Yale-Columbia Fest Spring ‘071
1/31/07 William Horowitz
pQCD vs. String Theory:LHC Heavy Flavors to Decide
William HorowitzColumbia University
January 31, 2006
With many thanks to Simon Wicks, Azfar Adil, Kurt Hinterbichler, Alex Hamilton, and
Miklos Gyulassy.
Yale-Columbia Fest Spring ‘072
1/31/07 William Horowitz
RHIC: Heavy ConfusionWhat produces the nonphotonic electron suppression??
pQCD Rad + ElLangevin w/ D ~ O(1)
In-medium fragmentation
We must find observable differences!
Yale-Columbia Fest Spring ‘073
1/31/07 William Horowitz
PHENIX: Light-Headed Stringy Conclusions?
Beyond assumptions inherent inQCD SYM IIB,
WHEN can ST calculations be used, WHEN is ST Langevin applicable, and WHAT does ST give for D?
Did PHENIX prematurely announce heavy flavor suppression as evidence of perfect fluidity?
Yale-Columbia Fest Spring ‘074
1/31/07 William Horowitz
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
hardS runs whereas SYM does not: SYM is something of an
unknown constant
– Taking SYM = S = .3 gives ~ 10Taking SYM ~ .05 => ~ 1.8 (keep in mind for later)
Yale-Columbia Fest Spring ‘075
1/31/07 William Horowitz
Langevin Scheme– 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:
ST here
Yale-Columbia Fest Spring ‘076
1/31/07 William Horowitz
Plugging in Numbers– Langevin pT reach:
• v(8 GeV e- from c) ~ 11
– D/(2T) = 4/1/2 from ST:• SYM = S = .3 => D/(2T) ~ 1
– Oversuppresses RAA
• SYM ~ .05 required for D/(2T) ~ 3
– Mass constraint, (for T = 350 MeV)• SYM = .3 this gives ~ .6 GeV
• SYM = .05 this gives ~ .25 GeV– Both charm and bottom satisfy this condition
– Not entirely unreasonable
Yale-Columbia Fest Spring ‘077
1/31/07 William Horowitz
• Use large LHC pT reach and identification of c and b to distinguish– RAA ~ (1-(pT))n(pT), pf = (1-)pi
– Asymptotic pQCD momentum loss:
– String theory drag momentum loss:
– Independent of pT and strongly dependent on m!!
– T2 dependence makes for a very sensitive probe
Mechanism Disambiguation: pQCD Rad+El and String
Theory
rad 3 Log(pT/2L)/pT el 2 Log((pT T)1/2/mg)/pT
ST 1 - Exp(- L), = T2/2m
Yale-Columbia Fest Spring ‘078
1/31/07 William Horowitz
WHDG LHC Predictions– Results from the full calculation
• Fluctuating number of gluons emitted, fluctuating path length
Yale-Columbia Fest Spring ‘079
1/31/07 William Horowitz
Details of Qualitative ST Study
– Allow local temperature variation as T(x,y) ~ med(x,y)1/3
– Nf = Nc = 3
– Stop energy loss at Tc ~ 160 MeV
– Reasonable agreement with Moore and Teaney D/2T = 3 results
Yale-Columbia Fest Spring ‘0710
1/31/07 William Horowitz
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)
Yale-Columbia Fest Spring ‘0711
1/31/07 William Horowitz
Mechanism Disambiguation: pQCD Rad+El and AV
• High-pT charm free from possible in-medium fragmentation effects– Distance traveled before fragmentation is
boosted formation time (given by uncertainty principle)• For D meson, t ~ .1 fm • ~ 21/2 p/m: (50 GeV) ~ 40, (100 GeV) ~ 80
– Clear signal: asymptotic pQCD Rad+El behavior modified by increased suppression at low momenta
Yale-Columbia Fest Spring ‘0712
1/31/07 William Horowitz
Examine the Ratio of c and b RAA
– Large qualitative differences
– STapprox indep of pT, and similar in magnitude for various 0 and SYM
– 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
Yale-Columbia Fest Spring ‘0713
1/31/07 William Horowitz
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.
Yale-Columbia Fest Spring ‘0714
1/31/07 William Horowitz
Backup: LHC Asymptopia