pQCD vs. String Theory:
LHC Heavy Flavors to Decide
William Horowitz
Columbia University
January 31, 2006
With many thanks to Simon Wicks, Azfar Adil,
Kurt Hinterbichler, Alex Hamilton, and Miklos
Gyulassy.
1/31/07
Yale-Columbia Fest Spring ‘07
William Horowitz
1
RHIC: Heavy Confusion
What produces the nonphotonic
electron suppression??
In-medium fragmentation
pQCD Rad + El
Langevin w/ D ~ O(1)
We must find observable differences!
1/31/07
Yale-Columbia Fest Spring ‘07
William Horowitz
2
PHENIX:
Light-Headed Stringy Conclusions?
Did PHENIX prematurely announce heavy flavor suppression as evidence of perfect fluidity?
Beyond assumptions inherent in
QCD  SYM  IIB,
WHEN can ST calculations be used,
WHEN is ST Langevin applicable, and
WHAT does ST give for D?
1/31/07
Yale-Columbia Fest Spring ‘07
William Horowitz
3
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 gives l ~ 10
Taking aSYM ~ .05 => l ~ 1.8 (keep in mind for later)
1/31/07
Yale-Columbia Fest Spring ‘07
William Horowitz
4
Langevin Scheme
– Langevin equations (assumes gv ~ 1 to neglect
radiative effects):
– Relate drag coef. to diffusion coef.:
– IIB Calculation:
ST here
• Use of Langevin requires relaxation time be large
compared to the inverse temperature:
1/31/07
Yale-Columbia Fest Spring ‘07
William Horowitz
5
Plugging in Numbers
– Langevin pT reach:
• gv(8 GeV e- from c) ~ 11
– D/(2pT) = 4/l1/2 from ST:
• aSYM = aS = .3 => D/(2pT) ~ 1
– Oversuppresses RAA
• aSYM ~ .05 required for D/(2pT) ~ 3
– Mass constraint,
(for T = 350 MeV)
• aSYM = .3 this gives ~ .6 GeV
• aSYM = .05 this gives ~ .25 GeV
– Both charm and bottom satisfy this condition
– Not entirely unreasonable
1/31/07
Yale-Columbia Fest Spring ‘07
William Horowitz
6
Mechanism Disambiguation:
pQCD Rad+El and String Theory
• Use large LHC pT reach and
identification of c and b to distinguish
– RAA ~ (1-e(pT))n(pT), pf = (1-e)pi
– Asymptotic pQCD momentum loss:
erad ~ a3 Log(pT/m2L)/pT
eel ~ a2 Log((pT T)1/2/mg)/pT
– String theory drag momentum loss:
eST ~ 1 - Exp(-m L),
m = plT2/2m
– Independent of pT and strongly dependent on m!!
– T2 dependence makes for a very sensitive probe
1/31/07
Yale-Columbia Fest Spring ‘07
William Horowitz
7
WHDG LHC Predictions
– Results from the full calculation
• Fluctuating number of gluons emitted,
fluctuating path length
1/31/07
Yale-Columbia Fest Spring ‘07
William Horowitz
8
Details of Qualitative ST Study
– Allow local temperature
variation as T(x,y) ~
rmed(x,y)1/3
– Nf = N c = 3
– Stop energy loss at Tc ~ 160
MeV
– Reasonable agreement with
Moore and Teaney D/2pT = 3
results
1/31/07
Yale-Columbia Fest Spring ‘07
William Horowitz
9
ST Results for the LHC
• RAA’s strikingly more suppressed (due to T2 dependence)
than for pQCD
• Regardless of normalization, more sophisticated calculation
maintains RAA decreasing with pT (as compared to strong
increase for pQCD)
1/31/07
Yale-Columbia Fest Spring ‘07
William Horowitz
10
Mechanism Disambiguation:
pQCD Rad+El and AV
• High-pT charm free from possible inmedium fragmentation effects
– Distance traveled before fragmentation is
boosted formation time (given by uncertainty
principle)
• For D meson, Dt ~ .1 fm
• g ~ 21/2 p/m: g(50 GeV) ~ 40, g(100 GeV) ~ 80
– Clear signal: asymptotic pQCD Rad+El
behavior modified by increased suppression at
low momenta
1/31/07
Yale-Columbia Fest Spring ‘07
William Horowitz
11
Examine the Ratio of c and b RAA
– Large qualitative
differences
– STapprox indep of pT, and
similar in magnitude for
various t0 and aSYM
– Dead cone effect creates
growth in pT for pQCD
– AV ratio will grow greater
than 1, peak at 50<pT<100,
then drop down to 1
again
1/31/07
Yale-Columbia Fest Spring ‘07
William Horowitz
12
Conclusions
• Three very different theories claim to explain the
surprisingly suppressed RHIC non-photonic electron RAA
– None are particularly unreasonable
• Year 1 of LHC will show qualitative differences between
energy loss mechanisms:
– dRAA(pT)/dpT > 0 => pQCD and/or AV; dRAA(pT)/dpT < 0 => ST
• Ratio of charm to bottom RAA will be a discerning
observable
– PID and large pT reach allow easy disentanglement of the three effects
– Ratio is: flat in ST; asymptotically approaching 1 from below in pQCD;
grows larger than 1 for pT > 50 GeV and approaches 1 from above in AV
– Ratio of RAA’s benefits from cancellation of large systematic errors due to
unknown p+p spectrum, binary scaling, etc.
1/31/07
Yale-Columbia Fest Spring ‘07
William Horowitz
13
Backup: LHC Asymptopia
1/31/07
Yale-Columbia Fest Spring ‘07
William Horowitz
14