1. J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007 Radiative jet energy loss in a three-dimensional hydrodynamical medium Jörg Ruppert Nuclear Theory, Department of Physics, McGill University, Montreal, Quebec, Canada In collaboration with: Steffen Bass, Charles Gale, Sangyong Jeon, Chiho Nonaka, Thorsten Renk, Simon Turbide, Guangyou Qin

2. J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007 Outline 1.What is medium tomography? (How) does it work in heavy ion collisions? 2.R AA as a tomographic tool 3.3D hydrodynamics 4.Jet quenching formalism AMY vs. AWS (BDMPS) 5.R AA in central and non-central collisions AMY vs. BDMPS 6.R AA at forward rapidity (AMY) 7.Outlook: R AA at LHC (AMY vs. BDMPS) 8.Conclusions

3. J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007 What is medium tomography and (how) does it work at RHIC?. “Usual” tomography: Uses known and adjustable source Let probe (particles or EM radiation) propagate through the (static) medium (assuming full knowledge of probe-medium interactions (!)) Measures the modification of the probe (in comparison to vacuum expectation) Information allows reconstruction of the density of the (static) medium RHIC “tomography”: Hard probes: partonic jets (created in the collision, calculable but not adjustable) Probe - medium interaction to be inferred from a) jet-quenching theory b) theoretical model of the dynamical medium Measures modification of specific quantities in comparison to vacuum averaged over many events Measurements of quantities (like R aa and particle correlations) do not allow at this point a reconstruction of the dynamical medium, but put (more or less stringent) constraints on the theoretical conjectures, especially on a).

4. J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007 P ositron E lectron T omography vs. RHIC Tomography http://teachers.web.cern.ch/teachers/ archiv/HST2002/ttgroup/vazques/pet.jpg BNL STAR

5. J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007 Jet tomography in HIC -- R AA Reference: Calculable process in vacuum: Jet fragmentation in pp Infer medium properties from the changes Necessary in-medium knowledge (to be tested by the measurement): (can be studied in p-A) Theoretical description of the partonic energy loss (gain) probabilities (or transition rates) Dynamical medium evolution model (constrained by plethora of soft observables)

6. J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007 Dynamical medium evolution - 3D relativistic fluid dynamics transport of macroscopic degrees of freedom based on conservation laws:  μ T μν =0  μ j μ =0 for ideal fluid: T μν = (ε+p) u μ u ν - p g μν and j i μ = ρ i u μ Equation of State needed to close system of PDE’s: p=p(T,ρ i )  connection to Lattice QCD calculation of EoS initial conditions (i.e. thermalized QGP) required for calculation Hydro assumes local thermal equilibrium, vanishing mean free path This particular implementation:  fully 3+1 dimensional, using (τ,x,y,η) coordinates  Lagrangian Hydrodynamics  coordinates move with entropy-density & baryon-number currents  trace adiabatic path of each volume element Bass & Nonaka, Phys. Rev. C75:014902, 2007

7. J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007 3D Hydro parameters EOS (entropy density)  =0  0 =0.5   =1.5  max =55 GeV/fm 3, n Bmax =0.15 fm -3  0 =0.6 fm/c longitudinal profile: transverse profile: Initial Conditions: Energy Density: Baryon Number Density: Parameters: Initial Flow: v L =  Bjorken’s solution); v T =0 Equation of State: Bag Model + excluded volume 1 st order phase transition (to be replaced by Lattice EoS) Bass & Nonaka, Phys. Rev. C75:014902, 2007

8. J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007 Hydro description of soft physics Bass & Nonaka, Phys. Rev. C75:014902, 2007

9. J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007 Im A rnold M oore Y affee to A rmesto S algado W iedemann ASW: path integral in opacity E>>  Q Medium of heavy scattering centers with Yukawa potentials Parton picks up per. momentum from medium Focus in the following on limit in many soft scattering approximation (BDMPS) Does only include radiation (no absorption) Assumes asymptotically high parent parton energy Comparison inspired by A. Majumders’ QM 2006 talk E.g. C. Salgado, U. Wiedemann, Phys.Rev. D. 68 014008 (2003); K. Eskola et al. Nucl. Phys. A.747, 511(2005); N. Armesto, C. Salgado, U. Wiedemann, Phys.Rev.D.72,064910 (2005). AMY: finite temperature field theory E>>  Q Hot thermal medium of quarks and gluons at high T Hard parton comes in on-shell Multiple soft hits from particles:  ~gT Long formation time induces multiple scattering Resummation of infinite series of ladder diagrams to inver rates of change of quark and gluon distributions Does include radiation and absorbtion, rates are also parent parton energy dependent E.g. Arnold, Moore, Yaffee, JHEP 0111:056, 2001, ibid 0112:009,2001, ibid 0206:030,2002, S. Turbide et al. Phys. Rev. C72:0140906 (2005).

10. J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007 is local, to use one to characterize quenching does not make much sense Differences in implementation AMY: transition rates ASW (in BDMPS limit): energy loss prob. Depends on trajectory Approximation analgous to r.h.s can be achieved assuming that transition rate is parent parton energy indepent, see Turbide et al. Phys. Rev. C 72, 014906 +Fragmentation

11. J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007 Theoretical reference in the vacuum: (neutral) pions at pp pp data -- theory in pp Central/mid-rapidityCentral/Forward rapidity Qin, Ruppert, Turbide, Gale, Nonaka, Bass, arXiv:0705.2575

12. J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007 Discriminative power of R aa ? (at mid-rapidity + central collisions) Caveats/assumptions: Possible collisional energy loss not (yet) included. Possible pre-equilibrium energy loss not (yet) included. Multiple soft scattering approx. and/or finite temperature field theory in weak coupling approx. works at RHIC. AMY/BDMPS Renk, Ruppert, Nonaka, Bass, Phys.Rev.C75:031902,2007 Qin, Ruppert, Turbide, Gale, Nonaka, Bass, arXiv:0705.2575 BDMPS different evolutions Discriminative power of R aa measurement in central collisions at mid-rapidity between diff. theory-models seems rather low (fixes essentially 1 parameter).

13. J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007 Discriminative power of R aa (at mid-rapidity + central collisions) (2) Schematic study: “Trial” energy loss probabilities Calculated R aa in comparison to data T. Renk, Talk Hard Probes 2006, Renk, hep-ph/0608333 Renk, arXiv:0704.3879 Renk, Eskola, arXiv:0706.4380

14. J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007 “Varying” the medium’s dynamics at RHIC: R aa vs. reaction plane in non-central collisions Central AMY - BDMPS Non-central, in- vers. out plane AMY - BDMPS

15. J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007 Ratio R aa in- vs. out of plane AMY - BDMPS

16. J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007 Neutral pion R aa as function of azimuth AMY - BDMPS

17. J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007 Jet quenching at next-to leading twist (Majumder, Nonaka, Bass, nucl-th/0703019)

18. J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007 “Varying” the jets’ kinematics: R aa at finite rapidity (in AMY) Quark+Antiquark distribution b=2.4 fm E=p T cosh y b=2.4 fm b=7.5 fm Qin, Ruppert, Turbide, Gale, Nonaka, Bass, arXiv:0705.2575

19. J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007 An example for a tomographic question in HIC jet quenching! Boost-invariant (Bjorken) vs. fully 3D expansion. Which is realized? b=7.5 fm Qin, Ruppert, Turbide, Gale, Nonaka, Bass, arXiv:0705.2575  However, N. B.: questions regarding jet-medium interaction and evolution model can only be disentangled IF one is assumed to be known (!).

20. J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007 Outlook: R AA at LHC (central collisions at mid-rapidity) AMY, LHC prediction, Charged hadron R AA Thanks to K.J. Eskola, H. Honkanen, H. Niemi, P.V. Ruuskanen, S.S. Rasanen for providing their 2D hydro medium calculation, Nucl.Phys.A774:805-808,2006. Qin, Ruppert, Turbide, Gale, Jeon, arXiv:0705.4468 BDMPS, LHC prediction, Charged hadron R AA Renk, Eskola, arXiv:0706.4380

21. J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007 Conclusions Jet tomography at RHIC is different from usual tomography: It’s a test of our theoretical understanding of jet - medium interaction and of the medium evolution (!) rather than a full “reconstruction” of the medium’s properties. Differential information is needed to discriminate theoretical models. R aa for central collisions and at mid-rapidity alone is not enough! Use all available other information on hard and soft-probes to constrain theoretical model as far as possible, especially there are new possibilities to get further tomographic constraints: Study R aa as a function of the reaction plane and at forward rapidites! Study R aa at higher energies (RHIC => LHC)! Study Di-Hadron correlations (Talk T. Renk, Friday)! Study hard-soft near-away side correlations (Mach cones)! The era of jet tomography has just begun. Differential experimental measurements and theoretical calculations suitable for direct comparison with the experiment (realistic implementation of jet-medium interaction and medium description) are essential!Thanks to all my collaborators !