1. 12/16/08 William Horowitz TECHQM 2 nd Workshop, LBNL 1 DGLV : M. Djordjevic and M. Gyulassy, Nucl.Phys.A733, 265 (2004) [nucl-th/0310076] WHDG : S. Wicks, W. Horowitz, M. Djordjevic, and M. Gyulassy, Nucl.Phys.A784, 426 (2007) [arXiv:nucl-th/0512076] WHDG@TECHQM : https://wiki.bnl.gov/TECHQM/index.php/WHDG WHDG @ TECHQM William Horowitz The Ohio State University Columbia University December 16, 2008 With many thanks to Ulrich Heinz, Abhijit Mujumder, Guangyou Qin, Simon Wicks, Magdalena Djordjevic and Miklos Gyulassy

2. 12/16/08 William Horowitz TECHQM 2 nd Workshop, LBNL 2 WHDG Overview Convolved rad+elastic: –Radiative energy loss dN g /dx kernel: no support as x , 1 Poisson convolution => P rad  ) –Any Poisson conv. leads to P(e > 1) > 0 –Collisional energy loss B-T mean loss (for light quarks) P el (  ): Gaussian, width from F-D thm

3. 12/16/08 William Horowitz TECHQM 2 nd Workshop, LBNL 3 Radiative Notation WHDG rad: First Order in Opacity Diagrams –Gluon momentum k –Exchange momentum q

4. 12/16/08 William Horowitz TECHQM 2 nd Workshop, LBNL 4 dN g /dx Kernel –Use DGLV see also Appendix B of WHDG –NB: x << 1 assumed, 1 – x  1, etc. here –Kinematics: 0 < k T < k max 0 < q T < q max M. Djordjevic and M. Gyulassy, Nucl.Phys.A733, 265 (2004) [nucl-th/0310076]

5. 12/16/08 William Horowitz TECHQM 2 nd Workshop, LBNL 5 dN g /dx Kinematics k max –Assume eikonality: k + >> k - and p + >> p - => k max ~ 2 E  Min(x,1-x) Equivalent to keeping virtuality finite GLV:  4E 2 Min[x 2,(1-x) 2 ] –  2 ); PLB538, 282 (2002) WHDG: 2 x (1-x) E q max WHDG:  3  E Really:  ET Let’s artificially vary this by factor of 2

6. 12/16/08 William Horowitz TECHQM 2 nd Workshop, LBNL 6 Kinematics Plots: dN g /dx k max –Note that dN g /dx  naturally as x  0, 1 –Dependence on kinematics is small k phase space 50% larger for second (dashed) case especially so for q max (100% larger) q max

7. 12/16/08 William Horowitz TECHQM 2 nd Workshop, LBNL 7 Kinematics Plots: P(  ) –k max –Differences further washed out by convolutions –q max

8. 12/16/08 William Horowitz TECHQM 2 nd Workshop, LBNL 8 Poisson Convolution –GLV Multigluons –Always leads to probability leakage: –Neglects correlations of non-Abelian gluons M. Gyulassy, P. Levai and I. Vitev, PLB538, 282 (2002) [nucl-th/0112071]  = dN g /dx P(  > 1)  0

9. 12/16/08 William Horowitz TECHQM 2 nd Workshop, LBNL 9 To Reweigh or Not to Reweigh –Reweigh P n (  ) –For moderate loss, not a large difference –Reweigh P(  )

10. 12/16/08 William Horowitz TECHQM 2 nd Workshop, LBNL 10 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

11. 12/16/08 William Horowitz TECHQM 2 nd Workshop, LBNL 11 Running  s ? –  s =.2,.3 – Not surprisingly, changes in  s make huge difference to P(  ) –  s =.3,.4

12. 12/16/08 William Horowitz TECHQM 2 nd Workshop, LBNL 12 WHDG thru KKP –Facilitate comparison between WHDG and HT –Elastic gain => D(z > 1) > 0

13. 12/16/08 William Horowitz TECHQM 2 nd Workshop, LBNL 13 WHDG Pros/Cons Advantages: –Includes finite kinematics E, p conserved at level of dN g /dx –Interference with production radiation –Includes elastic loss Disadvantages: –Static scattering centers –Simplistic rad Poisson conv. –Simplistic el Gaussian –Fixed  s See Djordjevic and Heinz, PRC77:024905 (2008); PRL101:022302 (2008)

14. 12/16/08 William Horowitz TECHQM 2 nd Workshop, LBNL 14 Conclusions Within WHDG: –rad kinematics under control –rad Poisson approx. seems OK –Pressing issues: Effect of running  s not yet explored (should be much easier to address in brick problem) –Weak coupling comp. under control? –Hope for quantitative understanding of QGP? Elastic loss, dynamic medium Ease of comparison: –Results fragmented through KKP –Temperature scans; standard output

15. 12/16/08 William Horowitz TECHQM 2 nd Workshop, LBNL 15 Backup Slides

16. 12/16/08 William Horowitz TECHQM 2 nd Workshop, LBNL 16 WHDG T and L Dependence –Decreasing T, L decreases loss

17. 12/16/08 William Horowitz TECHQM 2 nd Workshop, LBNL 17 q max Detail Inconsequential difference

18. 12/16/08 William Horowitz TECHQM 2 nd Workshop, LBNL 18 WHDG thru KKP

19. 12/16/08 William Horowitz TECHQM 2 nd Workshop, LBNL 19 WHDG thru KKP

20. 12/16/08 William Horowitz TECHQM 2 nd Workshop, LBNL 20 WHDG T and L Dependence Decreasing T, L decreases loss

21. 12/16/08 William Horowitz TECHQM 2 nd Workshop, LBNL 21 Error from QFT Ward Violation Identical expressions are not a surprise QFT Calculation –Gluon momentum carried away crucial for cancellation of gluon mass Classical case neglects both; effects cancel

22. 12/16/08 William Horowitz TECHQM 2 nd Workshop, LBNL 22 Resulting Expression –To lowest order in 1/E + –New: (1-x) 2 prefactor: naturally kills hard gluons m g 2 in numerator: fills in the dead cone!?! –What are the sizes of these effects?