Radiative jet energy loss in a three-dimensional hydrodynamica l medium

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

2. Outline What is medium tomography? (How) does it work in heavy ion collisions? RAA as a tomographic tool 3D hydrodynamics Jet quenching formalism AMY vs. AWS (BDMPS) RAA in central and non-central collisions AMY vs. BDMPS RAA at forward rapidity (AMY) Outlook: RAA at LHC (AMY vs. BDMPS) Conclusions

3. . • “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 allowsreconstruction 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 theoryb) theoretical model of the dynamical medium • Measures modification of specific quantities in comparison to vacuum averaged over many events • Measurements of quantities (like Raa and particle correlations) do notallow at this point a reconstruction of the dynamical medium, but put (more or less stringent) constraints on the theoretical conjectures, especially on a). What is medium tomography and (how) does it work at RHIC?

4. PositronElectronTomographyvs. RHIC Tomography BNL http://teachers.web.cern.ch/teachers/ archiv/HST2002/ttgroup/vazques/pet.jpg STAR

5. Jet tomography in HIC -- RAA • 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 thepartonic energy loss (gain) probabilities(or transition rates) • Dynamical medium evolution model(constrained by plethora of soft observables)

6. Dynamical medium evolution - 3D relativistic fluid dynamics • transport of macroscopic degrees of freedom • based on conservation laws: μTμν=0 μjμ=0 • for ideal fluid: Tμν= (ε+p) uμ uν- p gμν and jiμ = ρi uμ • Equation of State needed to close system of PDE’s: p=p(T,ρi) • 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. 0=0.6 fm/c max=55 GeV/fm3, nBmax=0.15 fm-3 0=0.5 =1.5 EOS (entropy density) =0 3D Hydro parameters • Initial Conditions: • Energy Density: • Baryon Number Density: • Parameters: • Initial Flow: vL=Bjorken’s solution); vT=0 • Equation of State: • Bag Model + excluded volume • 1st order phase transition (to be replaced by Lattice EoS) • Bass & Nonaka, Phys. Rev. C75:014902, 2007 transverse profile: longitudinal profile:

8. Hydro description of soft physics Bass & Nonaka, Phys. Rev. C75:014902, 2007

9. ArnoldMooreYaffee to ArmestoSalgado Wiedemann • ASW: path integral in opacity • E>> m~ 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 • AMY: finite temperature field theory • E>> m Q • Hot thermal medium of quarks and gluons at high T • Hard parton comes in on-shell • Multiple soft hits from particles: m~gT • Long formation time induces multiple scattering • Resummation of infinite series of ladderdiagrams to inver rates of change of quark and gluon distributions • Does include radiation and absorbtion,rates are also parent parton energy dependent Im 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). 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). Comparison inspired by A. Majumders’ QM 2006 talk

10. is local, to use oneto characterize quenching does not make much sense Differences in implementation AMY: transition rates ASW (in BDMPS limit): energy loss prob. Depends on trajectory +Fragmentation Approximation analgous to r.h.s can be achievedassuming that transition rate is parent parton energy indepent, see Turbide et al. Phys. Rev. C 72, 014906

11. Theoretical reference in the vacuum: (neutral) pions at pp Central/mid-rapidity Central/Forward rapidity pp data -- theory in pp Qin, Ruppert, Turbide, Gale, Nonaka, Bass, arXiv:0705.2575

12. Discriminative power of Raa?(at mid-rapidity + central collisions) BDMPS different evolutions AMY/BDMPS • 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. Renk, Ruppert, Nonaka, Bass, Phys.Rev.C75:031902,2007 Qin, Ruppert, Turbide, Gale, Nonaka, Bass, arXiv:0705.2575 Discriminative power of Raa measurement in central collisions at mid-rapidity between diff. theory-models seems rather low (fixes essentially 1 parameter).

13. Discriminative power of Raa(at mid-rapidity + central collisions)(2) Schematic study: “Trial” energy loss probabilities Calculated Raa in comparison to data T. Renk, Talk Hard Probes 2006, Renk, hep-ph/0608333 Renk, arXiv:0704.3879 Renk, Eskola, arXiv:0706.4380

14. “Varying” the medium’s dynamics at RHIC: Raa vs. reaction plane in non-central collisions Central AMY - BDMPS Non-central, in- vers. out plane AMY - BDMPS

15. Ratio Raa in- vs. out of plane AMY - BDMPS

16. Neutral pion Raa as function of azimuth AMY - BDMPS

17. Jet quenching at next-to leading twist (Majumder, Nonaka, Bass, nucl-th/0703019)

18. “Varying” the jets’ kinematics:Raa at finite rapidity (in AMY) b=2.4 fm Quark+Antiquark distributionb=2.4 fm E=pT cosh y b=7.5 fm Qin, Ruppert, Turbide, Gale, Nonaka, Bass, arXiv:0705.2575

19. 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. Outlook: RAA at LHC(central collisions at mid-rapidity) AMY, LHC prediction, Charged hadron RAA BDMPS, LHC prediction, Charged hadron RAA Renk, Eskola, arXiv:0706.4380 Qin, Ruppert, Turbide, Gale, Jeon, arXiv:0705.4468 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.

21. 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. Raa 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 tomographicconstraints: Study Raa as a function of the reaction plane and at forward rapidites! Study Raa 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 !