12/16/08 William Horowitz TECHQM 2 nd Workshop, LBNL 1 DGLV : M. Djordjevic and M. Gyulassy, Nucl.Phys.A733, 265 (2004) [nucl-th/ ] WHDG : S. Wicks, W. Horowitz, M. Djordjevic, and M. Gyulassy, Nucl.Phys.A784, 426 (2007) [arXiv:nucl-th/ ] : 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

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

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

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/ ]

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

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

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

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/ ]  = dN g /dx P(  > 1)  0

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(  )

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

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

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

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: (2008); PRL101: (2008)

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

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

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

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

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

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

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

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

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?