# Presentation: 554450

## LONG RANGE CORRELATIONS

**George Moschelli**

- Hot Quarks 2008
- Estes Park, Colorado

## OUTLINE

- Introduction
- Motivation from experiment
- “Long” vs “Short” range correlations
- CGC and Glasma
- Flux Tubes
- Correlation Function
- Qs Dependence
- Blast Wave
- Transverse Flow
- Results
- Glasma+Flow
- 200GeV62GeV fits
- Angular Correlations
- Summery

## PHOBOS: High pt Triggerd Ridge

- from Edward Wenger, RHIC & AGS User’s Meeting, ‘08

**Notes:**
Probably remove this slide

## PHOBOS: High pt Triggered Ridge

- from Edward Wenger, RHIC & AGS User’s Meeting, ‘08

- long range correlations

## PHOBOS: Untriggered Ridge

- from Edward Wenger, RHIC & AGS User’s Meeting, ‘08

**Soft Ridge:** two particle correlations with no high pt tag

**Very long range in rapidity?**
- v2 not yet removed

**Notes:**
Why does phi axis have 100 and 200?...degrees

## Flux Tubes and Glasma

**Flux Tubes:** longitudinal fields early on
- tubesquarks+gluons
**Correlated particles:** come from same flux tube
- Causally disconnected

- Cross sectional slices are the same

- Large 

**Notes:**
Causally disconnected: diffusion cannot erase these correlations
Light cones don’t overlap prior to freeze out

## Flux Tubes and the Correlation Function

- Partons from same flux tube are correlated
- Correlations between tubes are negligible

**Correlation Function:**

- flux tube transverse size ~ Qs-1 << RA

- correlation strength

- average number of tubes

**Notes:**
<N^2> R is a normalization picked in the Pruneau Volotion Gavin paper it is independent of efficiency

## Correlation Strength

- Gluon Rapidity Density
- Long range fluctuations scale the phase space density
- Energy and centrality dependence of correlation strength

- Dumitru, Gelis, McLerran & Venugopalan;
- Gavin, McLerran & Moschelli

- (Kharzeev & Nardi)

## Flow and Azimuthal Correlations

- Fluid cells

- STAR soft ridge

- Fireball cross section at freeze out

- r

- from Lanny Ray, RHIC & AGS User’s Meeting, ‘08

- Mean flow depends on position

- Opening angle for each fluid element depends on r

**Notes:**
Note ridge on lower right shows a broad gaussian shape in rapidity, our description would produce a flat ridge at the maximum peak height
Spike in top right comes from HBT and electrons from photon scattering

## Blast Wave and Correlation Function

- Single particle spectrum
- Correlations
- Cooper Frye Freeze Out

- Schnedermann, Sollfrank & Heinz

- Boltzman Distribution with rv=r

**Notes:**
Why do we devide f by number density again?...so that normalization of integral of r is same as integral of C

## STAR: Near Side Peak

- near side peak

- from Lanny Ray, RHIC & AGS User’s Meeting, ‘08

**Peak Amplitude**

**Peak ******** Width**

**Peak ******** Width**

**Implications for long range correlations?**

- Peak height and azimuthal width
- Rapidity width - structure too narrow to tell
- 	SG, Abdel-Aziz, Phys. Rev. Lett. 97 162302 (2006).

**Notes:**
Indicate 200 GeV and 62 GeV symbols

## Glasma + Blast Wave

**STAR measures:**

- Blast Wave v, T from singles
-  Uncertainty band
- Scale to fit 200 GeV
- Glasma Qs centrality dependence
-  	(Kharzeev and Nardi)

**We calculate:**

- 2Nbin/Npart

- STAR 200 GeV

**Peak Amplitude 200 GeV**

**Notes:**
Under We Calculate: we say deltaROE=integral_momenta{r(p1,p2)} this is for blast wave only. For black curve, deltaROE=integral*R*dN/dy

## 62 GeV Agreement!

- v and T from Blast Wave
- Scaled to fit 200 GeV
- Glasma Qs dependence 200 GeV62 GeV

- 2Nbin/Npart

## Angular Correlation Width

- Fit using gaussian + offset
- Range: -/2<</2
- 20% shift in fit range
- error band

**computed angular width is approximately independent of energy**

**Peak ******** Width**

**Notes:**
20% shift is uncertainty near side peak width

## Summery

- PHOBOS data indicates correlations at large 
- Long range correlations could come from CGC initial conditions
- Correlations are results of CGC + transverse flow

- THANK YOU!

## Backup Slides

## STAR: Untriggered Ridge

- from Lanny Ray, RHIC & AGS User’s Meeting, ‘08

**soft ridge: ****|********| < 2**

**Notes:**
Make backup slide

## Correlation Strength Derivation

## Blast Wave: v and T fits

- Fit momentum spectra in 200 GeV Au+Au
- Constrain 
- 10% systematic uncertainty in scale of v and T
- 62 GeV Au+Au: 5% smaller v, 10% smaller T

**Velocity @ r = R**

**temperature**

- Akio Kiyomichi, PHENIX

## Viscosity & Diffusion

- Momentum correlations