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Non-identical particle correlationat 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)

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Outline

From flow to non-id correlationBlast-Wave based example

Extracting space-time offset from non-id correlation functions

Extracting unique space-time information-K, -p, K-p correlation functions

New analysesBaryon-baryon correlations scattering lengths

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Use Blast wave parameterization for discussing flow

R

t

RsideRout

Kt = pair Pt

Hydro-inspired parameterizationBoost invariant longitudinal flow

Transverse flowLinear rapidity profile

Azimuthal oscillation in non-central

Tunable system size, shape and life time

Parameterizationof the final state

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

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Blast wave parameterization 2

22 /2/)(

/

),(

)cosh(,

tt

s

TuKT

e

r

eYmKxS

“Hydro-like” parameterization Boltzman with Flow

Flow: (r) = (0 +2 cos(2p)) r

– Grows linearly increasing r

– May vary with angle wrt event plane

Parameters: T, 0 and 2

System geometryElliptical box (fuzzy edges possible)

Parameters: Rx (in-plane) and Ry (out-of-plane)

TimeParameters: proper life time () and emission duration (t)

To calculate: - Spectra = integral over spaceand momentum azimuthal angle - v2(pt) = average of cos(2fp)overspace at a given pt - Hbt radii (pt) = standard deviations along out, side and long directions at a given pt

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AuAu 130 GeVFR. M. Lisa, Phys.Rev. C70 (2004) 044907

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Au-Au 200 GeV

T=106 ± 1 MeV<InPlane> = 0.571 ± 0.004 c<OutOfPlane> = 0.540 ± 0.004 cRInPlane = 11.1 ± 0.2 fmROutOfPlane = 12.1 ± 0.2 fmLife time () = 8.4 ± 0.2 fm/cEmission duration = 1.9 ± 0.2 fm/c2/dof = 120 / 86

Spectra

v2

HBT

Same thing from data availableat QM04

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Blast wave and space-time

RsideRout

RsideRout

PT=160 MeV/c PT=380 MeV/c

KT

Rout

Rside

RlongTime

Sketch by Scott Pratt

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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

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pion

Kaon

Proton

Distribution of emissionpoints at a given emission momentum.

Particles are correlated whentheir velocities are similar.Keep velocity constant: - Left, x = 0.73c, y = 0 - Right, x = 0.91c, y = 0

Dash lines: average emissionRadius. <Rx()> < <rx(K)> < <Rx(p)>

px = 0.15 GeV/c

px = 0.53 GeV/c px = 1.07 GeV/c

px = 2.02 GeV/cpx = 1.01 GeV/c

px = 0.3 GeV/c

Looking at different particles

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Blast wave and time shift

Time

spread for pions and kaonsemitted at mid-rapidity

t = cosh() <t()> > <t(K)>

Note: our Blast Wavefreeze-out at constant2 = (t2-z2)

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Boosting to pair rest frame where the action takes place

Particle 1source

Particle 2Source

Separation between particle1 and 2 andBoost to pairRest frame

r*out = T (rout – T t)

2 free parameters in the Gaussian approximationWidth of the distribution in pair rest frame

Offset of the distribution from zero

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Offsets

Parameters from best fit to central Au-Au @ 130 GeV

No tuning

LegendDot = -t

Dash = rout

Plain = r*out

-K

-p

K-p

13R.Lednicky, V. Lyuboshitz, B. Erazmus, D. Nouais, Phys.Lett. B 373 (1996) 30.

• Effective interaction time Effective interaction time shortershorter• Weaker correlationWeaker correlation

A) faster particle flying away

• Effective interaction time Effective interaction time largerlarger

• Stronger correlationStronger correlation

B) faster particle catching up

Measuring offset by kinematic selection

If space-time ordering, select between 2 configurations

One particle catching upParticles moving away from each others

Final state interactions yield different correlations for these 2 configuration

Always for Coulomb Sometimes for strong

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Final state interactions

k* Correlation function

Relative momentum in pair rest frame

Select particles with same velocities

Same momentum if same mass

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Example of -K correlation function

Pion slower Pion faster

STAR AuAu @ 130 GeV, central

Coulomb driven

Sensitive to kinematic selection

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-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

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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

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Gaussian fit parameter

Two parameter fitWidth

Related to both particle source size

Offset

Calculate offsets from models

130 GeV

Compilation by A. Kisiel (QM04)

200 GeV

STAR preliminary

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The dark side of the story

Large systematic errorsPurity correction

No to absorb it

Gaussian shape

Not so well known interactionWait, this is not so bad

Solution: look at relative variations

varying pt

varying centralityBut baseline problem

Baseline issuesPossibly due to event by event variation of spectra slope introduce

Study system with large statistical errors …

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Ξ*Ξ*

unlike-sign particles

like-sign particles

__ R from pi -pi

.... R*0.75

--- R*1.25

✗ Coulomb and strong Coulomb and strong interactioninteraction effects effects visible.visible.

✗ Ξ* peak is very Ξ* peak is very sensitive sensitive to the source to the source size, whilesize, while Coulomb Coulomb not as much.not as much.

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

RQMD simulationRQMD simulation

- correlation functions

Analysis by Petr Chaloupka

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Testing different hypothesis

STAR preliminary

source size << source size source size = source size

10 fm offset included in both calculations

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Wait until QM05 for more on

Moving on to baryon-baryon correlation

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p-, pbar-, p-bar, pbar-bar

STAR preliminary

Analysis by Gael Renault and Richard Lednicky

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Fit and extract source size

STAR preliminary

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From correlation functions to source size

Known scatt lengths

Unknown scattering lengthFit scattering lengths

Problem:2 different radii!

STAR preliminary

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Purity and residual correlation

Large contamination of p and Decay does not destroy correlation

or do not take away much momentum

Residual correlationsSome of them unknown

17% p- → p-- → p()-p-→ p-()+-→ p()-…

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Problem: 2 different radii

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The pbar- scattering lengths

Annihilation

Rep

ulsi

ve in

tera

ctio

n (n

egat

ive)

STAR preliminary

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High precision - scattering lengths

High statistics

Coulomb dominatedBut 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 pionFraction from HBT

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Why measuring - scattering lengths?

High precision theoretical prediction

Chiral perturbation theoryMain assumption: mass from quark condensate

Probe property of QCD vacuum

Experiments trying to catch up

E865 from kaon decay

Dirac. Pionium lifetime

Theory

Experiment

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Calculate correlation function using HBT radii and purity

Theory predication

Scattering lengths driven to large value away from theory and E865

Calculations systematicallyBelow data

Analysis by Michal Bystersky (Prague)

STAR preliminary

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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

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SummaryFrom 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 promisingWait until QM05

Attempt to measure p-p scattering lengths with high precision

New window onto the strong interaction

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Back up

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Hanna Gos (Warsaw/Nantes)

proton - antiproton

proton - proton

2 k* (GeV/c) 2 k* (GeV/c)