# Presentation: 174933

## The Implications of Flow Measurements 

- The Implications of Flow Measurements
- at RHIC

## There are known knowns. 

**There are known knowns. **
***These are things we know that we know. ***
**There are known unknowns. **
***That is to say, there are things that we know we don't know*****.**
** ****But there are also unknown unknowns. **
***There are things we don't know we don't know***

- _[Donald Rumsfeld](http://www.brainyquote.com/quotes/quotes/d/donaldrums148142.html)_

## Slide 3

## Promise of the Flow Probe

***From E******T****** Distributions***

***Large Pressure Gradients ************ Hydro Flow***

**Promise of the Flow Probe**

***“******Control Params.”***

***Hydro Flow exhibit specific scaling properties which can be (in)validated***

## Scaling Characteristics of   Hydrodynamic flow

**Fluid hydrodynamics is scale invariant**.
- Important parameters
-     **There are several generic scaling predictions that can be readily tested;**

***v******2******  should scale with KE******T***

***All scaling tests can be in/validated***

***Relationship between harmonics is specific***

## Eccentricity Scaling –

**Eccentricity Scaling –**
**Known Known's **

***Incomplete equilibration breaks the scale invariance of  ideal fluid dynamics ***

*Length scale for elliptic flow - *
*Time scale for elliptic flow -*

## Eccentricity Scaling – Known Known's 

**Eccentricity Scaling – Known Known's **

***The density is relatively constant for b = 0 – 8 fm***

*8 fm*

## Eccentricity Scaling – Known Known's 

**Eccentricity Scaling – Known Known's **

***Hydro calculations validate v******2****** scaling over broad range of centralities***

## Energy Dependence

**Energy Dependence**

***The change in multiplicity density is not reflected in v******2***

- 	Comparison of
-  s = 62.4 and 200 GeV

## The eccentricity scaled v2  is reasonable over the relevant centrality range

***The eccentricity scaled v******2 ****** is reasonable over the relevant centrality range***

**Experimental Truth or Myth **

**Notes:**
NpartとNcollの説明が必要
もしv2が反応関与部のεからくる圧力勾配のみで決まっているとしたら、v2/εは、どのようなサイズの衝突でも一定の値をとるはず。

## Eccentricity scaling

- http://xxx.lanl.gov/abs/nucl-ex/0610037

**Eccentricity scaling**
**Truth or Myth ?**

*Same*
*N**part*

*Hydro + AB*
*- Hirano*

*Same*
*eccentricity*

## The prediction for thermalization is explicit and specific

**Hexadecapole Flow  (v****4****)**
**As a predictor of Thermalization**

## The prediction for thermalization is 

**explicit and specific**

**Hexadecapole Flow  (v****4****)**
**As a predictor of Thermalization**

*1/Kn*

*A Story that must *
*change !!*

## We hold these truths to be self evident !

**initial state**

**pre-equilibrium**

**QGP and**
**hydrodynamic **
**expansion**

**hadronization**

**hadronic phase**
**and freeze-out**

_**Courtesy S. Bass**_

**We hold these truths to be self evident !**

*Scaling for identified hadrons** *

*Scaling for Heavy Quark** *

*Scaling for Phi Mesons** *

*Universal Scaling** *

*Charm Flow** *

## The partonic fluid is thermalized

***Quark Degrees of Freedom Evident***

## The ratio of the harmonics for quarks is compatible with hydrodynamic prediction

**initial state**

**pre-equilibrium**

**QGP and**
**hydrodynamic expansion**

**hadronization**

**hadronic phase**
**and freeze-out**

_**Courtesy S. Bass**_

**The ratio of the harmonics for quarks is compatible with hydrodynamic prediction**

*Scaling for Higher Harmonics** *

## Saturation of Elliptic flow consistent with a  soft EOS associated with Crossover

**Saturation of Elliptic flow consistent with a  soft EOS associated with Crossover**

**Transport Coefficient**

**Phys.Rev.Lett.94:232302,2005*** *

## Transport Coefficient Estimates - I

_**Model **_
_**Comparison**_

**Transport Coefficient Estimates - I**

***1-2 X the conjectured lower bound***

## Transport Coefficient

**Transport Coefficient**

***Thermalization facilitated by 2************3 processes***

*C. Greiner et al*

## Setting an upper limit on 

**QCD Sonic Boom**

***Gives sound speed directly;  Sets upper limit on viscosity.***

**Setting an upper limit on **
**The viscosity**

## QCD Sonic Boom?

**The data is compatible with the presence of a  Mach Cone away-side jet **

**Total 3PC jet correlations**

**QCD Sonic Boom?**

## CEP Search

**CEP Search**

**Lacey et al.**
**arXiv:0708.3512** [nucl-ex]* *

## How to find the CEP?

**How to find the CEP?**

***First estimate   T ~ 165-170  ******μ****** ~ 120-150 MeV***
***Need two energies ******immediately***

## Epilogue

**Flow measurements tell us that the hot QCD matter created at RHIC is a strongly coupled plasma that:**
** **
***flows *****as a (nearly) perfect fluid with systematic patterns consistent with *****quark degrees of freedom.****** ***
*** ***
**has a soft EOS and a viscosity to entropy density ratio  close to *****the conjectured quantum bound ***

***  ******A Wealth of other Experimental Results Provide Constraints ***
***   ******for first estimates of the Thermodynamic and Transport Properties ***
***   ******of the plasma***

***Extracted Transport Coefficients Suggest  Decay Trajectories “close’’ to the Critical End Point (CEP)***

***First estimate   T ~ 165-170  ******μ****** ~ 150-180 MeV ***
***Need two energies ***_***immediately***_

## Epilogue

**Strong evidence for crossover to the QGP at RHIC.**
** **
**Short emission lifetimes**
**Matter quenches Jets and *****flows *****as a (nearly) perfect fluid with systematic patterns consistent with *****quark degrees of freedom.****** ***
*** ***
**Matter has a soft EOS and a shear viscosity to entropy density ratio  *****lower *****than any other known fluid -- a value close to *****the conjectured quantum bound***
***Corresponding bulk viscosity to entropy density is large ***

***  ***

***Extracted Transport Coefficients Suggest  Decay Trajectories close to the Critical End Point (CEP)***
***Energy scans now required to do the trick !!***

***First estimate   T ~ 165  ******μ****** ~ 120 -150 MeV***
***Need two energies ***_***immediately***_

## The EOS of  the 

**The EOS is harder than that for the hadron gas but softer **
**than for the hard QGP ******** no strong first order phase transition**

*Hydro Calculations*
*(Bhalerao et al.)*

**The EOS of  the **
**Partonic Fluid is Soft **

## Slide 27

## A Crossover transition to the strongly coupled thermalized QGP occurs at RHIC

**initial state**

**pre-equilibrium**

**QGP and**
**hydrodynamic expansion**

**hadronization**

**hadronic phase**
**and freeze-out**

_**Courtesy S. Bass**_

**A Crossover transition to the strongly coupled thermalized QGP occurs at RHIC**

**We hold these truths to be self evident !**

## A Central Question of the Field?  

***A Central Question of the Field?  ***

**The location of the critical End point and the phase boundaries are fundamental to the QCD phase diagram***** !***

## The Space-Time probe

**hadronization**

**Are source Imaging measurements consistent with the crossover transition ?**

**A Cross Over strongly affects **
**the Space-time Dynamics**

**Theory indicate a crossover transition**

**The space-time extent (Source Image) can lend crucial insights**

- Puzzle ?

**The Space-Time probe**

## Source Imaging Methodology (1D)

**Source Imaging Methodology (1D)**

**Inversion of this integral equation**
****** ****Source Function**

_**1D Koonin Pratt Eqn.**_

***Reliable measurement of the full***
***1D Source Function ! ***

## Source Imaging Methodology (3D)

**Source Imaging Methodology (3D)**

_**3D Koonin Pratt Eqn.**_

***Reliable measurement of the full Source Function in 3D ! ***

## PHENIX Data

***Robust Experimental Source Functions obtained from moments***

**PHENIX Data**

- Contributions from
- l > 6 is negligible

## The transition is Not  a Strong 

***Source Function Comparison to Models Give robust life time estimates ************ Consistent with Crossover transition***

- _Therminator:_
- A.Kisiel et al. Comput.Phys.Commun.174, 669 (2006)
**Thermal model with Bjorken longitudinal  expansion and transverse Flow**
-  Spectra & yields constrain thermal properties
-  Transverse radius ρmax : controls
-    transverse extent
-  Breakup time in fluid element rest frame,
-       : controls longitudinal extent
-  Emission duration     : controls tails in
-   long and out directions
-   a controls x-t  correlations

**The transition is Not  a Strong **
**First order Phase Transition?**

## Boltzmann coincides with hydro for small values of  K

**Boltzmann coincides with hydro for small values of**  K

**Eccentricity Scaling –  A Known Known **

## Eccentricity Scaling – Known Known's 

***The density is relatively constant for b = 0 – 8 fm***

##  Lessons

*** ***_**Lessons**_
***``Dynamic recombination’’***
***2. ******Partonic Thermalization!***
***3. Strongly coupled QGP***

**The partonic fluid is thermalized**

## The partonic fluid is Strongly coupled? 

- KET & nq2 scaling validated for v4

***Quark recombination extend to lower pT/KE******T ******?***

## CEP Search

**CEP Search**