1/31/07William Horowitz Yale-Columbia Fest Spring ‘07 1 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.

1/31/07William Horowitz Yale-Columbia Fest Spring ‘07 2 RHIC: Heavy Confusion What produces the nonphotonic electron suppression?? pQCD Rad + El Langevin w/ D ~ O(1) In-medium fragmentation We must find observable differences!

1/31/07William Horowitz Yale-Columbia Fest Spring ‘07 3 PHENIX: Light-Headed Stringy Conclusions? 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? Did PHENIX prematurely announce heavy flavor suppression as evidence of perfect fluidity?

1/31/07William Horowitz Yale-Columbia Fest Spring ‘07 4 Regimes of Applicability String Regime –Large N c, 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 N c 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 gives ~ 10 Taking  SYM ~.05 => ~ 1.8 (keep in mind for later)

1/31/07William Horowitz Yale-Columbia Fest Spring ‘07 5 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

1/31/07William Horowitz Yale-Columbia Fest Spring ‘07 6 Plugging in Numbers –Langevin p T reach:  v(8 GeV e - from c) ~ 11 –D/(2  T) = 4/ 1/2 from ST:  SYM =  S =.3 => D/(2  T) ~ 1 –Oversuppresses R AA  SYM ~.05 required for D/(2  T) ~ 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

1/31/07William Horowitz Yale-Columbia Fest Spring ‘07 7 Use large LHC p T reach and identification of c and b to distinguish –R AA ~ (1-  (p T )) n(p T ), p f = (1-  )p i –Asymptotic pQCD momentum loss: –String theory drag momentum loss: –Independent of p T and strongly dependent on m!! –T 2 dependence makes for a very sensitive probe Mechanism Disambiguation: pQCD Rad+El and String Theory  rad   3 Log(p T /  2 L)/p T  el   2 Log((p T T) 1/2 /m g )/p T  ST  1 - Exp(-  L),  =  T 2 /2m

1/31/07William Horowitz Yale-Columbia Fest Spring ‘07 8 WHDG LHC Predictions –Results from the full calculation Fluctuating number of gluons emitted, fluctuating path length

1/31/07William Horowitz Yale-Columbia Fest Spring ‘07 9 Details of Qualitative ST Study –Allow local temperature variation as T(x,y) ~  med (x,y) 1/3 –N f = N c = 3 –Stop energy loss at T c ~ 160 MeV –Reasonable agreement with Moore and Teaney D/2  T = 3 results

1/31/07William Horowitz Yale-Columbia Fest Spring ‘07 10 ST Results for the LHC R AA ’s strikingly more suppressed (due to T 2 dependence) than for pQCD Regardless of normalization, more sophisticated calculation maintains R AA decreasing with p T (as compared to strong increase for pQCD)

1/31/07William Horowitz Yale-Columbia Fest Spring ‘07 11 Mechanism Disambiguation: pQCD Rad+El and AV High-p T 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  ~ 2 1/2 p/m:  (50 GeV) ~ 40,  (100 GeV) ~ 80 –Clear signal: asymptotic pQCD Rad+El behavior modified by increased suppression at low momenta

1/31/07William Horowitz Yale-Columbia Fest Spring ‘07 12 Examine the Ratio of c and b R AA –Large qualitative differences –STapprox indep of p T, and similar in magnitude for various  0 and  SYM –Dead cone effect creates growth in p T for pQCD –AV ratio will grow greater than 1, peak at 50<p T <100, then drop down to 1 again

1/31/07William Horowitz Yale-Columbia Fest Spring ‘07 13 Conclusions Three very different theories claim to explain the surprisingly suppressed RHIC non-photonic electron R AA –None are particularly unreasonable Year 1 of LHC will show qualitative differences between energy loss mechanisms: –dR AA (p T )/dp T > 0 => pQCD and/or AV; dR AA (p T )/dp T ST Ratio of charm to bottom R AA will be a discerning observable –PID and large p T 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 p T > 50 GeV and approaches 1 from above in AV –Ratio of R AA ’s benefits from cancellation of large systematic errors due to unknown p+p spectrum, binary scaling, etc.

1/31/07William Horowitz Yale-Columbia Fest Spring ‘07 14 Backup: LHC Asymptopia