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-  bar another proof of principle Outlook. Beyond the proof of principle!

3 Why measuring  -  scattering lengths? High precision theoretical prediction Chiral perturbation theory Main assumption:  mass from quark condensate Probe property of QCD vacuum Experiments trying to catch up E865 from kaon decay Dirac. Pionium lifetime Theory Experiment

4 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    

5 Can STAR compete? StatisticsSourcePion purityInteraction model Kaon decay - Dynamical effect calculable Not an issueReliable Dirac5% stat. error in |a 0 -a 2 | at present Measured, but its influence is < 5% in |a 0 -a 2 | e + e -,  +  - rejected by Č &  detectors |a 0 -a 2 | -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

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 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 k T /centrality dependence provide a key handle on systematic errors 4 k T 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  + -  - Correlation function STAR preliminary

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

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 -  +   scattering length f 0 from NA49 CF Fit CF(  +   ) by RQMD with SI scale: f 0  sisca f 0 input f 0 input = fm sisca = 0.6  0.1 Compare with ~0.8 from S  PT & BNL E865 K  e  ++ CF=Norm [ Purity RQMD(r*  Scale  r*)+1-Purity] RL nucl-th/

13 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 statistics The full statistics will be necessary to reach high precision STAR preliminary

14 Second proof of principle: p-  bar correlation

15 p- , pbar- , p-  bar, pbar-  bar STAR preliminary Analysis by Gael Renault and Richard Lednicky

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

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

18 But problem with baryon-baryon Residual correlations Large contamination of p and  Decay does not destroy correlation  or  do not take away much momentum Residual correlations Some of them unknown 17% p-  → p-   -  → p(   )-   p-    → p-  (  )  + -  → p(   )-  …

19 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 (k T 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!