Investigation of jet quenching and elliptic flow within a pqcd-based partonic transport model Oliver Fochler Z. Xu C. Greiner Institut für Theoretische Physik Goethe Universität Frankfurt Strongly Interacting Matter under Extreme Conditions Hirschegg 17 January 2010-22 January 2010 O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 1 / 26
Introduction Heavy ion collisions are complicated! Need models and theories for Initial state Medium evolution High-p T physics Phase transition Freeze-out Some tools: Parameterizations (e.g. Bjorken) Hydrodynamics Transport models Lattice QCD pqcd (BDMPS, ASW, AMY,...) Problem No model can describe all (most) aspects of the medium evolution. O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 2 / 26
Introduction a Key observables Jet quenching, R AA (high-p t physics) a HP 2008, C. Vale Elliptic flow, v 2 (bulk physics) Difficult to describe within one model (Partonic) Transport with only 2 2 processes: Need unphysical cross sections for v 2. ( R AA too small) BAMPS results 2 3 processes + pqcd cross sections enough elliptic flow What about R AA? O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 3 / 26
Outline 1 The Model - BAMPS 2 Static Medium - Brick Scenario 3 Central and Non-Central Au+Au Collisions 4 Sensitivity on the LPM Cut-Off O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 4 / 26
Partonic Transport Model - BAMPS BAMPS = Boltzmann Approach to Multiple Particle Scattering 1 Microscopic transport simulations with full dynamics. Attack various problems within one model. (elliptic flow, R AA, thermalization,...) Solve Boltzmann equation for 2 2 and 2 3 processes based on LO pqcd matrix elements. p µ µ f (x, p) = C 2 2 (x, p) + C 2 3 (x, p) 1 Z. Xu, C. Greiner, Phys. Rev. C71 (2005) O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 5 / 26
Partonic Transport Model - BAMPS Implemented processes gg gg and gg ggg Massless Boltzmann particles Sample transition probabilities for (test)particles in a given Spatial cell, V Time step, t Use small angle cross section for gg gg and Gunion-Bertsch matrix element for gg ggg dσ gg gg dq 2 9πα 2 s (q 2 + m2 D )2 Mgg ggg 2 = 72π2 α 2 ss 2 (q 2 + m2 D )2 48πα sq 2 k 2 [(k q ) 2 + m 2 D ] Debye screening: m 2 D = d Gπα s d 3 p (2π) 3 1 p N cf O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 6 / 26
Some Results from BAMPS Recall Jan Uphoff s talk on Wednesday.. Fast thermalization, 1 fm/c Z. Xu, C. Greiner, PRC 71 (2005) Small viscosity, η/s 0.1 0.2 Z. Xu, C. Greiner, H. Stoecker PRL 101 (2008), Z. Xu, C. Greiner PRL 100 (2008) Investigate heavy quark production and dynamics in preparation Can serve as reference for viscous hydro I. Bouras et al. PRL 103 (2009) Investigate hydrodynamic shocks / Mach cones I. Bouras et al. PRL 103 (2009) / in preparation O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 7 / 26
Landau-Pomeranchuk-Migdal (LPM) Effect LPM effect Multiple emission Interference Not realizable in transport model with classical particles. Discard possible interference effects (Bethe-Heitler regime) Parent must not scatter during formation time of emitted gluon. M gg ggg 2 M gg ggg 2 Θ (λ τ) Affects: Total cross section σ gg ggg dq 2 dk 2 dy dφ M gg ggg 2 Θ (λ τ) Sampling of outgoing momenta O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 8 / 26
Landau-Pomeranchuk-Migdal (LPM) Effect LPM effect Multiple emission Interference Not realizable in transport model with classical particles. Discard possible interference effects (Bethe-Heitler regime) Parent must not scatter during formation time of emitted gluon. M gg ggg 2 M gg ggg 2 Θ (λ τ) Affects: Total cross section σ gg ggg dq 2 dk 2 dy dφ M gg ggg 2 Θ (λ τ) Sampling of outgoing momenta O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 8 / 26
Reference Frames for the LPM Cut-Off lab frame λ = 1/R = 1/ nσ O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 9 / 26
Reference Frames for the LPM Cut-Off lab frame λ = 1/R = 1/ nσ CM frame O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 9 / 26
Reference Frames for the LPM Cut-Off lab frame λ = 1/R = 1/ nσ CM frame τ = 1/k β = tanh y γ = cosh y Total boost: γ = γ γ ( 1 + β β ) = cosh y 1 β 2 (1 + β tanh y cos θ) ( Θ (λ τ) Θ k γ ) Θ λ ( k 1 λ ) Θ (B (cosh y + A sinh y)) A = β cos θ, B = k Λ g p 1 β 2 Integral cuts: σ gg ggg dq 2 s/4 dk 2 ymax 1/λ 2 y min dy dφ ( ) β 1 (thermal particles): Θ (λ τ) Θ k cosh y λ O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 9 / 26
Reference Frames for the LPM Cut-Off lab frame λ = 1/R = 1/ nσ CM frame τ = 1/k β = tanh y γ = cosh y Total boost: γ = γ γ ( 1 + β β ) = cosh y 1 β 2 (1 + β tanh y cos θ) ( Θ (λ τ) Θ k γ ) Θ λ ( k 1 λ ) Θ (B (cosh y + A sinh y)) A = β cos θ, B = k Λ g p 1 β 2 Integral cuts: σ gg ggg dq 2 s/4 dk 2 ymax 1/λ 2 y min dy dφ ( ) β 1 (thermal particles): Θ (λ τ) Θ k cosh y λ O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 9 / 26
v 2 and R AA for Central Collisions Integrated v 2 as function of N part Gluonic R AA for b = 0 fm OF, Z. Xu, C. Greiner, PRL 102 (2009) We ll come back to this later.. O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 10 / 26
Energy Loss in a Static Medium Brick Constant temperature T Only gluons, N f = 0 Static medium, no expansion α s = 0.3 m 2 D = 8 π N cα s T 2 T = 400 MeV O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 11 / 26
Energy Loss in Binary Collisions Elastic de/dx for different T E-spectrum (T = 400 MeV, E 0 = 50 GeV) Elastic energy loss ( ) de dx 2 2 C R παst 2 2 ln 4ET md 2 Broad distribution Not: Mean energy loss + momentum diffusion (Gaussian) O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 12 / 26
Energy Loss in gg ggg Processes Total de/dx for different T E-spectrum (T = 400 MeV, E 0 = 50 GeV) Large differential energy loss due to gg ggg Roughly de/dx E Rapid evolution of the energy spectrum O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 13 / 26
Energy Loss in gg ggg Processes Cross sections (T = 400 MeV) Reasonable partonic cross sections over the whole energy range. Definition of the energy loss E matters: E = E in max(e i out ) E = ω O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 14 / 26
Energy Loss in gg ggg Processes Cross sections (T = 400 MeV) Energy loss in single gg ggg Reasonable partonic cross sections over the whole energy range. Definition of the energy loss E matters: E = E in max(e i out ) E = ω O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 14 / 26
Gluon Radiation from the Gunion-Bertsch Matrix Element Energy spectrum Angular distribution Emission at small angles not allowed due to LPM cut-off Θ ( k γ ) λ Effect more pronounced for small gluon energies. O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 15 / 26
Accumulated Transverse Momenta p 2 /λ ˆq (t) (E 0 = 50 GeV) ˆq: Transverse momentum accumulated over path length L. ˆq (L) = 1 ( ) L i p 2 ˆq (t) = 1 t p 2 t 0 λ d t E( t) i We extend investigation to 2 3 processes. O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 16 / 26
Setup for Au+Au Collisions in BAMPS Au+Au at RHIC energy 200 AGeV Currently limited to gluons α s = 0.3 Mini-Jet initial conditions (lower cut-off p 0 = 1.4 GeV) Glück-Reya-Vogt PDFs Wood-Saxon density profile + Glauber model Formation time for each parton t f = cosh(y)/p T Free streaming applied to cells where ε < ε c (choices: ε c = 0.6 GeV/fm 3 or ε c = 1 GeV/fm 3 ) O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 17 / 26
v 2 and R AA for Central Collisions Integrated v 2 as function of N part Gluonic R AA for b = 0 fm Elliptic flow generated in BAMPS compatible with experiment. Suppression of gluon jets slightly stronger than found by Wicks et al. (Nucl.Phys.A784). OF, Z. Xu, C. Greiner, PRL 102 (2009) O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 18 / 26
Non-Central R AA and High-p T Elliptic Flow Differential v 2 for b = 7 fm Gluon R AA for b = 0 and b = 7 fm O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 19 / 26
R AA and v 2 from Elastic Collisions with Fixed σ Gluon R AA for fixed σ = 10 mb Time evolution of v 2 Elastic collisions can t get R AA and v 2 right simultaneously For binary σ = 10 mb: R AA too strong, v 2 still too weak OF, Z. Xu, C. Greiner, PRL 102, 202301 (2009) O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 20 / 26
Sensitivity on the LPM Cut-Off Parameters in BAMPS Coupling strength α s Critical freeze-out energy density ε c LPM cut-off The effective implementation of the LPM cut-off requires Λ g > τ. Only qualitative argument, introduce factor X to test sensitivity. ) ) Θ (k γλg Θ (k X γλg O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 21 / 26
Sensitivity on the LPM Cut-Off σ gg ggg for different X (T = 400 MeV) de/dx for different X (T = 400 MeV) σ gg ggg dq 2 ) dk 2 y Θ (k X γ Λ g Large X reduces total cross section Sampling of outgoing particles affected in non-trivial way Energy loss per collision only slightly affected, main contribution to the change in energy loss from change in σ. O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 22 / 26
Sensitivity on the LPM Cut-Off R AA for different X (b = 7 fm) v 2 for different X (b = 7 fm) O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 23 / 26
Summary Partonic transport based on pqcd including 2 3 processes provides means of investigating medium and high-p T physics within a common framework. Integrated gluon v 2 ok, gluon R AA slightly below analytic reference More quantitative and detailed studies needed More accurate identification b centrality class needed Need to include light quarks Need fragmentation (hadronization) scheme Need to investigate more (differential) observables O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 24 / 26
Thank you! O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 25 / 26
Sensitivity on the LPM Cut-Off σ gg ggg for different X (T = 400 MeV) E gg ggg for different X (T = 400 MeV) O. Fochler Jets and v 2 in Partonic Transport Hirschegg, January 2010 26 / 26