1. 7/7/09 William Horowitz WHDG Brick and Comparing WHDG to ASW-SH William Horowitz The Ohio State University July 7, 2009 With many thanks to Brian Cole, Ulrich Heinz, and Yuri Kovchegov

2. 7/7/09 William Horowitz Outline Context Pedagogy (Some) brick results Comparing WHDG to ASW-SH Pedagogy Surprise! Conclusions TECHQM @ CERN2

3. 7/7/09 William Horowitz TECHQM @ CERN3 pQCD Success at RHIC: –Consistency: R AA (  )~R AA (  ) –Null Control: R AA (  )~1 –GLV Prediction: Theory~Data for reasonable fixed L~5 fm and dN g /dy~dN  /dy Y. Akiba for the PHENIX collaboration, hep-ex/0510008 (circa 2005)

4. 7/7/09 William Horowitz TECHQM @ CERN4 Trouble for High-p T wQGP Picture –v 2 too small –NPE supp. too large STAR, Phys. Rev. Lett. 98, 192301 (2007)  0 v 2 PHENIX, Phys. Rev. Lett. 98, 172301 (2007) NPE v 2 Pert. at LHC energies? C. Vale, QM09 Plenary (analysis by R. Wei) WHDG

5. 7/7/09 William Horowitz TECHQM @ CERN5 Multiple Models –Inconsistent medium properties –Distinguish between models Bass et al., Phys.Rev.C79:024901,2009 WHDG, Nucl.Phys.A784:426-442,2007 Bass et al.

6. 7/7/09 William Horowitz TECHQM @ CERN6 Quantitative Parameter Extraction Vary input param. Find “best” value PHENIX, PRC77:064907,2008 Need for theoretical error

7. 7/7/09 William Horowitz pQCD Rad. Opacity Exp. (I) All orders in L / expression for d N g /d x N g : number of emitted gluons x : “momentum fraction carried by gluon” –Small x regime, x << 1 –Assumed length scales:    << << L Debye screening mass  Mean free path Medium length L –Localized scattering centers; partons see many centers and radiate coherently (crucial!) TECHQM @ CERN7

8. 7/7/09 William Horowitz pQCD Rad. Opacity Exp. (II) Eikonality assumed p + >> p - k + >> k - –Radiation emitted forward –Parent parton continues moving forward –Partons move on straight-line paths First order in opacity –Interference w/ vacuum rad. crucial 8 mgmg M TECHQM @ CERN

9. 7/7/09 William Horowitz FOO dN g /dx WHDG Rad: , M, m g depend on T TECHQM @ CERN9

10. 7/7/09 William Horowitz d N g /d x to P (  ) –Opacity expansion => d N g /d x Single gluon emission spectrum –Approx. multi-gluon fluct. w/ Poisson conv. Prob. to lose mom. frac.  p f = (1-  ) p i Assumes incoherent emission of non-Abelian gluons TECHQM @ CERN 10

11. 7/7/09 William Horowitz TECHQM @ CERN11 WHDG Collisional Loss –Gaussian distribution Mean loss for light quarks: –Braaten-Thoma, PRD44, 2625 (1991) –Width given by Fluctuation-Dissipation theorem –Poisson conv. not well approx by Gaussian for realistic, small num of scatterings See Simon Wicks’ thesis

12. 7/7/09 William Horowitz Typical Results Original Brick TECHQM @ CERN12 Wiedemann Brick =.4

13. 7/7/09 William Horowitz TECHQM @ CERN13 Running  s ? –  s =.2,.3 – Not surprisingly, changes in  s make huge difference to P(  ) –  s =.3,.4

14. 7/7/09 William Horowitz TECHQM @ CERN14 WHDG thru KKP –Facilitate comparison between WHDG and HT –Elastic gain => D(z > 1) > 0

15. 7/7/09 William Horowitz FOO dN g /dx WHDG Rad: , M, m g depend on T TECHQM @ CERN15

16. 7/7/09 William Horowitz Differences WHDG Rad m g =  /√2 M =  /2 k max = 2 x (1- x ) E  exp ( z ) L/ (T) q max = √(3  E )  s =.3 ASW-SH m g =  M =  k max = x E  theta ( z ) L/ q max = ∞  s = 1/3 TECHQM @ CERN16

17. 7/7/09 William Horowitz Where Did k max ’s Come From? (I) DGLV –Light cone momenta –Note x + def.! –Always on-shell ASW-SH –4-momenta –Note x E def.! –Always on-shell TECHQM @ CERN17 The same in the eikonal limit!

18. 7/7/09 William Horowitz Where Did k max ’s Come From? (II) DGLV –Light cone momenta –Note x + def.! –Always on-shell – k T < x + E + = 2 x + E –Forward travel ASW-SH –4-momenta –Note x E def.! –Always on-shell – k T < x E E –Forward travel TECHQM @ CERN18 Same physics: cutoff when gluons radiated at 90 o

19. 7/7/09 William Horowitz Compare Apples to Apples Differences must be due to non-eikonality GLV( x E ) in red; ASW-SH( x E ) in blue TECHQM @ CERN19

20. 7/7/09 William Horowitz Large E Limit – GLV( x E ) in red; ASW-SH( x E ) in blue –For most values of x, naïve interpretation holds What’s going on at small x ? TECHQM @ CERN20

21. 7/7/09 William Horowitz Interpretation Physically: –Typical k T ~  => typ.  ~  System wants to radiate lots of glue at x ~  / E BUT, this is right at our k T cutoff: –k T ~  <  ~ k T, max : the system will always take advantage of all the “phase space” we give it Analytically: –More natural way to write d N g /d x TECHQM @ CERN21

22. 7/7/09 William Horowitz Consequences At large energies, is E ind. –Large irreducible systematic uncertainty for some observables –For T = 485 GeV, L = 2 fm,  s = 0.3: ≈ 1, k max = x E ≈ 2, k max = 2 x E –Note that R AA becomes insensitive to details of k max (goes to 1) TECHQM @ CERN22

23. 7/7/09 William Horowitz Conclusions –Current phen. comparisons of pQCD to data unsatisfactory –WHDG not oversuppressed Opacity expansion suffers from large systematic errors –Strong dependence on k max = # x E # is not specified by framework –Similar dependence on IR cutoff, m g –Irreducible? Consequences for other models, parameter extractions? WHDG Brick and Comparison to ASW-SH23

24. 7/7/09 William Horowitz Supplement 24TECHQM @ CERN

25. 7/7/09 William Horowitz Eikonality Sets in for all x TECHQM @ CERN25 X =.1 E X =.01 E X =.001 E X =.00001 E