ランジュバン方程式を用いた重いクォークの QGP 流体中での拡散過程赤松幸尚（東京大学）初田哲男、平野哲文（東京大学） RCNP ’07/10/29.

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ランジュバン方程式を用いた重いクォークの QGP 流体中での拡散過程赤松幸尚（東京大学）初田哲男、平野哲文（東京大学） RCNP ’07/10/29

Introduction Purpose : understanding transport property of quark-gluon plasma (QGP) QGP at relativistic heavy ion collisions (RHIC, LHC) Heavy quarks (c,b) as impurities mass ~ 1.5GeV (charm) 4GeV (bottom) Light particles (u,d,s,g) as QGP fluid temperature ~ 200MeV life time ~ 10fm

Heavy quark energy loss Radiation : dominant in γv~1/g Collision : dominant in γv~1 Brownian motion : collision only collision intervalrelaxation time typical timescale of Brownian motion

Flowchart of calculation time Initial condition of heavy quarks …0.6fm …0fm Brownian motion BANG ! Full 3D hydrodynamics T(x), u(x) Heavy quark spectrum PYTHIA (momentum space), # of binary collisions (space) Electron spectrum QGP Independent fragmentation by PYTHIA Experiment c(b)→D(B)→e - +ν e +π Future work _

Relativistic Brownian motion of heavy quarks Γ and D can depend of p Fluctuation-dissipation theorem (Ito discretization) On the rest frame of QGP (which is determined by hydrodynamics) drag force noise

Model for Brownian motion Langevin equation on the local rest frame α: dimensionless parameter T : local temperature (information from hydro simulation) α τ R [fm] (T=0.2GeV) τ R =1/Γ(T) AdS/CFT(3.7)pQCD(0.6) QGP life time(~10fm) drag force noise

Initial conditions of charm quark |Y|<1.0 Initial p T distributionInitial spatial distribution y x Au 5.5 fm ∝ # of binary collisions via PYTHIA Au drag force will soften.

RESULTS of RESULTS of LANGEVIN SIMULATIONS LANGEVIN SIMULATIONS

Charm spectrum Similar results in other centralities Large τ R  small quenching p T distribution R AA (p T ) |Y|<1.0 _initial

Charm spectrum Large τ R  small quenching Similar results in other centralities p T distribution R AA (p T ) |Y|<1.0 _initial _τ R =25fm

Charm spectrum Large τ R  small quenching Similar results in other centralities R AA (p T ) p T distribution |Y|<1.0 _initial _τ R =25fm _τ R =7.4fm

Charm spectrum Similar results in other centralities p T distribution R AA (p T ) |Y|<1.0 _initial _τ R =25fm _τ R =7.4fm _τ R =2.5fm Small τ R  large quenching

Charm spectrum Small τ R  large quenching Similar results in other centralities p T distribution R AA (p T ) |Y|<1.0 _initial _τ R =25fm _τ R =7.4fm _τ R =2.5fm _τ R =0.74fm

Charm spectrum Similar results in other centralities p T distribution R AA (p T ) |Y|<1.0 _initial _τ R =25fm _τ R =7.4fm _τ R =2.5fm _τ R =0.74fm Small τ R  large quenching Almost thermalized for τ R <2.5

Charm spectrum Similar results in other centralities p T distribution R AA (p T ) |Y|<1.0 _initial _τ R =25fm _τ R =7.4fm _τ R =2.5fm _τ R =0.74fm On the way to thermalization for larger τ R

Charm spectrum V 2 (p T )= pT Drag force generates charm v 2. Elliptic flow parameter |Y|<1.0

Charm spectrum V 2 (p T )= pT v 2 seems to reach hydrodynamic limit for strong drag force. Drag force generates charm v 2. Elliptic flow parameter |Y|<1.0 π 0 : v2~0.1

Charm spectrum V 2 (p T )= pT Drag force generates charm v 2. Elliptic flow parameter |Y|<1.0 v 2 seems to reach hydrodynamic limit for strong drag force. v 2 gradually increases up to high p T for weak drag force.

Difference between charm and electron p T distribution Charm distribution Electron from charm through weak decay __ charm __ electron |Y|<1.0 independent fragmentation by PYTHIA

Electron spectrum c→D (S) →e - +ν e +π(K) via PYTHIA _ p T distribution |Y|<1.0 R AA (p T )|Y|<1.0

Electron spectrum τ R dependence is still seen clearly above p T ~1GeV. c→D (S) →e - +ν e +π(K) via PYTHIA _ p T distribution |Y|<1.0 R AA (p T )|Y|<1.0

Electron spectrum c→D (S) →e - +ν e +π(K) via PYTHIA _ p T distribution |Y|<1.0 R AA (p T )|Y|<1.0 Saturation for strong drag force. On the way to thermalization for weak drag force.

Electron spectrum τ R dependence is less clear below p T ~1GeV. c→D (S) →e - +ν e +π(K) via PYTHIA _ p T distribution |Y|<1.0 R AA (p T )|Y|<1.0

Electron spectrum |Y|<1.0 PRELIMINARY ! Elliptic flow parameter STAY TUNED ! Need high statistics in higher p T region.

Experimental Data

Summary and outlook 1. Full 3D hydrodynamics + Langevin approach to transport of heavy quark in QGP. 2. Charm spectra contain the information of drag force of heavy quark. 3. Electron spectrum would also have the information of drag force. (Need more statistics) 4. Compare with experiments and extract the drag force parameter in Langevin equation. 5. Prediction of mass (bottom), energy (LHC) and size (Cu) dependence towards comprehensive understanding of the transport property of QGP.

Summary and outlook 1. Full 3D hydrodynamics + Langevin approach to transport of heavy quark in QGP. 2. Charm spectra contain the information of drag force of heavy quark. 3. Electron spectrum would also have the information of drag force in high p T region. (Need more statistics) 4. Compare with experiments and extract the drag force parameter in Langevin equation. 5. Prediction of mass (bottom), energy (LHC) and size (Cu) dependence towards comprehensive understanding of the transport property of QGP.