# Presentation: 183766

## What did we learn fromv2(pT; m) at RHIC?

_**Tetsufumi Hirano**_** and Miklos Gyulassy**

- The Berkeley School, LBNL, CA, May 19, 2005

## Slide 2

## Basis of the Announcement

_*Integrated*_ elliptic flow

- NA49(’03)

- PHENIX white paper

_*Differential*__ _elliptic flow

## Are Hydro Results Consistentwith Each Other? What does it mean?

- PHENIX white paper, nucl-ex/0410003

- elliptic flow

- pT spectra

- p

- 

**Purposes of this talk**
** ****To clarify the origin of difference among hydro results**
** ****To claim the importance of viscous effects in the hadron phase **
**(“Dissipative Hadronic Corona”)**

## Modeling of Hadron Phase and Freezeout

**Modeling of Hadron Phase and Freezeout**

*T*c

- QGP phase

- Hadron phase

**

**P**artial
**C**hemical
**E**quilibrium
- EOS

- Hirano & Tsuda;
- Teaney;
- Kolb & Rapp

- Teaney, Lauret
-  & Shuryak;
- Bass & Dumitru

*T*ch

*T*th

**H**adronic
**C**ascade

**C**hemical
**E**quilibrium
- EOS

*T*th

- Kolb, Sollfrank,
- Huovinen & Heinz;
- Hirano;...

- Ideal hydrodynamics

- Sudden freezeout: **=0infinity

*T*

- ~1 fm/*c*

- ~3 fm/*c*

- ~10-15
-        fm/*c*

## Tth<Tch

- Chemical parameters  particle ratio
- Thermal parameters  *p*t spectra

- Statistical model
*T*ch>*T*th
- (conventional) hydro
*T*ch=*T*th

-  No reproduction
- of ratio and spectra
- simultaneously

## Many people don’t know this...

- P.Huovinen, QM2002 proceedings

## Extension of Parameter Space

**Extension of Parameter Space**

***i*

- Introduction of chemical potential
- for each hadron!

- Single *T*f in hydro
- Hydro works?
- Both ratio and
- spectra?

## Chemical Potential & EoS

- EOS

- Example of chem. potential

- Partial chemical equilibrium (PCE)

- Expansion dynamics is changed
- (or not)?

- T.H. and K.Tsuda(’02)

**

## Does Dynamics change?

**Model PCE**

**Model CE**

- Contour(T=const.)

*T*(**) at origin

- T.H. and K.Tsuda(’02)

- <*v*r>(*T*th)

**

## pT Spectra

- How to fix *T*th in conventional hydro
-  Response to *p*T slope
-  Spectrum harder with decreasing *T*th
-  Up to how large *p*T?

*T*th independence of slope in chemically frozen hydro
-  No way to fix *T*th
-  Suggests necessity of
-  (semi)hard components

- Charged hadrons in AuAu 130AGeV

**C**hemical
**E**quilibrium

**P**artial
**C**hemical
**E**quilibrium

- T.H. and K.Tsuda (’02)

## Elliptic Flow

- T.H. and K.Tsuda (’02)

- Kolb and Heinz(’04)

- Is *v*2(*p*T) really sensitive
- to the late dynamics?

- 0.4

- 0.6

- 0.8

- 0.2

- 0

- 0.4

- 0.6

- 0.8

- 0.2

- 0

- 1.0

- 140MeV

- 100MeV

- transverse momentum (GeV/c)

## Mean pT is the Key

- Slope of *v*2(*p*T) ~ *v*2/<*p*T>

- Response to* *decreasing *T*th
- (or increasing **)

*v*2

- PCE

- CE

*v*2/<*p*T>

- <*p*T>

**

**

**

- Generic feature!

## Cancel between v2 and <pT> 

- pT

- v2(pT)

- <pT>

- v2

- pT

- v2(pT)

- v2

- <pT>

- pT

- v2(pT)

- v2

- <pT>

-  Tth
-  

- Chemical Eq.

- Chemical F.O.

## Why <pT> behaves differently?

- Simplest case: Pion gas

- Longitudinal expansion
-  *pdV* work!

- d*E*T/d*y* should decrease with
- decreasing *T*th.
-  <*E*T>d*N*/d*y* should so.

**CFO**: d*S*/d*y* = const.
-  d*N*/d*y* = const.
-  <*p*T> MUST decreases
**CE**: d*S*/d*y* = const.
- d*N*/d*y* decreases (mass effect)
- <*p*T> _can increase_ as long as <*E*T>d*N*/d*y* decreases.

- Result from the 1st law of thermodynamics & Bjorken flow

- dET/dy

- proper time

- ideal hydro

## Are Hydro Results Consistentwith Each Other? What does it mean?

- PHENIX white paper, nucl-ex/0410003

- elliptic flow

- pT spectra

- p

- 

## Summary of Results

| Models for
Hadron
Phase | v2(pT,m) | pT
spectra | Yield
or ratio | Viscous
effect | Caveat |
| --- | --- | --- | --- | --- | --- |
| Chemical
Equilibrium | Yes | Yes* | No | No | * P (Pbar) yields
<< exp. data |
| Partial
Chemical
Equilibrium | No | Yes* | Yes | No | *Only low pT for pions |
| Hadronic Cascade | Yes | Yes | Yes | Yes* | *Kinetic approach
Boundary
(QGPhadron)
Artificial viscosity |

## Summary

**What have we learned?**
- From hydro+cascade analyses, viscosity is mandatory in the hadron phase: QGP as a perfect fluid and _hadrons as a __“viscous”__ fluid_.
- v2 is sensitive to the early stage of collisions, whereas v2(pT) can also be sensitive to the late stage since v2(pT) is manifestation of interplay between radial flow (<pT>) and elliptic flow (v2).
**Comment**
- Conventional (chem. equilibrium & ideal) hydro makes full use of _neglecting chemical f.o._ to reproduce v2(pT) and pT spectra. _Accidental reproduction!_

## QGP

**QGP**

- Fuzzy image
- if focus is not adjusted yet.

**QGP**

- Wanna see this?

- Fine-tune the “hadronic” focus!

**focus:**
**hadron corona**

- The importance of the dissipative
- hadronic corona to understand
- “perfect fluid” sQGP core!

## BONUS SLIDES!

## Finite Mean Free Path & Viscosity

- See, e.g. Danielewicz&Gyulassy(1985)

- For ultra-relativistic particles, the shear viscosity is

_*Ideal*_ hydro:
-   0  shear viscosity  0

- Transport cross section

## FAQ

- We cannot say “Hydro works very well at RHIC”
- anymore?

- Yes/No. Only a hydro+cascade model does a good job.
- Nevertheless, HBT puzzle!
- QGP as a perfect fluid. Hadron as a viscous fluid.

- 2. Why ideal hydro can be used for chemically frozen
- hydro?

- We can show                    from
-     AND                  .
- One has to distinguish “chemical freeze out”
-     from “chemical non-equilibrium”.

## Today’s Breaking News 

- Ideal hydrodynamics with
- chemical equilibrium
-  “accidentally” reproduces
- transverse momentum
- dependence of the elliptic flow at RHIC. (T.H.)

**The Berkeley Tribune**

- May 19 2005

## Large radial flow reduces v2 for protons

- Radial flow pushes protons to high pT regions
- Low pT protons are likely to come from fluid elements with small radial flow

- Even for positive elliptic flow of matter,  v2 for heavy particles can be ***negative ***in low pT regions!

- High pT
- protons

- Low pT
- protons

*x*

*y*

*p*T

- Blast wave peak
- depends on **

## v2(pT) Stalls in Hadron Phase?

- D.Teaney(’02)

- Pb+Pb, SPS 17 GeV, b=6 fm

- Hadronic rescattering via RQMD
- does not change *v*2(*p**T*) for !

- Solid lines are guide to eyes

- Mechanism for stalling *v*2(*p**T*)
- Hydro (chem. eq.):
-       Cancellation between
*v*2 and <*p*T>
- Effect of EoS
- Hydro+RQMD:
-       Effective viscosity
- Effect of finite **