1. Andrej Ficnar Columbia University INT 10-2A June 25, 2010 High order DGLV Monte Carlo and q models of jet quenching ^

2. DGLV approach color-screened Yukawa potential (GW model) inverse formation time cascade amplitudes () Gyulassy, Levai, Vitev, Nucl.Phys.B594:371-419,2001 Djordjevic, Gyulassy, Nucl.Phys.A733:265-298,2004 Opacity expansion of radiative energy loss including finite masses of quarks and gluons ( ) INT 10-2A, June 25, 2010 2/13

3. Monte Carlo computation In essence: input:,,,,,,, opacity order, number of sampling points & range of output: inclusive gluon distribution and statistical error for each For each order, do the importance sampling Monte Carlo of: according to uniformly according to Flexible: easy implementation of different potentials or different distributions of scattering centers (e.g. dynamical potential) computations Buzzatti, Ficnar, Gyulassy, Wicks, to be published INT 10-2A, June 25, 2010 3/13

4. Monte Carlo computation Having in mind (for RHIC) and Poissonian distribution, it is enough to go to Time per per is roughly seconds Current Fortran code tested up to 1+... + 9 order (S. Wick's thesis C-code) Motivation: building a Monte Carlo bridge between thin ( ) and thick ( ) plasma approximation INT 10-2A, June 25, 2010 4/13

5. BDMPS Multiple soft scattering approximation ( ): Moliere-like Gaussian diffusion in transverse momentum space main approximation: Start from the path integral formulation: Baier, Dokshitzer, Mueller, Peigne, Schiff, Nucl.Phys.B483:291,1997 dipole approximation  MSS Zakharov, JETP Lett. 70 (1999) 176-182 Wiedemann, Nucl.Phys. B588 (2000) 303-344 Zakharov, JETP Lett. 63 (1996) 952-957 INT 10-2A, June 25, 2010 5/13

6. BDMPS transport coefficient characterizes medium’s rescattering properties: it gives transverse momentum squared per unit path length transferred to the parton only this parametric function of time controls both the and distributions of radiated glue ASW studied this distribution keeping the finite kinematics ( ) and fitting a large to the data Armesto, Salgado, Wiedemann, Phys.Rev.D69:114003,2004 INT 10-2A, June 25, 2010 6/13

7. BDMPS If kinematics are ignored, the - integrated induced intensity spectrum is predicted to scale with via the variable z: where: and The opacity series in this approximation misses the leading term: Arnold, Phys.Rev.D79:065025,2009 BDMPS INT 10-2A, June 25, 2010 7/13

8. BDMPS By explicit Monte Carlo calculations up to 9th order in opacity we investigate whether the radiated energy loss spectrum scales well with z, i.e. is alone sufficient to describe radiative processes relevant to LHC and RHIC conditions INT 10-2A, June 25, 2010 8/13

9. DGLV & BDMPS z-scaling 1  x-dependence in upper bound in kt makes difference z 1)  scaling broken by up to 100% INT 10-2A, June 25, 2010 Arnold’s opacity expansion 9/13

10. DGLV & BDMPS z-scaling 2  energy loss spectrum at intermediate opacity depends in detail on and INT 10-2A, June 25, 2010 10/13

11. DGLV & ASW 1 INT 10-2A, June 25, 2010 slow convergence of opacity series (small formation time) 11/13

12. DGLV & ASW 1 INT 10-2A, June 25, 2010 11/13

13. DGLV & ASW 1 INT 10-2A, June 25, 2010 11/13

14. DGLV & ASW 1 INT 10-2A, June 25, 2010 11/13

15. DGLV & ASW 1 INT 10-2A, June 25, 2010 11/13

16. DGLV & ASW 1 INT 10-2A, June 25, 2010 11/13

17. DGLV & ASW 1 INT 10-2A, June 25, 2010 11/13

18. DGLV & ASW 1 INT 10-2A, June 25, 2010 11/13

19. DGLV & ASW 1 INT 10-2A, June 25, 2010 11/13

20. DGLV & ASW 1 INT 10-2A, June 25, 2010 ASW < 0 11/13

21. DGLV & ASW 1 INT 10-2A, June 25, 2010 ASW < 0 due to slower convergence  distribution > xE is important 11/13

22. dead cone effect finite opacity n=5 interpolates between thin and thick thin plasma (n=1) thick plasma (n=∞) DGLV & ASW 2 INT 10-2A, June 25, 2010 12/13

23. Summary and Outlook Constructed a new transparent Fortran Code DGLV-BFW Demonstrated a practical bridge between thin and thick plasma approximations We can now compute and study triple differential radiative (jet shape) effects up to (and beyond) 9th order in the opacity BDMPS z-scaling broken by up to 100% kinematic limits are important energy loss spectrum at intermediate opacity depends in detail on and Outlook: Nonhomogenous dynamical QCD medium with gluon number fluctuations (A. Buzzatti’s talk) INT 10-2A, June 25, 2010 13/13