# Presentation: 422166

## Non-identical particle correlationat RHIC*From flow to strong interaction

*With a lot of help from STAR HBT group*

- *Similar analyses at AGS and SPS (see Mike Lisa’s talk)

## Outline

- From flow to non-id correlation
- Blast-Wave based example
- Extracting space-time offset from non-id correlation functions
- Extracting unique space-time information
- -K, -p, K-p correlation functions
- New analyses
- 
- Baryon-baryon correlations
-  scattering lengths

## Use Blast wave parameterization for discussing flow

- Hydro-inspired parameterization
- Boost invariant longitudinal flow
- Transverse flow
- Linear rapidity profile
- Azimuthal oscillation in non-central
- Tunable system size, shape and life time

- Parameterization
- of the final state

- Inspired by E.Schnedermann, J. Sollfrank, and U. Heinz, PRC 48 (2002) 2462

## Blast wave parameterization 2

- “Hydro-like” parameterization
- Boltzman with Flow
- Flow: (r) = (0 +2 cos(2p)) r
- Grows linearly increasing r
- May vary with angle wrt event plane
- Parameters: T, 0 and 2
- System geometry
- Elliptical box (fuzzy edges possible)
- Parameters: Rx (in-plane) and Ry (out-of-plane)
- Time
- Parameters: proper life time () and emission duration (t)

- To calculate:
-   - _Spectra_ = integral over space
- and momentum azimuthal angle
-   - _v2(pt)_ = average of cos(2fp)over
- space at a given pt
-   - _Hbt radii (pt)_ = standard deviations along out, side and long directions at a given pt

## AuAu 130 GeV

- FR. M. Lisa, Phys.Rev. C70 (2004) 044907

## Au-Au 200 GeV

- T=106 ± 1 MeV
- <InPlane> = 0.571 ± 0.004 c
- <OutOfPlane> = 0.540 ± 0.004 c
- RInPlane = 11.1 ± 0.2 fm
- ROutOfPlane = 12.1 ± 0.2 fm
- Life time () = 8.4 ± 0.2 fm/c
- Emission duration = 1.9 ± 0.2 fm/c
- 2/dof = 120 / 86

- Spectra

- v2

- HBT

- Same thing from data available
- at QM04

## Blast wave and space-time

- Rside

- Rout

- Rside

- Rout

- PT=160 MeV/c

- PT=380 MeV/c

****

- Rlong

- Time

- Sketch by
- Scott Pratt

## Shopping off in the transverse plane

- Probability density of emitting a pion with px = 500 MeV/c, py=0

- Y

- X

- Infinite system

- Bounded system

-  Squeeze out (x here) and side (y here) against the edge
-  pt dependence of both side and out

## Looking at different particles

- pion

- Kaon

- Proton

- Distribution of emission
- points at a given emission momentum.
- Particles are correlated when
- their velocities are similar.
- Keep velocity constant:
-   - Left, x = 0.73c, y = 0
-   - Right, x = 0.91c, y = 0
- Dash lines: average emission
- Radius.
-  <Rx()> < <rx(K)> < <Rx(p)>

- px = 0.15 GeV/c

- px = 0.53 GeV/c

- px = 1.07 GeV/c

- px = 2.02 GeV/c

- px = 1.01 GeV/c

- px = 0.3 GeV/c

## Blast wave and time shift

- Time

-  spread for pions and kaons
- emitted at mid-rapidity

- t =  cosh()  <t()> > <t(K)>

- Note: *our* Blast Wave
- freeze-out at constant
- 2 = (t2-z2)

## Boosting to pair rest frame where the action takes place

- Particle 1
- source

- Particle 2
- Source

- Separation
- between particle
- 1 and 2 and
- Boost to pair
- Rest frame

- r*out = T (rout – T t)

- 2 free parameters in the Gaussian approximation
- Width of the distribution in pair rest frame
- Offset of the distribution from zero

## Offsets

- Parameters from best fit to central Au-Au @ 130 GeV
- No tuning
- Legend
- Dot = -t
- Dash = rout
- Plain = r*out

- -K

- -p

- K-p

## Measuring offset by kinematic selection

- If space-time ordering, select between 2 configurations
- One particle catching up
- Particles moving away from each others
- Final state interactions yield different correlations for these 2 configuration
- Always for Coulomb
- Sometimes for strong

## Final state interactions

- k* Correlation function
- Relative momentum in pair rest frame
- Select particles with same velocities
- Same momentum if same mass

## Example of -K correlation function

- Example of -K correlation function

- Pion slower

- Pion faster

- STAR AuAu @ 130 GeV, central

- Coulomb driven
- Sensitive to kinematic selection

## -K correlation at 130 GeV

- Ratios of correlation functions
- Side and long must be flat for symmetry
- Out, along the pair transverse velocity is not flat
- Pion and kaon sources are shifted

- Phys. Rev. Lett. **91** (2003) 262302

## Comparing correlation functions directly to models

- Calculate correlation functions from models accounting for Coulomb and strong interactions
- Code by R.Lednicky

- Phys. Rev. Lett. **91** (2003) 262302

## Gaussian fit parameter

- Two parameter fit
- Width
- Related to both particle source size
- Offset
- Calculate offsets from models

- 130 GeV

- Compilation by A. Kisiel (QM04)

- 200 GeV

- STAR preliminary

## The dark side of the story

- Large systematic errors
- Purity correction
- No  to absorb it
- Gaussian shape
- Not so well known interaction
- Wait, this is not so bad
- Solution: look at relative variations
- varying pt
- varying centrality
- But baseline problem

- Baseline issues
- Possibly due to event by event variation of spectra slope introduce

-  Study system with
- large statistical errors ...

## - correlation functions

**Coulomb and strong interaction**** effects visible.**
**Ξ* peak is very sensitive ****to the source size, while**** Coulomb not as much.****  **

- Rout=10fm ,
- Rside=5.5fm ,
- Rlong=6.9 fm

- - correlation functions

- Analysis by Petr Chaloupka

## Testing different hypothesis

- STAR preliminary

-  source size <<  source size

-  source size =  source size

- 10 fm offset included
- in both calculations

## Wait until QM05 for more on  

- Moving on to baryon-baryon correlation

## p-, pbar-, p-bar, pbar-bar 

- STAR preliminary

- Analysis by Gael Renault and Richard Lednicky

## Fit and extract source size

- STAR preliminary

## From correlation functions to source size

*Known* scatt lengths

- Unknown scattering length
- Fit scattering lengths

**Problem:**
**2 different radii!**

- STAR preliminary

## Purity and residual correlation 

- Large contamination of p and 
- Decay does not destroy correlation
-  or  do not take away much momentum
- Residual correlations
- Some of them unknown

- 17% p- → p-
- - → p()-
- p-→ p-()
- +-→ p()-
- ...

## Problem: 2 different radii

## The pbar- scattering lengths

- Annihilation

- Repulsive interaction (negative)

- STAR preliminary

## High precision - scattering lengths

- High statistics
- Coulomb dominated
- But calculable
- Purity measured by HBT
- Source measured by HBT
- Can we keep the systematic errors under control?
- Key crosscheck: source size and purity vary with pT range and centrality  but scatt lengths do NOT

- Source

- +

- -

- -

- 

- Measured by HBT

- Uncorrelated pion
- Fraction  from HBT

## Why measuring - scattering lengths?

- Why measuring - scattering lengths?

- High precision theoretical prediction
- Chiral perturbation theory
- Main assumption:  mass from quark condensate
- Probe property of QCD vacuum
- Experiments trying to catch up
- E865 from kaon decay
- Dirac. Pionium lifetime

- Theory

- Experiment

## Calculate correlation function using HBT radii and purity 

- Theory predication

**Scattering lengths driven to large **
**value away from theory and E865**

**Calculations systematically**
**Below data**

- Analysis by Michal Bystersky (Prague)

- STAR preliminary

## Twicking the chi2 map to estimate our sensitivity

- 1, 2 and 3  contours

- Rescale purity and size and refit

- From  ~250k central events
- Looks like we will use all the statistics we can get

- STAR preliminary

## SummaryFrom flow to strong interaction

- Non-id correlation probe a unique feature of flow
- Space-time offset between sources of different particle species
- Nice qualitative results from -K, -p, K-p
- Systematic errors being worked out
- Blast Wave agree with data qualitatively

- Baryon-baryon correlation are promising
- But hard because of large feeddown
- Residual correlations
- Measure unknown scattering lengths
-  very promising
- Wait until QM05
- Attempt to measure p-p scattering lengths with high precision
- New window onto the strong interaction

## Back up

- Hanna Gos (Warsaw/Nantes)

- proton - antiproton

- proton - proton

- 2 k* (GeV/c)

- 2 k* (GeV/c)