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## Measuring scattering lengths at STAR

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**Measuring scattering lengths at STAR**Michal Bystersky (Prague) and Fabrice Retière (TRIUMF)**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!**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**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 **Can STAR compete?**Yes, if systematic errors can be kept under control**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**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**p+-p- Correlation function**STAR preliminary**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**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.**NA49 correlation study of interaction**CF=Norm[Purity RQMD(r*Scaler*)+1-Purity] +scattering length f0 from NA49 CF RL nucl-th/0112011 + Fit CF(+) by RQMD with SI scale: f0siscaf0input f0input = 0.232 fm - sisca = 0.60.1 Compare with ~0.8 from SPT & BNL E865 K e**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**p-L, pbar-L, p-Lbar, pbar-Lbar**STAR preliminary Analysis by Gael Renault and Richard Lednicky**From correlation functions to source size**Problem: 2 different radii! STAR preliminary Known scatt lengths Unknown scattering length Fit scattering lengths**The pbar-L scattering lengths**pp STAR preliminary Repulsive interaction (negative) Annihilation**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 …**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!