# Presentation: 505514

## Correlation Functions:Getting Into Shape D.Brown, P.Danielewicz, S.Petriconi and S.Pratt

- Scott Pratt                                                                                    Michigan State University

## Main Goal: Determine S

**Measure C(q****x****,q****y****,q****z****)**

- Scott Pratt                                                                                    Michigan State University

## Visualizing S

**S****P****(r) = distribution of relative coordinates **

- Scott Pratt                                                                                    Michigan State University

## Visualizing S

**Visualizing S**

- Scott Pratt                                                                                    Michigan State University

## Lifetimes fromHBT

**Lifetimes from****HBT**

- Scott Pratt                                                                                    Michigan State University

## Frightening Results from RHIC

**Frightening Results from RHIC**

_**Hydro overpredicts:**_
** ****R****side**** by 0% **
**R****beam**** by ~ 50%**
** ****R****out****  by ~ 50%**

**HYDRO+URQMD**

- Scott Pratt                                                                                    Michigan State University

## Simple Boltzmann Calculation (GROMIT)T. Humanic, AMPT, D. Molnar, S.P.

**Simple Boltzmann Calculation (GROMIT)****T. Humanic, AMPT, D. Molnar, S.P.**

** ****Underpredicts *****R********* !**** **
** ****Underpredicts ******** !**** **
** ****Slightly overpredicts ******

- Scott Pratt                                                                                    Michigan State University

## Frightening results from RHIC

**Suggests NO LATENT HEAT**
**Not so many extra degrees of freedom**
**Incompatible with Lattice EOS**
**Hard-EOS cascade does better (AMPT....)**
**Still has problems with R****side**
**Independent measurement would help**

- Scott Pratt                                                                                    Michigan State University

## Can one determine Rout/Rlong/Rsidewith other classes of correlations?

**Classical Coulomb IMF-IMF Correlations****	****	****	****	****	****	****Kim et al, PRC, (92)**
**Lednicky q+/q- correlations**

- Scott Pratt                                                                                    Michigan State University

## Coulomb correlations

**Classically, determined by trajectories**

**Q**

- Scott Pratt                                                                                    Michigan State University

## Coulomb correlations

- Scott Pratt                                                                                    Michigan State University

## Classical Coulomb correlations

- Scott Pratt                                                                                    Michigan State University

## pK+ correlations

**R****out****=8 fm, R****side**** = R****beam**** = 4 fm**

**Classical approximation works well for Q > 50 MeV/c**

- Scott Pratt                                                                                    Michigan State University

## pK+ correlations

- Rout=8 fm, Rside = Rbeam = 4 fm

- Scott Pratt                                                                                    Michigan State University

## Coulomb correlations

** ****Sensitive to shape / lifetime !!!**
**Difficulty: Correlation in tails ~ 1%**
** ****Residual interactions can be subtracted away**

- Scott Pratt                                                                                    Michigan State University

## Strong interactions

**Everything determined by phase shifts**

- Scott Pratt                                                                                    Michigan State University

## Strong interactions

- Scott Pratt                                                                                    Michigan State University

## p+ correlations

- Rout=8 fm, Rside = Rbeam = 4 fm

- Scott Pratt                                                                                    Michigan State University

## Angular Moments

**Defining,**

**Using identities for Y****lm****s,**

- Scott Pratt                                                                                    Michigan State University

## Moments

** ****L=0**** **
** ****L=1, M=1**** **
** ****L=2, M=0,2**** **
** ****L=3, M=1,3**

**Angle-integrated shape**

**Lednicky offsets**

**Shape (R****out****/R****side****, R****long****/R****side****)**

***Boomerang *****distortion**

- Scott Pratt                                                                                    Michigan State University

## Blast Wave Moments

**Blast Wave Moments**

** ****(z ******** -z)****  C****L+M=even****(q) = 0**** **
** ****(y ******** -y)****  Imag C****L,M**** = 0**

- Scott Pratt                                                                                    Michigan State University

## Cartesian Harmonics

- Scott Pratt                                                                                    Michigan State University

## Cartesian Harmonics

- Scott Pratt                                                                                    Michigan State University

## Expansions...

**Advantage: More intuitive**

- Scott Pratt                                                                                    Michigan State University

## Conclusions

**Strong and Coulomb provide 3-d resolving power**
**Resonances : ********, K*, ********, ************...**
**Small Q****inv**** : pK, ********p, pp, ...**** **
**Moment analyses are POWERFUL**
**Reduces to 1-d problems for each L,M**
**Cartesian moments **

- Scott Pratt                                                                                    Michigan State University

## CorAL, version 1.0Correlation Analysis LibraryDave Brown, Mike Heffner, Scott Pratt

**Calculate |********(q,r)|****2**
**(********, ********p, pp, pn, nn, ********K, pK, p********, ********, p********, ...)**
**Correlations from models**
**Gaussian, Blast Wave, OSCAR files...**
**Fitting capability**
**Imaging capability**
**Integrated Y****Lm**** and Cartesian moment analyses**
**Available Summer 2005**

- Scott Pratt                                                                                    Michigan State University

## Strong interactions

- One can integrate analytically,

- Scott Pratt                                                                                    Michigan State University