# Presentation: 214447

## System Size and Energy Dependence of Elliptical Flow

- Richard Bindel
- University of Maryland
- For the                     collaboration
- Division of Nuclear Physics, Maui
-  September 19th, 2005

**Notes:**
My name is Richard Bindel and I’m representing the phobos collaboration.  Today I’ll be speaking about the system size and energy dependence of elliptic flow

##                 Collaboration (Aug 2005)

-                 Collaboration (Aug 2005)

**Notes:**
Phobos is a collaboration of aboutg 60 scientists from 8 institutions.  The large fraction of students is highlighted in red.

## Motivation For Studying Flow

-  Flow probes the very early thermalization of the system

-  Elliptic flow as a function of:

-  Energy
-  Centrality

-  Pseudorapidity
-  Momentum

-  Can be used to constrain theory.

**Notes:**
Flow has been studied at RHIC for many years now, mainly because it is an excellent probe of the early thermalization of the system.  

A number of differential flow measurements can be used to constrain theory
Phobos has made measurements of flow as a function of ...

## Two Flow Measurement Methods

- Track Based Method

**Notes:**
Phobos uses two techniques to measure flow
In the track based technique, the azimuthal pattern of hits in the detector is used to determine a reaction plane and then tracks from the spectrometer are correlated to that reaction plane
In the hit based technique, the azimuthal pattern of hits in one part of the detector is used to determine a reaction plane, and then the azimuthal distribution from another part of the detector is correlated to measure the flow signal
Two techniques gives us confidence in our measurement

## Motivation for Comparing Species

- Mid-central AuAu
- collision

- Central CuCu collision

- Two similar
- system sizes!

- roughly
- same number
- of participants

**Notes:**
I’d like to specifically point out the motivation for comparing flow in AuAu to CuCu

This diagram helps point out that the size of the participant region is roughly the same for mid-central AuAu collisions as it is for the most central CuCu collisions.  

In some respects, these two collisions are very similar....

## Motivation for Comparing Species

- Some observables
- scale with number
- of participants

- Similar dN/d

- Mid-central AuAu
- collision

- Central CuCu collision

- Two similar
- system sizes!

- 200 GeV

- roughly
- same number
- of participants

**Notes:**
For example, with roughly the same number of participants, we measure a remarkably similar dN/d.

However...

## Motivation for Comparing Species

- 200 GeV

- Some observables
- scale with number
- of participants

- Similar dN/d

- Mid-central AuAu
- collision

- Central CuCu collision

- Two similar
- system sizes!

- We expect **flow** to depend on **geometry**!

- Two similar
- system sizes!

- roughly
- same number
- of participants

**Notes:**
However, we expect the flow to depend on the geometry of the system

## Motivation for Comparing Species

- 200 GeV

- Some observables
- scale with number
- of participants

- Similar dN/d

- Mid-central AuAu
- collision

- Central CuCu collision

- Two similar
- system sizes!

- We expect flow to depend on geometry!

- Two similar
- system sizes!

**roughly**
**same number**
**of participants**

- Elliptical

- Circular

**Using two species lets us change the geometry**
**while holding the number of participants constant**

**Notes:**
And since participant region is elliptical while the other is circular, these should have relatively different flow

Essentially measuring two species lets us change the geometry while holding the number of participants constant

## Eccentricity: A measure of “Geometry”

- Mid-central AuAu
- collision

- Central CuCu collision

- Elliptical

- Circular

- We need a way to quantify the geometry of the participating nucleons

- The shape is characterized
- by the **eccentricity** (****)

**Notes:**
We characterize the shape by the eccentricity -- epsilon

## Eccentricity: A measure of “Geometry”

- Nucleus A

- Nucleus B

- Participant Nucleons

- A model of a
- AuAu collision:

**Notes:**
Here we have a model of a gold gold collision, with two nuclei, A and B, and the overlapping participant region in purple

## Eccentricity: A measure of “Geometry”

- Nucleus A

- Nucleus B

- Participant Nucleons

- A model of a
- AuAu collision:

- b

- Using the impact parameter as the x-axis, we define the standard eccentricity using the widths of the distribution in the x and y directions

**Notes:**
We can define the STANDARD eccentricity using the width of the spatial distributions in both the x and y directions,

	the difference of sigma y2, sigma x2 over the sum of sigma y2 and sigma x2

## Eccentricity: A measure of “Geometry”

- Nucleus A

- Nucleus B

- Participant Nucleons

- A model of a
- AuAu collision:

- b

- Using the impact parameter as the x-axis, we define the standard eccentricity using the widths of the distribution in the x and y directions

- y2

- x2

**Notes:**
We can define the STANDARD eccentricity using the width of the spatial distributions in both the x and y directions,

	the difference of sigma y2, sigma x2 over the sum of sigma y2 and sigma x2

## The Phobos Elliptic Flow Data Set

- preliminary

- preliminary

- PHOBOS

**Sizable v****2**** for Cu+Cu**

- from
- 0% to 40%
-   centrality

**Notes:**
In 5 years of running, phobos has produced a comprehensive flow data set.  Here we’ve integrated from 0 to 40% centrality.

CuCu still has the same trianglular shape as AuAu did, but the magnitude is surprisingly large!
Certainly larger was predicted by transport models.  
You can see that the CuCu doesn’t quite reach 5%, but it’s at least 4%

## The Data: Something’s Amiss...

***preliminary***

***PHOBOS 200 GeV  h******±***

***Statistical errors only***

**Cu+Cu**
**preliminary**

**Au+Au**

- PHOBOS  200 GeV Hit Based
- Statistical errors only

**Elliptic flow is high even for the most central bin in Cu+Cu**

**How does it relate to the eccentricity?**

- || < 1

**Notes:**
Now I’m showing you the centrality dependence with number of participants on the x axis.  You can see that in the gold system, for the most central events, the flow tends towards zero.  Copper, even at the highest centrality, still has 3% flow

## The Data: Something’s Amiss...

***preliminary***

***PHOBOS 200 GeV  h******±***

***Statistical errors only***

**Cu+Cu**
**preliminary**

**Au+Au**

- PHOBOS  200 GeV Hit Based
- Statistical errors only

**For CuCu, the eccentricity drops to zero by N****Part**** of 100**

- || < 1

**Notes:**
The inset is a plot showing what we expect the eccentricity (defined in the standard way) to behave versus Npart

We see that, at the highest Nparts, the eccentricity should drop to zero, which is understandable, since we suspect that the participant region is roughly circular in this case.  We also suspect the flow should drop to zero, however, as I mentioned, it doesn’t

## The Data: Something’s Amiss...

- v2 near mid-rapidity

**Dividing by the eccentricity shows no connection between the two species.**

- || < 1

**Notes:**
If we proceed by dividing the flow by the standard eccentricity, we find that the two systems are in no way similar though we expect that flow should be very geometry dependent.

Clearly the data is showing us something different, and so we went back to reexamine our assumptions about eccentricity

## The Data: Something’s Amiss...

- ?

- What went wrong?

- We reexamine our definition of eccentricity

## Reexamining Eccentricity

- Eccentricity is not directly measurable

- We use a Glauber model to relate eccentricity to our NPart bins.

- What goes into making this plot...?

## Reexamining Eccentricity

-  impact parameters and are sorted by the number
-  of participants.

## Reexamining Eccentricity

***Au-Au***

***Cu-Cu***

- When we examine the eccentricity distribution for CuCu,
-  it looks much broader than AuAu

- Also, notice that there are many more events with ***negative***
-  eccentricity.

## Meaning of Negative Eccentricity

- b

- y2

- x2

- Here we revisit the standard definition of eccentricity applied to a
- Gluaber model.

**Notes:**
As I mentioned before, we take the spread of the distribution in the x and y directions, having defined the x axis to lie along the impact parameter

## Meaning of Negative Eccentricity

- b

- y2

- x2

- Here we revisit the standard definition of eccentricity applied to a
- Gluaber model.

- Negative eccentricity results when
- x2 > y2, apparently due to fluctuations
- in the positions of the nucleons.

- Because of its smaller size, CuCu is more susceptible to fluctuations

## Redefining Eccentricity

- One reasonable method is to realign the coordinate system
- to maximize the ellipsoidal shape (a principal axis transformation)

- “Participant” eccentricity
- Opposed to “standard” eccentricity

## Standard and Participant Eccentricity

***Au-Au***

***Au-Au***

***Cu-Cu***

***Cu-Cu***

***Mean eccentricity shown in black***

- Standard Eccentricity

- Participant  Eccentricity

**Notes:**
And participant eccentricity

## Impact of Eccentricity Fluctuations

**Fluctuations in eccentricity are important for the Cu-Cu system.  **

***Must use care in doing Au-Au to Cu-Cu flow comparisons.  Eccentricity scaling depends on definition of eccentricity. ***

## Elliptic Flow Puzzle Solved?

**“****Participant Eccentricity” **
**allows v****2**** scaling from **
**Cu+Cu to Au+Au**

## <dN/dy> / <S> scaling

**Notes:**
Another popular way to look at this is the flow divided by the eccentricity versus one over the overlap area, S, times dN/dy.  One caveat is that phobos measures particles in eta, so we’ve applied a correction factor.

On this plot, we have not only Copper data from Phobos and Gold data from Phobos and Star, but also Lead from Cern, and energies spanning several order of magnitude.  

## Conclusions

- Phobos has continued to expand its extensive flow data set using two techniques
- Studying CuCu compared to AuAu allows us to vary the geometry while holding Npart constant
- The expectation that elliptic flow scales with eccentricity continues to seem reasonable
- Careful consideration is needed when using eccentricity

## Back-up Slides

## Limiting Fragmentation (Au+Au)

## Limiting Fragmentation (Cu+Cu)

## Compared to JAM Model

***Here JAM uses a 1 fm/c formation time.  Hydro (160) has kinetic freezeout temperature at 160 MeV***

***Statistical errors only***

**Notes:**
The low, red line is a prediction from the JAM model.  The upper two lines are hydro curves that were thought to be unrealistically high, but were included for comparison.  It turns out though that these curves are closer to the data.

Here we can also see the second surprise - that is that the flow is anomalously large for central collisions

## Two Flow Measurement Methods

***PHOBOS preliminary Cu-Cu, h******±***

***Hit based 200 GeV***

***Track based 200 GeV***

- Good agreement
- between methods

- || < 1

**Notes:**
For the runs in which we have used both techniques, they have agreed nicely, assuring us that our measurement is reasonable