Radiative jet energy loss in a threedimensional hydrodynamica

Radiative jet energy loss in a three-dimensional hydrodynamica� l medium Jörg Ruppert Nuclear Theory, Department of Physics, Mc. Gill University, Montreal, Quebec, Canada In collaboration with: Steffen Bass, Charles Gale, Sangyong Jeon, Chiho Nonaka, Thorsten Renk, Simon Turbide, Guangyou Qin 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. RAA as a tomographic tool 3. 3 D hydrodynamics 4. Jet quenching formalism AMY vs. AWS (BDMPS) 5. RAA in central and non-central collisions AMY vs. BDMPS 6. RAA at forward rapidity (AMY) 7. Outlook: RAA at LHC (AMY vs. BDMPS) 8. Conclusions 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 Raa and particle correlations) do not allow at this point a reconstruction of the dynamical medium, but put (more or less stringent) constraints on theoretical conjectures, especially on a). J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007

Positron. Electron. Tomography vs. RHIC Tomography BNL http: //teachers. web. cern. ch/teachers/ archiv/HST 2002/ttgroup/vazques/pet. jpg J. Ruppert STAR Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007

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): • • Theoretical description of (can be studied in p-A) the partonic energy loss (gain) probabilities (or transition rates) • Dynamical medium evolution model (constrained by plethora of soft observables) J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007

Dynamical medium evolution - 3 D relativistic fluid dynamics • • Ø 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 Eo. S • • initial conditions (i. e. thermalized QGP) required for calculation Hydro assumes local thermal equilibrium, vanishing mean free path This particular implementation: Ø fully 3+1 dimensional, using (τ, x, y, η) coordinates Ø Lagrangian Hydrodynamics Ø coordinates move with entropy-density & baryon-number currents Ø trace adiabatic path of each volume element Bass & Nonaka, Phys. Rev. C 75: 014902, 2007 J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007

3 D Hydro parameters Initial Conditions: • Energy Density: • transverse profile: longitudinal profile: Baryon Number Density: Parameters: 0=0. 6 fm/c max=55 Ge. V/fm 3, n. Bmax=0. 15 fm-3 0=0. 5 =1. 5 • EOS (entropy density) =0 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 Eo. S) Bass & Nonaka, Phys. Rev. C 75: 014902, 2007 J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007

Hydro description of soft physics Bass & Nonaka, Phys. Rev. C 75: 014902, 2007 J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007

Arnold Moore Yaffee to Armesto Salgado Wiedemann 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~g. T • 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 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 Im E. g. Arnold, Moore, Yaffee, JHEP 0111: 056, 2001, ibid 0112: 009, 2001, ibid 0206: 030, 2002, S. Turbide et al. Phys. Rev. C 72: 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 J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007

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 achieved is local, to use one to characterize assuming that transition rate is parent parton energy indepent, see Turbide et al. Phys. Rev. C 72, 014906 quenching does not make much sense Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, J. Ruppert Montreal, 2007

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, ar. Xiv: 0705. 2575 J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007

Discriminative power of Raa? (at mid-rapidity + central collisions) AMY/BDMPS different evolutions Caveats/assumptions: Renk, Ruppert, Nonaka, Bass, Phys. Rev. C 75: 031902, 2007 • Possible collisional energy loss not (yet) Qin, Ruppert, Turbide, Gale, Nonaka, Bass, ar. Xiv: 0705. 2575 included. • Possible pre-equilibrium energy loss not Discriminative power of Raa measurement in (yet) included. • Multiple soft scattering approx. and/or finite central collisions at mid-rapidity between temperature field theory in weak coupling diff. theory-models seems rather low (fixes approx. works at RHIC. essentially 1 parameter). J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007

Discriminative power of Raa (at mid-rapidity + central collisions) Schematic study: “Trial” energy loss probabilities (2) Calculated Raa in comparison to data T. Renk, Talk Hard Probes 2006, Renk, hep-ph/0608333 Renk, ar. Xiv: 0704. 3879 Renk, Eskola, ar. Xiv: 0706. 4380 J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007

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

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

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

“Varying” the jets’ kinematics: Raa at finite rapidity (in AMY) b=2. 4 fm Quark+Antiquark distribution b=2. 4 fm E=p. T cosh y b=7. 5 fm Qin, Ruppert, Turbide, Gale, Nonaka, Bass, ar. Xiv: 0705. 2575 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 3 D expansion. Which is realized? b=7. 5 fm Qin, Ruppert, Turbide, Gale, Nonaka, Bass, ar. Xiv: 0705. 2575 However, N. B. : questions regarding jet-medium interaction and evolution model can only be disentangled IF one is assumed to be known (!). J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007

Outlook: RAA at LHC (central collisions at mid-rapidity) AMY, LHC prediction, Charged hadron RAA Qin, Ruppert, Turbide, Gale, Jeon, ar. Xiv: 0705. 4468 BDMPS, LHC prediction, Charged hadron RAA Renk, Eskola, ar. Xiv: 0706. 4380 Thanks to K. J. Eskola, H. Honkanen, H. Niemi, P. V. Ruuskanen, S. S. Rasanen for providing their 2 D hydro medium calculation, Nucl. Phys. A 774: 805 -808, 2006. 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. 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 tomographic constraints: 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 ! J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007