Possible String Theoretic Deviations from pQCD in Heavy Quark Energy Loss at LHC

CERN Heavy Ion Forum

16/1/07

William Horowitz

Possible String Theoretic Deviations from pQCD in Heavy

Quark Energy Loss at LHC

William HorowitzColumbia University

Frankfurt Institute for Advanced Studies (FIAS)June 1, 2007

With many thanks to Miklos Gyulassy, Simon Wicks, Ivan Vitev, Jorge Casalderrey-Solana.


26/1/07

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)


36/1/07

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


46/1/07

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


56/1/07

William Horowitz

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

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


66/1/07

William Horowitz

Give up on pQCD?

Old and Busted: pQCDNew Hotness: AdS/CFT


76/1/07

William Horowitz

If You Ask Me…

Use the LHC to Test the Two!Let’s look at Heavy Quark Jet Suppression


86/1/07

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!


96/1/07

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)


106/1/07

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


116/1/07

William Horowitz

Model Inputs– 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 medium densities for LHC:– PHOBOS (dNg/dy = 1750); CGC (dNg/dy = 2900)


126/1/07

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


136/1/07

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)


146/1/07

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


156/1/07

William Horowitz

But There’s a Catch (I)

– 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: (|)


166/1/07

William Horowitz

LHC RcAA(pT)/Rb

AA(pT) Prediction(with speed limits)

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


176/1/07

William Horowitz

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

ALICE Physics Performance Report, Vol. II


186/1/07

William Horowitz

Zoom In

– Factor ~2-3 increase in ratio for pQCD

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


196/1/07

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


206/1/07

William Horowitz

Conclusions (cont’d)• Additional LHC 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


216/1/07

William Horowitz

J. P. Blaizot, E. Iancu, U. Kraemmer, A. Rebhan, hep-ph/0611393

AdS/CFT


226/1/07

William Horowitz

Backups


236/1/07

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


246/1/07

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


256/1/07

William Horowitz

RHIC e-


266/1/07

William Horowitz

RHIC c, b RAA(pT)


276/1/07

William Horowitz

RHIC RcAA(pT)/Rb

AA(pT)


286/1/07

William Horowitz

n(pT)


296/1/07

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


306/1/07

William Horowitz

Drag Picture• The Heavy Quark Brachistochrone:

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

Documents

Possible String Theoretic Deviations from pQCD in Heavy Quark Energy Loss at LHC