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-Lbar another proof of principle
• Outlook. Beyond the proof of principle!

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Why measuring p-p scattering lengths?

• High precision theoretical prediction
• Chiral perturbation theory
• Main assumption p 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 p-p scattering lengths at
STAR

• Rely on very high statistics
• Calculate coulomb using state-of-the-art code
• Measure purity from ???? CFs
• Measure source size from ???? CFs
• Can the systematic errors be kept under control?

p
Source
L
p-
p-
Uncorrelated pion fraction l from ????
Measured by ????
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Can STAR compete?
Yes, if systematic errors can be kept under
control
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Expected source of systematic errors

• Shape and size of the source
• What is the effect of non-Gaussian source?
• solution imaging, non-G parametrization,
  simulations
• Purity
• l depends heavily on Gaussian assumption
• solution imaging, non-G parametrization,
  simulations
• Momentum resolution
• Solution careful study of detector response
• Interaction calculation
• Cross-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 lengths
• If we dont, 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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p-p- Correlation function
STAR preliminary
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Fit by build a chi2 map
STAR preliminary
STAR preliminary
Theory predication
Scattering lengths driven to large value away
from theory and E865
Calculations systematically Below data
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Why are we so far off?

• No, it is not physics
• Shape of the source
• So 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
CFNorm Purity RQMD(r ? Scale?r)1-Purity
??? scattering length f0 from NA49 CF
RL nucl-th/0112011
???
Fit CF(???) by RQMD with SI scale f0 ?
sisca f0input f0input 0.232 fm
-
sisca 0.6?0.1 Compare with 0.8 from S?PT
BNL E865 K ? e???
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Twicking the chi2 map to estimate our sensitivity
Rescale purity and size to get the predicted
scattering lengths
1, 2 and 3 s contours
STAR preliminary
Contour made with 1 of the available
statistics The full statistics will be necessary
to reach high precision
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Second proof of principlep-Lbar correlation
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p-L, pbar-L, p-Lbar, pbar-Lbar
STAR preliminary
Analysis by Gael Renault and Richard Lednicky
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From correlation functions to source size
Problem 2 different radii!
STAR preliminary
Known scatt lengths
Unknown scattering length Fit scattering lengths
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The pbar-L scattering lengths
pp
STAR preliminary
Repulsive interaction (negative)
Annihilation
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But problem with baryon-baryonResidual
correlations

• Large contamination of p and L
• Decay does not destroy correlation
• p or g do not take away much momentum
• Residual correlations
• Some of them unknown

17 p-L ? p-L 10 L-L ? p(p)-L 7 p-S0 ?
p-L(g) 5 S-L ? p(p0)-L
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Conclusion and outlook

• STAR has the statistics to measure the p-p
  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!