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

J. Ruppert Early Time Dynamics in Heavy Ion Collisions, ETD-HIC, Montreal, 2007

Radiative jet energy loss in a three-dimensional

hydrodynamical mediumJörg 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


Outline

1. What is medium tomography? (How) does it work in heavy ion collisions?

2. RAA as a tomographic tool

3. 3D hydrodynamics 4. Jet quenching formalism AMY vs. AWS

(BDMPS)5. RAA in central and non-central collisions

AMY vs. BDMPS6. RAA at forward rapidity (AMY)

7. Outlook: RAA at LHC (AMY vs. BDMPS)

8. Conclusions


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 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 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).


PositronElectronTomography vs. RHIC Tomography

http://teachers.web.cern.ch/teachers/archiv/HST2002/ttgroup/vazques/pet.jpg

BNL

STAR


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 the

partonic energy loss (gain) probabilities (or transition rates)

• Dynamical medium evolution model (constrained by plethora of soft observables)


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


3D Hydro parameters

max( , , ) ( , ; ) ( )x y W x y b Hεε η η=

max( , , ) ( , ; ) ( )BBn x y W x y bn Hη η=

EOS (entropy density)

=0

€

B1

4 = 233 [MeV]

η0=0.5 η=1.5

εmax=55 GeV/fm3, nBmax=0.15 fm-3

0=0.6 fm/c

longitudinal profile:longitudinal profile: transverse profile:transverse profile:Initial Conditions:• Energy Density:

• Baryon Number Density:

Parameters:

• Initial Flow: vL=η 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


Hydro description of soft physics

Bass & Nonaka, Phys. Rev. C75:014902, 2007


Im

Arnold Moore Yaffee to Armesto Salgado Wiedemann

ASW: path integral in opacityE>> 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 theoryE>> 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 ladderdiagrams 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).


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 achievedassuming that transition rate is parent parton energy indepent, see Turbide et al. Phys. Rev. C 72, 014906

+Fragmentation


Theoretical reference in the vacuum: (neutral) pions at pp

pp data -- theory in pp

Central/mid-rapidity Central/Forward rapidity

Qin, Ruppert, Turbide, Gale, Nonaka, Bass, arXiv:0705.2575


Discriminative power of Raa?(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/BDMPSRenk, Ruppert, Nonaka, Bass, Phys.Rev.C75:031902,2007Qin, Ruppert, Turbide, Gale, Nonaka, Bass, arXiv:0705.2575

BDMPS different evolutions

Discriminative power of Raa measurement incentral collisions at mid-rapidity betweendiff. theory-models seems rather low (fixes essentially 1 parameter).


Discriminative power of Raa

(at mid-rapidity + central collisions) (2)

Schematic study: “Trial” energy lossprobabilities

Calculated Raa in comparisonto data T. Renk, Talk Hard Probes 2006,

Renk, hep-ph/0608333Renk, arXiv:0704.3879Renk, Eskola, arXiv:0706.4380


“Varying” the medium’s dynamics at RHIC: Raa vs. reaction plane in non-central

collisions

CentralAMY - BDMPS

Non-central, in- vers. out planeAMY - BDMPS


Ratio Raa in- vs. out of plane

AMY - BDMPS


Neutral pion Raa as function of azimuth

AMY - BDMPS


Jet quenching at next-to leading twist

(Majumder, Nonaka, Bass, nucl-th/0703019)


“Varying” the jets’ kinematics:Raa at finite rapidity (in AMY)

Quark+Antiquark distributionb=2.4 fmE=pT cosh y

b=2.4 fm

b=7.5 fm



An example for a tomographic question in HIC jet quenching!

Boost-invariant (Bjorken) vs. fully 3D expansion. Which is realized?

b=7.5 fm


However, N. B.: questions regarding jet-medium interaction and evolution model can only be disentangled IF one is assumedto be known (!).


Outlook: RAA at LHC(central collisions at mid-rapidity)

AMY, LHC prediction, Charged hadron RAA

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 RAA

Renk, Eskola, arXiv:0706.4380


ConclusionsJet 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’sproperties.

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 newpossibilities 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 measurementsand theoretical calculations suitable for direct comparison with the experiment (realisticimplementation of jet-medium interaction and medium description)are essential! Thanks to all my collaborators !

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

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