1. 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.

2. 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!

3. 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?

4. 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)

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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)

11. 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

12. 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

13. 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.

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