Measuring scattering lengths at STAR
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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!