07

William Horowitz

Drag Picture• The Heavy Quark Brachistochrone:

J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D75:106003, 2007


1121/05/07

William Horowitz

– Use large LHC 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)


1221/05/07

William Horowitz

A Note on LHC pT Reach

• More on pT limits from the AdS side later

ALICE Physics Performance Report, Vol. II


1321/05/07

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


1421/05/07

William Horowitz

Models– AdS/CFT Drag

• “Obvious”: s = SYM, TSYM = TQCD

– D/2T = 3 inspired: s = .05

– pQCD/Hydro inspired: s = .3 (D/2T ~ 1)

• “Alternative”: = 5.5, TSYM = TQCD/31/4

– WHDG convolved radiative and collisional energy loss

• s = .3

– WHDG radiative energy loss (similar to ASW)• = 40, 100

– All use realistic, nonuniform medium with Bjorken expansion

• Two extrapolations to LHC:– PHOBOS (dNg/dy = 1750); CGC (dNg/dy = 2900)


1521/05/07

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


1621/05/07

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

– Ratio starts below 1; independent of pT

RcAA(pT)/Rb

AA(pT) 1 - s n(pT) L2 log(Mb/Mc) ( /pT)


1721/05/07

William Horowitz

LHC RcAA(pT)/Rb

AA(pT) Prediction

• Recall the Prediction 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)

– ST ratio is flat and many times smaller than pQCD at only moderate pT


1821/05/07

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: (|)


1921/05/07

William Horowitz

LHC RcAA(pT)/Rb

AA(pT) Prediction(with speed limits)

– O: corrections unlikely for smaller momenta– |: corrections likely for higher momenta


2021/05/07

William Horowitz

Zooming In

– Factor ~2-3 increase in ratio for pQCD

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


2121/05/07

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


2221/05/07

William Horowitz

Conclusions– PID and large pT reach will give the LHC a unique

position to make discoveries in the heavy quark sector• 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 will be an important observable

– Ratio is: flat in ST; asymptotically approaching 1 from below in pQCD

• While future AdS/CFT calculations could well alter the ST predictions shown here, it is highly unlikely that a pQCD mechanism can be found that allows mass effects to persist out to momenta orders of magnitude larger than Mq

– A measurement of this ratio NOT going to 1 will be a clear sign of new physics: pQCD predicts ~ 2-3 times increase in this ratio by 30 GeV—this can be observed in year 1 at the LHC


2321/05/07

William Horowitz

Conclusions (cont’d)• Additional LHC 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

– Mach cone may be due to radiated gluons: from pQCD the away-side dip should widen with increasing parton mass

– 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

21/05/07 william horowitz cern heavy ion forum 1 possible string theoretic deviations from pqcd in...

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