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Measuring scattering lengths at STAR

Michal Bystersky (Prague) and Fabrice Retière (TRIUMF)

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Outline

Measuring scattering length at STAR, motivation and strategy

First look at the scattering length from pion-pion correlation function. A proof of principle.

p-bar another proof of principle

Outlook. Beyond the proof of principle!

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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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Strategy for measuring - scattering lengths at STAR

Rely on very high statistics

Calculate coulomb using state-of-the-art code

Measure purity from

CF’s

Measure source size from CF’s

Can the systematic errors be kept under control?

Source

+

- -

Measured by

Uncorrelated pion fraction from

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Can STAR compete?

Statistics Source Pion purity Interaction model

Kaon decay - Dynamical effect calculable

Not an issue Reliable

Dirac 5% stat. error in |a0-a2| at present

Measured, but its influence is < 5% in |a0-a2|

e+e-, + -

rejected by Č & detectors

|a0-a2|-2 -1/2 better than 1%

STAR + Not known. Need to be measured

Not known.

Need to be measured

Code from R. Lednicky and S. Pratt

Yes, if systematic errors can be kept under control

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Expected source of systematic errors

Shape and size of the sourceWhat is the effect of non-Gaussian source?

solution: imaging, non-G parametrization, simulations

Purity depends heavily on Gaussian assumption

solution: imaging, non-G parametrization, simulations

Momentum resolutionSolution: careful study of detector response

Interaction calculationCross-check models

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kT/centrality dependence provide akey handle on systematic errors

4 kT x 6 centrality = 24 independent systems in Au-Au collisions

We should measure the same scattering lengthsIf we don’t, back to square one

More cross-check with Cu-Cu and d-Au

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First look at the data

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+-- Correlation function

STAR preliminary

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Fit by build a chi2 map

Theory predication

Scattering lengths driven to large value away from theory and E865

Calculations systematicallyBelow data

STAR preliminarySTAR preliminary

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Why are we so far off?

No, it is not physics

Shape of the sourceSo far, Gaussian assume but NA49 Fig.

Error in parameterization (e.g. wrong frame)

Issues with the calculation

This is work in progress. No conclusion to be drawn at that stage.

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NA49 correlation study of interaction

-

+ scattering length f0 from NA49 CF

Fit CF(+) by RQMD with SI scale: f0 sisca f0

input f0

input = 0.232 fm

sisca = 0.60.1 Compare with

~0.8 from SPT & BNL E865

K e

+

CF=Norm [Purity RQMD(r* Scaler*)+1-Purity]

RL nucl-th/0112011

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Twicking the chi2 map to estimate our sensitivity

1, 2 and 3 contours

Rescale purity and size to get the predicted scattering lengths

Contour made with ~1% of the available statisticsThe full statistics will be necessary to reach high precision

STAR preliminary

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Second proof of principle:p-bar correlation

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

STAR preliminary

Analysis by Gael Renault and Richard Lednicky

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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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The pbar- scattering lengths

Annihilation

Rep

ulsi

ve in

tera

ctio

n (n

egat

ive)

STAR preliminary

pp

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But problem with baryon-baryonResidual correlations

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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Conclusion and outlook

STAR has the statistics to measure the scattering length with very high accuracy

The challenge is beating down the systematic errors

We have a handle varying source size (kT or centrality)

We will probably need to use imaging to avoid making assumptions about the source shape

Stay tune; RHIC is entering the era of high precision QCD looking at two-particle correlation!