# Presentation: 058521

## Hydrodynamic Modeland Hard Probe

- Tetsufumi Hirano
*RIKEN BNL Research Center*

_*OUTLINE*_
- Introduction
- Hydro+jet model
- Back-to-back correlations
*R**AA* for protons
- Jet quenching at ** ~ 2
- Summary

_*References*_
- T.H. and Y.Nara,
- Phys.Rev. C**66**, 041901(2002);
- Phys.Rev.Lett. **91**, 82301(2003);
- nucl-th/0307015;
- nucl-th/0307087.

- JPS meeting @ Miyazaki, Sep.9, 2003

- Collaboration with Yasushi Nara (Arizona)

## Introduction

_*Introduction*_

- 1. Jet quenching

- 2. Jet acoplanarity
- (transverse momentum imbalance)

- correlate ?

- Gyulassy, Plumer (’90)
- Wang, Gyulassy (’92)
- and a lot of work

- Bjorken (’82)
- Appel (’86)
- Blaizot, McLerran (’86)
- Rammerstorfer, Heinz (’90)

- g

- g

- g

- Au 100*A* GeV

- Au 100*A* GeV

## High pT data at RHIC

- From D. d’Enterria(PHENIX),
- talk at QM2002. See also,
- S.S.Adler et al.(PHENIX),
- PRL91,072301(2003).

- From D.Hardtke (STAR),
- talk at QM2002.
- See also, C.Adler et al.
- (STAR), PRL90,082302(2003).

- ???

## Initial or Final ?

- D.Kharzeev *et al*., Phys.Lett.B**561**, 93(2003).

- Parton saturation*N*part scaling
*gg**g *(no b-to-b)

- I.Vitev and M.Gyulassy,
- Phys.Rev.Lett. **89**, 252301(2002)

- pQCD+Cronin+shadowing
- +jet quenching+simple expansion

**Our approach (“final effect”): **
**Dynamical simulation of both a QGP fluid and minijets**

## Model

- Jet quenching
- Jet acoplanarity

- Interaction 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

## PYTHIA(+Hydro)

_*PYTHIA(+Hydro)*_

*N*

*N*

- 3

- 4

- Fragmentation:
- Independent
- Fragmentation
- Model

- PYTHIA

- 3D Hydro

- PYTHIA

- hadrons

- hadrons

- PDF:
- Collinear: CTEQ5LO
- kT: Gaussian

- Parton energy loss

- pQCD LO:

- *Initial and final state radiation are included.

## 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)

## Suppression Factor for 0

- GLV formula with
*C*=0.27 quantitatively
- reproduces the data

- Data from  S.S.Adler et al. (PHENIX),
- PRL91,072301(2003).

- Our starting point of
- the following discussion

- b=2.8fm

- Simplified GLV 1st order formula:

- M.Gyulassy *et al*., NP**B594**, 371 (2000).

## Back-to-Back

- Correlations

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

- From D.Hardtke (STAR), talk at QM2002. See also, C.Adler et al.(STAR), PRL90,082302(2003).

- Central collisions

- Peripheral collisions

- Disappearance of away-side peaks!

- ???

**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.

## 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

## Disappearance of B-to-B

- energy loss

- +Cronin effect

- +broadening

- Energy loss is dominant, but insufficient.

- Nucleon
- inside a nucleus

- Target nucleus

- Beam direction

- Hot matter

- Hot matter

## RAA for

- Protons

## Are Protons and Anti-Protons Suppressed ?

_*Are Protons and Anti-Protons Suppressed ?*_

-  jet quenching ??

******protons****  **

**************h**

- J.Velkovska, talk at DNP;
- PHENIX, nucl-ex/0305036.

- C.Seife, Science298,718(2002)

## pT Spectra for Identified Hadrons

*p**T*,cross depends on
-  particle species!

- c.f.) *p**T*,cross~ inflection point
- for kaons and protons

## RAA and Ratio for Identified Hadrons

- Absence of jet
- quenching?
_***No! Radial flow***_

**Similar mechanism for ratio and *****v*****2**

## Jet Quenching

- at **~2

## Jet Quenching at Off-Midrapidity

- BRAHMS, PRL91,072305(2003)

## Hydro+Jet at Off-Midrapidity

- charged

- Dynamical effects should be
-  identical between **=0 and 2.

- Steeper pQCD component
- in forward rapidity.

## Hydro+Jet at Off-Midrapidity (cond.)

- Indication of dense
- partonic matter in
- forward rapidity
-  regions (**~2)

- Jet quenching
-   Shift of a spectrum
- Modification factor
-   Ratio at some *p**T*

## Summary

-   _QGP in Au+Au collisions at RHIC ?_
- Final state effects are consistent with
- intermediate ~ high *p**T* data (*R**AA*, b-to-b, ...).
- Strongly encouraged by recent *d*+Au data.
* *_***Dynamical model***_** (hydro+jet) for heavy-ion physics**
** ****Dominant effect of back-to-back correlations**
****** ****Parton energy loss**
** ****Hadron species dependent transverse dynamics**
******Interplay**** between radial flow and jet quenching**
** ****How large dense matter in longitudinal direction? **
******Jet quenching in forward rapidity region ****(******~2)**

## Recent Data in d+Au Collisions

- Something happens
- only in AuAu collisions

- Jet quenching scenario is
- favored and initial state
- effect is ruled out.
- But, this does not  mean
- saturation model itself
- is killed.

- PRL**91**,(03)072302;
- 072303;
- 072304;
- 072305.

## Backup slides

## Brief Summary of Our Hydro Results

-  Full 3D hydro!
-  No Bjorken scaling ansatz
-  No cylindrical symmetry
-  (**s, *x, y*) coordinate

- T.Hirano, Phys.Rev.C65(2002)011901.

- T.Hirano and K.Tsuda, Phys.Rev.C66(2002)054905.

- Suppression of radial flow, elliptic
- flow and HBT radii in comparison
- with the conventional hydro results.

## Limit of Hydrodynamics @ High pT

- Need hard
- components?

_*Limit of Hydrodynamics @ High p*__*T*_

*p*T slope for pions becomes
- insensitive to *T*th in considering
- early chemical freezeout.

- PHENIX data
- @130AGeV

- Also one of the strong
- motivations of constructing
- the hydro+jet model

- T.Hirano and K.Tsuda, Phys.Rev.C66(2002)054905.

## Results from PYTHIA

- PHENIX 0
-  in *pp* collisions@200GeV,
- hep-ex/0304038.

- UA1 charged
- in *pp* collisions@200GeV,
- Nucl.Phys.B335, 261(1990).

## Time Evolution in Hydro+Jet Model

- Free
- streaming

- Hydro evolution

_*Time Evolution in Hydro+Jet Model*_

**

**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

- CGC?
- Prethermaliztion?

## Parton Energy Loss

_*Parton Energy Loss*_

- Position of a jet

- Adjustable parameter

- Parton density
- from hydrodynamic
- simulations
- We have already
- had a solution!

- Initial
- 4-momentum
- of a jet in local
- rest frame

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

- Simplified GLV formula 1st order in opacity expansion

- Relevant for
- heavy-ion
- collisions

## Azimuthal Correlation Function

- Associated
- particles

- Trigger
- particles

_*Azimuthal Correlation Function*_

- 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

## 1. Effect of Parton Energy Loss

- Hot matter

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

*C*=0.27 From fitting *R*AA

## 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

## 3. Effect of Broadening

- Transverse momentum
- orthogonal to its direction
- of motion

- Hot matter

- Model 1 (BDMPS):

- Model 2 (XNW):

## Surface Emission Dominance ?

- Initial positions of jets which survive at final time

**Completely**

**Partially**

- No quenching

*C*=0.25

*C*=1.0

- 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).

## Hydro and Hydrojet

- PT spectrum becomes
- _convex_ to _concave._
- Inflection points at
- ~ 2.8 GeV/c (kaons)
- ~ 3.5 GeV/c (protons)

- Radial flow pushes
- heavier particles to
- high pT.

## Elliptic Flow for Identified Hadron

- PHENIX, nucl-ex/0305013.

*v*2,*p*>*v*2, hardly obtained
- by using hydrodynamics.

## Elliptic Flow for Identified Hadrons(cond.)

- Hydro results:
- Low *p**T*
- Defference comes from mass
- High *p**T*
- All *v*2’s merge (*p**T*>>*m*)

- Interchanging behavior
-  of *v*2 for id. hadrons
- Comes from hadron species
-  dependence of *p**T*,cross

*v*2,*K*<*v*2, ???

## Why RAA(=0)>RAA(~2)?

**Jet quenching is**
**a shift of spectrum.**

*p**T*

- (1/*p**T*)*dN*/*dp**T*

**“****parallel shift”**

*p**T*

- (1/*p**T*)*dN*/*dp**T*

**Different slope,**
**but same shift**

- 0

- 0

***R******AA***** is a ratio at a *****p******T*****.**