# Presentation: 809135

## A dynamical approach to jet quenching

- in relativistic heavy ion collisions
- Tetsufumi Hirano
*Physics Department, University of Tokyo*

**Outline:**
- Introduction & Motivation
- Hydrodynamics
- The hydro+jet model
- Results@130A GeV
- Results@200A GeV
- Summary

**References:**
- T.Hirano and Y.Nara,
- Phys. Rev. C **66**, 041901(R) (2002).
- See also,
- T.Hirano and K.Tsuda,
- Phys. Rev. C **66**, 054905 (2002).

- KEK Theory Seminar

- Dec.6, 2002

**Collaborator:**
- Yasushi Nara (Univ. of Arizona)

## Schematic Picture of Space-Time Evolution 

*z*
- (collision axis)

*t*

- QGP phase

- Mixed phase?

- Hadron phase

- 0

- hadrons

- photons
- leptons

- Schematic Picture of Space-Time Evolution

- jets

- 3つの重要なポイント
- 局所熱平衡
- 膨張
- 相転移

## Why Hydrodynamics ?

- 膨張&冷却
- 物質の集団的な流れ
- 相転移
-       **DYNAMIC!**
**実験データ**

- Large gap!

**Lattice QCD**
- 状態方程式
- 輸送係数
- スペクトル関数
**Effective Theories**
- スペクトル関数の変化
- カイラル対称性(の回復)
- Critical end point
- At fixed *T *or *n*B
-         **STATIC!**

- 理論側

- 熱力学量の時空発展
- 状態方程式を通しての
- 相転移の記述
-  Cooper-Fryeの公式を
- 用いた粒子分布の導出

- 現象

- Large gap!

- HYDRODYNAMICS

## 相対論的流体モデル

*E*:エネルギー密度
*p*:圧力
*n*B:Netなバリオン密度
*u***:4元速度

- 擬ラピディティ分布

- 横運動量分布

- +

- 状態
- 方程式

## Introduction & Motivation

_**The Hydro+Jet Model**_** **
- (as a dynamical tool to analyze jet quenching)
- Soft : Full 3D hydrodynamics
-  (with early chemical f.o.)
- Hard: pQCD with parton energy
-  loss

- A recent result from hydro
- with early chemical freeze-out
- pT slope is insensitive to Tth.
-      T.Hirano and K.Tsuda, PR**C66**,054905(2002).

- Hard components can fill in
- the difference between the data
- and the hydro result.

- pT spectra, RAA(pT) and C2()
- in moderate high pT (2-10 GeV/c)
- @RHIC

- Au+Au 130*A* GeV (central)

## Jet Tomography

- g

- g

- g

- jet

- Figures from M.Gyulassy’s talk

- Does jet quenching contain
- information about QGP?

## Why jets at RHIC and LHC?

- Pb+Pb@20*A* GeV
**in ~ 32 mb
**jet ~ 0.1 mb
*N*coll = 923 (*b*=2 fm)
-    ~3 jets/event

- Au+Au@200*A* GeV
**in ~ 40 mb
**jet ~ 20 mb
*N*coll = 1067 (*b*=2 fm)
-   ~500 jets/event

- Our definition of a jet:
- A parton with *p*T>2 GeV/*c *just after a collision
- (often called “mini-jet”)

- SPS

- RHIC

- Copious jets at RHIC and LHC!
-  Need contribution from jets

- LHC

- Pb+Pb@5500*A* GeV
**in ~ 90 mb
**jet ~ 90 mb
*N*coll = 2600 (*b*=2 fm)
-   ~2600 jets/event

- *pp:PYTHIA with CTEQ5L+K factor(K=2), AA:standard Woods-Saxon nuclear density

## Hydro + Jet

## The Hydro+Jet Model

- 3

- 4

*x*1*f**a*

*x*2*f**b*

- Fragmentation:
- Independent
- Fragmentation
- Model

- PYTHIA

- 3D Hydro

- PYTHIA

- hadrons

- hadrons

- PDF:
- Collinear: CTEQ5L
- kT: Gaussian
-      <kT2>=1GeV2/*c*2

- Parton energy loss:*dE*/*dx*
- (I will discuss later...)

- UA1
- p+pbar
- 200 GeV

- PHENIX
- p+p 200GeV

- *Initial and final state radiation are included.

## Time Evolution in the Hydro+Jet Model

- Free
- streaming

- Hydro evolution

**

**0

- Energy loss

- Fragmentation

**f

- =0.6fm/*c*

- ~10fm/*c*

- 0

- Formation time~0 fm
- For jets with *p*T>2GeV/*c*,
- 1/*p*T<0.1fm/*c*<<1fm/*c*
- Momentum dist. from
- PYTHIA ver. 6.2

- Thermalization time
- = Initial time of fluids
- Initial parameters in hydro have been already tuned.

- After hydro simulation, all survival jets fragment into hadrons.
- We neglect interaction of fragmented hadrons.

- Jets

- Full 3D
- hydro

- Particle spectra
- through Cooper-
- Frye formula

## Jets and Hydro Evolution in the Transverse Plane

- Initial configuration of jets
- Prop. to # of binary collisions
- Assuming jets move along
- straight paths
- (eikonal approximation)

- Au+Au 200*A*GeV, *b*=8 fm
- transverse plane@midrapidity

- Gradation
-  *Themalized* parton density
- Plot (open circles)
-  Jets (*p*T>2GeV/*c*)

**(fm-3)

- x(fm)

- y (fm)

## Phenomenological Parton Energy Loss

- partonic medium

- Phenomenological Parton Energy Loss

** ****Incoherent Model:**

**: energy deposit per scattering
**: mean free path
**: parton-parton cross section
**: thermalized parton density

- From hydro simulation

- Jet

**

**

**

**

**

- *Neglecting energy loss
- in the hadron phase.

## Results

- @130AGeV
- & 200AGeV

## 0 Spectra in sNN1/2=130 GeV Central Collisions

- HIJING:
*dE*/*dx* = 0.25 (GeV/fm)

- <dE/dx>~0.85 GeV/fm
- @**0=0.6 fm/c
- Onset of hard component
- pT~1.5 GeV/c

- X.-N. Wang, NPA698(2002)296c

- the best fit value

## Models for Parton Energy Loss

- “Transport” coefficient *q*

- A model motivated by
- a) GLV 1st order, or b) BDMPS for *E*>*E*cr

- M.Gyulassy *et al*., Nucl.Phys.**B571**(2000)197; R.Baier *et al*., Nucl.Phys.**B483**(1997)291.

**Incoherent model**

**Coherent (LPM) model**

*L*~*R*Au
**=0.5 GeV/c

*,   a*: free (adjustable) parameter

## Suppression Factor (PHENIX)

- From D. d’Enterria, talk at QM2002.

- 0-10% Central

- (Ncoll=975±94)

- RAA(2 GeV/c) ~0.45

- RAA(8 GeV/c) ~ 0.16

## Suppression Factor in sNN1/2=200 GeV Central Collisions

- Suppression factor *R*AA
-   Incoherent model: increase
-   Coherent model: almost flat

- Experimental data (PHENIX):
-                gradually decrease

*R*AA(*p*T) depends on the
- models of parton energy loss.

## Back-to-Back Correlations of High pT Hadrons

- p+p

- A+A

- Associated
- particles

**

*p*T (GeV/c)

- Triggered
- particles

- 0.7

- -0.7

- 0

- 2

- 4

- 6

- STAR

## Back-to-Back Correlation (STAR)

- From D.Hardtke, talk at QM2002.

- 4<pt(trig)<6 GeV/c data

- Central 0-5%

- Peripheral 60-80%

## RAA and C2 in sNN1/2=200 GeV Central Collisions

- Near-side jets:
- Almost independent
- Away-side jets:
- Depend on magnitude of
- energy loss

- We fail simultaneous
-  reproduction of RAA and C2.
- Need another mechanism

## Surface Emission Dominance ?

- Initial positions of jets which survive at final time

**Completely**

**Partially**

- *E*=0

- *E*=0.25*qL*eff2

- *E*=1.0*qL*eff2

- An interesting signature may be events in which the hard
- collision occurs near the edge of the overlap region, with
- _one jet escaping without absorption and the other fully_
- _absorbed_.  --J.D.Bjorken, FERMILAB-Pub-82/59-THY (1982).

## Summary

- We construct the Hydro+Jet model as a
-  dynamical approach to the physics of jet
-  quenching.
**Au+Au 130AGeV**
- The onset of hard contribution
-    pT~1.5 GeV/c for pions
- <dE/dx>=0.2 GeV/fm
-  (      HIJING:0.25 GeV/fm)
- <dE/dx>~0.85 GeV/fm @**0=0.6 fm/c for
-    incoherent model* *

## Summary (contd.)

**Au+Au 200AGeV**
- RAA(pT) is sensitive to the model dE/dx.
- No parameter which reproduces RAA(pT)
-    and the disappearance of b-to-b correlation
-    simultaneously.
-     Need other mechanisms (deflection of
-    jets?)
-  (Partial?) surface emission of jets may
-   happen in central  collisions.

## Spare Slides

## Suppression Factor in sNN1/2=130 GeV Central Collisions

## Jet Quenching Ratein 130A GeV Collisions

- One should check LPM case

-  ** prop. to ~1/**

*N*(**)/*N*(**0)@5GeV/c

## Hydro@200GeV

*E*0=40000MeV/fm3
- Flat region **flat=4.0
- Width **Gauss=0.8
- Binary collision scaling
- in transverse plane

## Relative PseudorapidityDependence of Jets

-  |**|<0.5
- Clear peak at **=0
-  0.5<|**|<1.4
- No peak at **=0

## Intrinsic kT of Partons in Nuclei?

- of disappearance of
- back-to-back correlation!

- Gaussian primordial *k*T distribution
- of partons

- Intrinsic *k*T of Partons in Nuclei?

- Triggered: 4<*p*T<6 GeV/*c*,
- Associated: 2<*p*T<*p*T,trig

- Back-to-back correlation of jets
- Energy loss (0.25qLeff2)
- + intrinsic *k*T

- collinear

- intrinsic kT

## Discussions

- Many observables to be analyzed
*v*2 in high pT region
- pT spectra for (anti-)protons
- RAA(pT) in non-central collisions
- (RAA really scales with Npart ?)
- Jet quenching in off midrapidity region
- and so on...
- Many effects to be included
- Deflection of jets in medium
- Interaction between fragmented
-  hadrons and thermalized hadrons
- (hydro+jet+hadronic cascade model ?)