1. Possible String Theoretic Deviations from pQCD in Heavy Quark Energy Loss at LHC
William Horowitz
Columbia University
Frankfurt Institute for Advanced Studies (FIAS)
May 21, 2007
With many thanks to Miklos Gyulassy.
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2. pQCD Success at RHIC: (circa 2005) Consistency: RAA(h)~RAA(p)
Y. Akiba for the PHENIX collaboration, hep-ex/
Consistency: RAA(h)~RAA(p)
Null Control: RAA(g)~1
GLV Prediction: Theory~Data for reasonable fixed L~5 fm and dNg/dy~dNp/dy
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3. Trouble for wQGP Picture
D. Teaney, Phys. Rev. C68, (2003)
Hydro h/s too small
v2 too large
A. Drees, H. Feng, and J. Jia, Phys. Rev. C71: (2005)
(first by E. Shuryak, Phys. Rev. C66: (2002))
e- RAA too small
M. Djorjevic, M. Gyulassy, R. Vogt, S. Wicks, Phys. Lett. B632:81-86 (2006)
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4. 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
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5. Qualitative AdS/CFT Successes:
sstrong=(3/4) sweak, similar to Lattice
h/sAdS/CFT ~ 1/4p << 1 ~ h/spQCD
e- RAA ~ p, h RAA; e- RAA(f)
Mach wave-like structures
Give up on pQCD?
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6. Ideal Hydro? pQCD elastic: h/s ~ 1
Hydro merely propagates initial conditions; its results are highly dependent on them
pQCD elastic: h/s ~ 1
pQCD r+e PC: h/s ~ .1?
AdS: universal lower bound for all infinitely coupled systems h/s ~ 1/4p
Glauber initial state =>
ideal (ST) hydro
CGC initial state =>
viscous (pQCD) hydro
T. Hirano, U. W. Heinz, D. Kharzeev, R. Lacy, Y. Nara, Phys. Lett. B636: (2006)
Must understand initial state better before reaching a conclusion:
A. Adil, M. Gyulassy, T. Hirano, Phys. Rev. D73: (2006)
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7. Simultaneous p, e- Suppression
pQCD is not falsified:
Elastic loss?
Uncertainty in c, b contributions
In-medium fragmentation?
Resonances?
A. Adil and I. Vitev, hep-ph/
Naïve pQCD => large mass, small loss
But p, h RAA ~ e- RAA!
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/
H. Van Hees, V. Greco, and R. Rapp, Phys. Rev. C73, (2006)
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8. 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
PHENIX, Phys. Rev. Lett. 98, (2007)
WH, Acta Phys. Hung. A27:
GREL 40-50%
MPC 30%
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9. 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!
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10. Drag Picture The Heavy Quark Brachistochrone: CERN Heavy Ion Forum
J Friess, S Gubser, G Michalogiorgakis, S Pufu, Phys Rev D75:106003, 2007
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11. Looking for a Robust, Detectable Signal
Use large LHC pT reach and identification of c and b to distinguish
RAA ~ (1-e(pT))n(pT), where pf = (1-e)pi (i.e. 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: epQCD vs. eAdS indep of pT!!
dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST
erad ~ as L2 log(pT/Mq)/pT
eST ~ 1 - Exp(-m L), m = pl1/2 T2/2Mq
S. Gubser, Phys.Rev.D74: (2006)
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12. A Note on LHC pT Reach More on pT limits from the AdS side later
ALICE Physics Performance Report, Vol. II
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13. Regimes of Applicability
String Regime
Large Nc, constant ‘t Hooft coupling ( )
Small quantum corrections
Large ‘t Hooft coupling
Small string vibration corrections
Only tractable case is both limits at once
Classical supergravity (SUGRA)
RHIC/LHC Regime
Mapping QCD Nc to SYM is easy, but coupling is hard
aS runs whereas aSYM does not: aSYM is something of an unknown constant
Taking aSYM = aS = .3 (D/2pT ~ 1); D/2pT ~ 3 => aSYM ~ .05
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14. Models
AdS/CFT Drag
“Obvious”: as = aSYM, TSYM = TQCD
D/2pT = 3 inspired: as = .05
pQCD/Hydro inspired: as = .3 (D/2pT ~ 1)
“Alternative”: l = 5.5, TSYM = TQCD/31/4
WHDG convolved radiative and collisional energy loss
as = .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)
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15. LHC c, b RAA pT Dependence
LHC Prediction Zoo: What a Mess!
Let’s go through step by step
Naïve expectations born out in full numerical calculation:
dRAA(pT)/dpT > 0 => pQCD; dRAA(pT)/dpT < 0 => ST
Significant rise in RAA(pT) for pQCD Rad+El
Large suppression leads to flattening
Use of realistic geometry and Bjorken expansion allows saturation below .2
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16. 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)/RbAA(pT) ~ 1 - as n(pT) L2 log(Mb/Mc) ( /pT)
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17. LHC RcAA(pT)/RbAA(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
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18. But There’s a Catch
Speed limit estimate for applicability of AdS/CFT drag computation
g < gcrit = (1 + 2Mq/l1/2 T)2
~ 4Mq2/(l T2)
Limited by Mcharm ~ 1.2 GeV
Ambiguous T for QGP
smallest gcrit for largest
T = T(t0, x=y=0): (O)
largest gcrit for smallest T = Tc: (|)
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19. LHC RcAA(pT)/RbAA(pT) Prediction (with speed limits)
O: corrections unlikely for smaller momenta
|: corrections likely for higher momenta
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20. Zooming In Factor ~2-3 increase in ratio for pQCD
Possible distinction for Rad only vs. Rad+El at low-pT
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21. 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
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22. 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
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23. Conclusions (cont’d) Additional LHC Goodies:
Adil Vitev in-medium fragmentation results in a much more rapid rise to 1 for RcAA/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
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