Measuring Scattering Lengths at STAR: Insights into Pion Correlation Functions and QCD

1. Measuring scattering lengths at STAR Michal Bystersky (Prague) and Fabrice Retière (TRIUMF)

2. 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!

3. 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 Why measuring p-p scattering lengths? Theory Experiment

4. 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? Strategy for measuring p-p scattering lengths at STAR p+ Source L p- p- Uncorrelated pion fraction l from  Measured by 

5. Can STAR compete? Yes, if systematic errors can be kept under control

6. 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

7. 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 don’t, back to square one • More cross-check with Cu-Cu and d-Au

8. First look at the data

9. p+-p- Correlation function STAR preliminary

10. Fit by build a chi2 map STAR preliminary STAR preliminary Theory predication Calculations systematically Below data Scattering lengths driven to large value away from theory and E865

11. 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.

12. NA49 correlation study of  interaction CF=Norm[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siscaf0input f0input = 0.232 fm - sisca = 0.60.1 Compare with ~0.8 from SPT & BNL E865 K  e

13. 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

14. Second proof of principle:p-Lbar correlation

15. p-L, pbar-L, p-Lbar, pbar-Lbar STAR preliminary Analysis by Gael Renault and Richard Lednicky

16. From correlation functions to source size Problem: 2 different radii! STAR preliminary Known scatt lengths Unknown scattering length Fit scattering lengths

17. The pbar-L scattering lengths pp STAR preliminary Repulsive interaction (negative) Annihilation

18. 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 …

19. 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!