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Andrej Ficnar Columbia University

High order DGLV Monte Carlo and q models of jet quenching. ^. Andrej Ficnar Columbia University. INT 10-2A June 25, 2010. DGLV approach. Opacity expansion of radiative energy loss including finite masses of quarks and gluons ( ).

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Andrej Ficnar Columbia University

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

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

  3. Monte Carlo computation Buzzatti, Ficnar, Gyulassy, Wicks, to be published • 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 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 Baier, Dokshitzer, Mueller, Peigne, Schiff, Nucl.Phys.B483:291,1997 • Multiple soft scattering approximation ( ): Moliere-like Gaussian diffusion in transverse momentum space • main approximation: • Start from the path integral formulation: Zakharov, JETP Lett. 70 (1999) 176-182 Wiedemann, Nucl.Phys. B588 (2000) 303-344 dipole approximation  MSS 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: BDMPS Arnold, Phys.Rev.D79:065025,2009 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  scaling broken by up to 100%  x-dependence in upper bound in kt makes difference Arnold’s opacity expansion z<1 domain is not relevant for LHC (at least for L>1) INT 10-2A, June 25, 2010 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 slow convergence of opacity series (small formation time) INT 10-2A, June 25, 2010 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 ASW < 0 INT 10-2A, June 25, 2010 11/13

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

  22. DGLV & ASW 2 dead cone effect thin plasma (n=1) finite opacity n=5 interpolates between thin and thick thick plasma (n=∞) 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

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