# Presentation: 251767

## Dynamical Parton Energy Loss

**in Relativistic Heavy Ion Collisions**
- Tetsufumi Hirano
*Physics Department, University of Tokyo*

**Outline:**
- Jet tomography
- Jet quenching
- Jet acoplanarity
- Hydro+jet model
- Results
- Suppression factor
- Correlation function
- Summary

**Reference:**
- T.Hirano and Y.Nara,
- Phys. Rev. C **66**, 041901(R) (2002).

- Tokyo-Adelaide Joint Workshop on
- Quarks, Astrophysics and Space Physics

- Jan.6-10, 2003

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

**Notes:**
First of all, I’d like to thank Hatsuda-san and Sasaki-san for inviting me this workshop.
Today’s title is “...”.
This is the outline of my talk.
In the first part of my talk, I briefly review the idea of jet tomography and the related experimental data.
In the second part, I will give you a possible interpretation of those experimental data by using the hydro+jet model recently proposed by Yasushi Nara and myself.
Finally, I will summarize my talk.

## Introduction

- Recent important hadronic
- observables in _high __*p*__T_ regions
- at Relativistic Heavy Ion Collider (RHIC)
- Suppression of the yields
- Disappearance of back-to-back correlations
- The diagnostic tools for dence matter
- (Quark Gluon Plasma?)
- “jet tomography”

**Notes:**
As already mentioned by Hamagaki-san, recent important observables in high pT regions at RHIC are suppression of the yields of hadrons and disappearance of back-to-back correlations.
As I will explain soon, high pT hadrons are believed to be the diagnostic tools for dense matter produced in heavy-ion collisions.
This is sometimes called “jet tomography”.

## Jet Tomography

_*Jet Tomography*_

- g

- g

- g

- Tool 1. Jet quenching

- Figures taken from M.Gyulassy’s presentation

- Hot matter
- produced
- in a collision

- Tool 2. Jet acoplanarity
- (transverse momentum imbalance)

- correlate ?

- CT (computed tomography) scan

- Gyulassy, Plummer (’90)

- Bjorken(’82)
- Appel (’86)
- Blaizot
- McLerran (’86)

**Notes:**
I suppose some of you are not familiar with the term `tomography’.
But I believe you have heard CT scan in medical situation. CT is an abbreviation of `computed tomography’.
This is a picture of the cross section of a man. But I cannot diagnose whether he is healthy or not because I’m just a physicist, not physician.
Anyway, jet tomography is an analogy of CT scan.

One important thing in the tomographic approach is that probes are under control. In high-energy nucleon-nucleon collisions, spectrum in high pT regions can be calculated by perturbative QCD. So we naively expect that the spectral changes may contain information about the systems.

Let’s suppose hot matter is produced in a collision. And an energetic parton is also produced inside the hot matter.
Throughout traversing this medium, the parton loses its energy like this. The resultant high pT spectrum is shifted to low pT regions. This phenomenon is called jet quenching.

The other interesting phenomenon is jet acoplanarity. Acoplanarity means the transverse momentum imbalance between two correlated jets.

These are tomographic tools in heavy ion collisions.

## Tool 1. Jet Quenching

- Energy loss in vacuum
- (~fragmentation)

**: string tension

- Nucleon-nucleon collisions

- Jet

- In hot (deconfined) matter

- Nucleus-nucleus collisions

- Additional energy loss in matter

- Jet

- Baier *et al.*, (1997)

- In vacuum

**Notes:**
Let’s go to the details about jet quenching.

In nucleon nucleon collisions, partons losses their energy in vacuum and energy loss per unit length is almost the same as the string tension.

On the other hand, there is an additional energy loss in nucleus-nucleus collisions like this.

Some pQCD based analyses show that the total energy loss is represented by using characteristic energy E_critical, where E_critical is represented by screening mass, length of medium, and the inverse mean free path.

Due to the additional energy loss, pT spectrum is changed.

## Tool 1. Jet Quenching (contd.)

- From D. d’Enterria, talk at QM2002.

- 0-10% Central

- (Ncoll=975±94)

**PHENIX Preliminary**

- Spectrum is shifted to lower *p*T

- Yield is suppressed

- Suppression!

- 0 *p*T spectrum

- Suppression Factor by PHENIX

**Notes:**
These are the experimental data.

Left figure shows pT spectrum of pi^0 measured by the PHENIX collaboration which is already presented by Hamagaki-san.

Red points shows the result in central Gold-Gold collisions and blue points is the result in pp collisions scaled up by number of binary collisions.
If a heavy-ion collision is simply superposition of the nucleon-nucleon collisions, we expect the result becomes blue plots. But, in the real world, the spectrum is shifted to lower pT regions or, in other word, yield of pions is suppressed.

This is consistent with the jet quenching picture. The jet quenching is often quantified by taking the ratio between these two spectra. Phenix observed that suppression factor R_AA gradually decreases with pT. Let me remind you that we cannot observe the suppression at SPS energies.

This is the experimental situation of jet quenching at present.

## Tool 2. Jet Acoplanarity

- Associated
- particles

- Trigger
- particles

_*Tool 2. Jet Acoplanarity*_

- p+p

- A+A

**

*p*T (GeV/c)

- 0.7

- -0.7

- 0

- 2

- 4

- 6

- STAR

- Strength of away-side peaks
- are the same in no jet quenching case

- Back-to-back correlations of high pT hadrons

**Notes:**
Let’s go to the details about jet acoplanarity.

According to the STAR collaboration, we first sdefine trigger particles in this momentum window. pT is between 4 to 6 GeV/c. This blue arrows represent such particle. Then, we also define associated particles like this. Here green arrows correspond to associated particles.

Let’s define the azimuthal correlation function as a function of the relative azimuthal angle between trigger and associated particles.

In pp collisions, this blue guy and these green guys correlate with each other.
On the other hand, there are many jets in AuAu collisions. In addition to the correlated hadrons, there are background hadrons like this.
So the resultant correlation function becomes like this figure.
In pp collisions, correlation function is finite only near zero and plus-minus pi, while in AuAu collisions without jet quenching, there is a background and the near-side and away-side peaks are prominent from the background. 

We found the strength of away-side peaks are the same in no jet quenching case.

## Tool 2. Jet Acoplanarity (contd.)

- From D.Hardtke (STAR), talk at QM2002.

- Central collisions

- Peripheral collisions

- Disappearance of away-side peaks!

- ???

- Experimental Data by STAR

**Notes:**
Recently, STAR collaboration at RHIC obtains a very interesting result on the correlation function.
In peripheral collisions, the away-side peaks have almost the same strength as  the ones in pp collisions. This means that peripheral collisions are almost similar to the superposition of pp collisions.
On the other hand, in central collisions, the near-side peak has the same strength as the one in pp collisions, but the away-side peaks are completely vanishing.
I will show you what leads to this phenomenon later.

## Model

- Jet quenching
- Jet acoplanarity

- Interplay between soft and hard is *important!*

- Hydro + Jet model

- Soft (hydrodynamics)
- Space-time evolution of matter
- Phase transition between QGP
- and hadrons
- Particle spectra in low *p*T region

- Hard (mini-jets)
- Production of (mini-)jets
- Propagation through fluid elements
- Fragmentation into hadrons

- Interaction between fluids and mini-jets through parton energy loss

**Notes:**
Let me explain our approach to the physics of high pT region in relativistic heavy-ion collisions.

As I mentioned in previous slides, both jet quenching and jet acoplanarity are manifestation of interplay between soft physics and hard physics.
Along the line of thought, we develop the hydro+jet model.

This model is mainly composed of two parts.One is the soft part. The other is the hard part. We can describe space-time evolution of matter, phase transition between QGP and hadrons by using hydrodynamics. We also calculate particle spectra in low pT regions.
In the hard part,  the dynamics of mini-jets such as production, propagation and fragmentation are described.

Interaction between fluid elements and mini-jets are considered through parton energy loss.

## The Hydro+Jet Model

_*The Hydro+Jet Model*_

*N*

*N*

- 3

- 4

- Fragmentation:
- Independent
- Fragmentation
- Model

- PYTHIA

- 3D Hydro

- PYTHIA

- hadrons

- hadrons

- PDF:
- Collinear: CTEQ5LO
- 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.

**Notes:**
This is the overview of the hydro+jet model.

First, we produce mini-jets by using a famous event generator PYTHIA.We take into account the following relevant pQCD leading order processes.This formula represents the inclusive invariant cross section of mini-jets. This is the elementary cross section, and f and g are collinear and transverse parton distribution functions. Here we employ CTEQ5 leading order for collinear part and Gaussian function for transverse part. As for the fragmentation scheme, we employ Independent Fragmentation Model. This model with K=2 provides good agreement with the p-pbar and pp data at the RHIC energy.

In heavy-ion collisions, produced high pT partons have to traverse a hot medium and lose their energy like this cartoon.The space-time evolution of hot medium are obtained from a full 3-dimensional hydrodynamic simulations.

## Jets and Hydro Evolution in the Transverse Plane

- Initial configuration of mini-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)
-  Mini-jets (*p*T>2GeV/*c*)

**(fm-3)

- x(fm)

- y (fm)

**Notes:**
Before going to models for parton energy loss, let me show you an animation of our simulation.

We simulate fluid and minijets simultaneously. This movie is a sample of our hydro+jet simulations in non-central Gold-Gold collision at the RHIC energy. Collision axis is perpendicular to the screen.
Color gradation represents thermalized parton density and open circles represents minijets.
Here, initial configuration of mini-jets is supposed to be proportional to the number of binary collisions.
For the purpose of illustration, I switch off the fragmentation into hadrons.
Inside the partonic phase, jets lose their energy.

## Parton Energy Loss

- Coherent model

- Position of a jet

- Adjustable parameter

- Parton density
- from hydrodynamic
- simulations

- Jet

*l*: coherence length

- Coherent radiation

- Initial enegy
- of a jet

- Landau-Pomeranchuk
- -Migdal effect
- ~Destructive interference
- of radiation

- M.Gyulassy *et al*. (2000)

**Notes:**
We employ two models of parton energy loss.

One is the coherent model. If the system dynamically expands, the energy loss of a parton is represented by this equation. Here C is the adjustable parameter,  rho is the parton density, x is the position and E is the initial energy of a jet. In the hydro+jet approach, rho is obtained from hydrodynamic simulations. I should comment that C is the only one adjustable parameter in this analysis.
The picture of energy loss in the coherent model is like this. Jet interacts with some partons in the medium simultaneously and emits gluons.However, emitted gluons interfere with each other due to large formation time. This is the so-called Landau-Pomeranchuk-Migdal effect in QCD.

## Parton Energy Loss (contd.)

- _In_coherent model

- partonic medium

- Jet

**

**

**

**

**

- Total incoherent energy loss
- The sum of single scattering

- Adjustable parameter

- Mean free path

**Notes:**
The second model is more simplified one.
The energy loss per unit length is supposed to be proportional to the inverse mean free path. At each mean free path, jet loses constant energy epsilon. The inverse mean free path is rewritten by parton-parton cross section and the parton density. In this approach, the product of epsilon and sigma is an adjustable parameter.
Anyway, total incoherent energy loss results from the sum of sigle scattering in the incoherent model.

## Suppression Factor

- Coherent model
- Almost flat
- Incoherent model(**=0.06)
- Increase with *p*T
- Experimental data
- Gradually decrease

- The coherent model with
*C*=0.25 quantitatively
- reproduces the data
- below *p*T~6 GeV/*c*

- Data from D. d’Enterria, talk at QM2002.

**Notes:**
Let’s go to the results from the hydro+jet model.

We first calculate pT spectra with and without jet quenching. Then we take those ratio.

Red lines shows the results from the coherent model with various adjustable parameters. This corresponds C=0.1, this is 0.25, and this is 1.0. Above 3 GeV/c, R_AA is almost flat.

Green line shows the result from the incoherent model. We choose an adjustable parameter to quantitatively reproduce the PHENIX data near 3 GeV/c. R_AA increases with pT above 3 GeV/c. We found the behavior of the incoherent model completely disagree with the PHENIX data.

Anyway, the coherent model with C=0.25 quantitatively reproduces the PHENIX data below 6 GeV/c. However we overpredict the data above 6 GeV/c. This is an open question of this jet quenching business.

## Three Possible Effects on Back-to-back Correlations

| 1.Energy loss
of jets | 2. Primordial kT
of initial partons | 3. Broadening
of jets |
| --- | --- | --- |
| Final state | Initial state | Final state |
| 

Absorption | 

“Cronin effect” | 

Random walk
behavior |

- Nucleon
- inside a nucleus

- Target nucleus

- Beam direction

- Hot matter

- Hot matter

**Notes:**
Based on the previous results from the coherent model, let’s discuss the three possible effects on back-to-back correlations for high pT hadrons.

First one is the amount of parton energy loss.

## 1. Effect of Parton Energy Loss

_*1. Effect of Parton Energy Loss*_

- Hot matter

- Simultaneous reproduction of
*R*AA and *C*2 ?
- Another mechanism is needed!

**Notes:**
If the energy loss is considerably large, the away-side jets are likely to be absorbed by hot medium. This may cause the disappearance of the away-side peaks.

Left panel shows the suppression factor which I have already shown. Right panel shows the dependence of the magnitude of parton energy loss on the
back-to-back correlations.

As I showed, C=0.25 reproduces the suppression factor. However, the away-side peaks does not disappear. The result is represented by black line. We can still see small away-side peaks. Although we underestimate the suppression factor by taking C=1.0 like this, we can obtain the disappearance of away side-peaks.

So we fail to reproduce R_AA and C_2 simultaneously only by the effect of the parton energy loss.

Therefore this suggests that we need another mechanism.

## Three Possible Effects on Back-to-back Correlations

| 1.Energy loss
of jets | 2. Primordial kT
of initial partons | 3. Broadening
of jets |
| --- | --- | --- |
| Final state | Initial state | Final state |
| 

Absorption | 

“Cronin effect” | 

Random walk
behavior |

- Nucleon
- inside a nucleus

- Target nucleus

- Beam direction

- Hot matter

- Hot matter

**Notes:**
Next, let’s see the effect of primordial transverse momentum of initial partons. This is often called Cronin effect.

## 2. Effect of Intrinsic kT

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

- Primordial *k*T distribution

_*2. Effect of Intrinsic k*__*T*_

- collinear

- intrinsic kT

- Nucleon
- inside a nucleus

- Target nucleus

- Beam direction

*C*=0.25
*C*=0.3
*C*=0.5

**Notes:**
Let’s suppose that a nucleon inside a incident nucleus goes through multiple scattering inside colliding two nuclei and then produce one pair jet.

If colliding partons have only collinear momentum, the produced partons have the same transverse momentum due to kinematics.
On the other hand, intrinsic transverse momentum releases the constraint and may affect the back-to-back correlations.

We have already taken into account the intrinsic kT 1 GeV^2/c^2 in the previous analysis. Cronin effect can be parametrized phenomenologically by increasing this value. Please keep in mind that kT square is found to be about 2 GeV^2 at SPS energies.

Intrinsic kT also affects the hadron yield, so we readjust parameter so as to reproduce suppression factor.

We found that the result with 2 GeV^2 is almost the same as the one with 1 GeV^2. So the reasonable value of intrinsic kT is insufficient to the disappearance of back-to-back correlation.

## Three Possible Effects on Back-to-back Correlations

| 1.Energy loss
of jets | 2. Primordial kT
of initial partons | 3. Broadening
of jets |
| --- | --- | --- |
| Final state | Initial state | Final state |
| 

Absorption | 

“Cronin effect” | 

Random walk
behavior |

- Nucleon
- inside a nucleus

- Target nucleus

- Beam direction

- Hot matter

- Hot matter

**Notes:**
Finally, we take into account the broadening of jets.

## 3. Effect of Broadening

_*3. Effect of Broadening*_

- Transverse momentum
- orthogonal to its direction
- of motion
-                           R.Baier *et al*., (1997)

- Hot matter

- Reduction of the away-side peaks:
- ~60% from parton energy loss &
-            intrinsic *k*T
- ~40% from broadening

**Notes:**
In addition to the parton energy loss, the broadening of jets is also manifestation of final state interaction.

The average transverse momentum orthogonal to its direction of motion is quantitatively related with the parton energy loss.
We take this effect into account and calculate the correlatation function.

Black line represents the no quenching case, green line represents the result without broadening, and red line is the result with broadening.

We obtain complete disappearance of away-side peaks. About 60 % reduction comes from parton energy loss and intrinsic kT and remaining 40% comes from broadening.

Therefore we found the disappearance of back-to-back correlations is caused by complex mechanism.

## Summary

- The hydro+jet model for analyzing high *p*T regions
- in relativistic heavy ion collisions
**Suppression factor**
- Coherent model with *C*=0.25 quantitatively
- reproduces the data below *p*T~6 GeV/*c*
- How do we obtain the decreasing *R*AA ?
**Back-to-back correlations**
- All three effects (energy loss, intrinsic *k*T, and
- broadening) are responsible for disappearance
- of back-to-back correlations.

**Notes:**
Let me summarize my talk.

We developed the hydro+jet model for analyzing high pT region in relativistic heavy-ion collisions.
We found the coherent model with C=0.25 quantitatively reproduces the PHENIX data below 6 GeV/c.
However, we cannot obtain the decreasing R_AA.
We also investigated the back-to-back correlations. All three effects such as energy loss, intrinsic kT, and broadening, are found to be responsible for disappearance of back-to-back correlations.

Thank you.