2. 1 Non-identical particle correlation at RHIC* From flow to strong interaction With a lot of help from STAR HBT group *Similar analyses at AGS and SPS (see Mike Lisa’s talk)

3. 2 Outline From flow to non-id correlation Blast-Wave based example Extracting space-time offset from non-id correlation functions Extracting unique space-time information  -K,  -p, K-p correlation functions New analyses  Baryon-baryon correlations  scattering lengths

4. 3 Use Blast wave parameterization for discussing flow R tt Rside Rout Kt = pair Pt Hydro-inspired parameterization Boost invariant longitudinal flow Transverse flow Linear rapidity profile Azimuthal oscillation in non-central Tunable system size, shape and life time Parameterization of the final state Inspired by E.Schnedermann, J. Sollfrank, and U. Heinz, PRC 48 (2002) 2462

5. 4 Blast wave parameterization 2 “Hydro-like” parameterization Boltzman with Flow Flow:  (r) = (  0 +  2 cos(2  p )) r –Grows linearly increasing r –May vary with angle wrt event plane Parameters: T,  0 and  2 System geometry Elliptical box (fuzzy edges possible) Parameters: Rx (in-plane) and Ry (out- of-plane) Time Parameters: proper life time (  ) and emission duration (  t) To calculate: - Spectra = integral over space and momentum azimuthal angle - v2(pt) = average of cos(2f p )over space at a given pt - Hbt radii (pt) = standard deviations along out, side and long directions at a given pt

6. 5 AuAu 130 GeV FR. M. Lisa, Phys.Rev. C70 (2004) 044907

7. 6 Au-Au 200 GeV T=106 ± 1 MeV = 0.571 ± 0.004 c = 0.540 ± 0.004 c R InPlane = 11.1 ± 0.2 fm R OutOfPlane = 12.1 ± 0.2 fm Life time (  ) = 8.4 ± 0.2 fm/c Emission duration = 1.9 ± 0.2 fm/c  2 /dof = 120 / 86 Spectra v2v2 HBT Same thing from data available at QM04

8. 7 Blast wave and space-time Rside Rout RsideRout P T =160 MeV/cP T =380 MeV/c KTKT R out R side  R long Time Sketch by Scott Pratt

9. 8 Shopping off in the transverse plane Probability density of emitting a pion with px = 500 MeV/c, py=0 Y X Infinite systemBounded system  Squeeze out (x here) and side (y here) against the edge  pt dependence of both side and out

10. 9 pion Kaon Proton Distribution of emission points at a given emission momentum. Particles are correlated when their velocities are similar. Keep velocity constant: - Left,  x = 0.73c,  y = 0 - Right,  x = 0.91c,  y = 0 Dash lines: average emission Radius.  p x = 0.15 GeV/c p x = 0.53 GeV/cp x = 1.07 GeV/c p x = 2.02 GeV/cp x = 1.01 GeV/c p x = 0.3 GeV/c Looking at different particles

11. 10 Blast wave and time shift Time  spread for pions and kaons emitted at mid-rapidity t =  cosh(  )  > Note: our Blast Wave freeze-out at constant  2 = (t 2 -z 2 )

12. 11 Boosting to pair rest frame where the action takes place Particle 1 source Particle 2 Source Separation between particle 1 and 2 and Boost to pair Rest frame  r* out =  T (  r out –  T  t) 2 free parameters in the Gaussian approximation Width of the distribution in pair rest frame Offset of the distribution from zero

13. 12 Offsets Parameters from best fit to central Au-Au @ 130 GeV No tuning Legend Dot = -  t Dash =  r out Plain =  r* out  -K  -p K-p

14. 13 R.Lednicky, V. Lyuboshitz, B. Erazmus, D. Nouais, Phys.Lett. B 373 (1996) 30. Effective interaction time shorter Effective interaction time shorter Weaker correlation Weaker correlation A) faster particle flying away Effective interaction time larger Effective interaction time larger Stronger correlation Stronger correlation B) faster particle catching up Measuring offset by kinematic selection If space-time ordering, select between 2 configurations One particle catching up Particles moving away from each others Final state interactions yield different correlations for these 2 configuration Always for Coulomb Sometimes for strong

15. 14 Final state interactions k* Correlation function Relative momentum in pair rest frame Select particles with same velocities Same momentum if same mass

16. 15 Example of  -K correlation function Pion slower Pion faster STAR AuAu @ 130 GeV, central Coulomb driven Sensitive to kinematic selection

17. 16  -K correlation at 130 GeV Ratios of correlation functions Side and long must be flat for symmetry Out, along the pair transverse velocity is not flat Pion and kaon sources are shifted Phys. Rev. Lett. 91 (2003) 262302

18. 17 Comparing correlation functions directly to models Calculate correlation functions from models accounting for Coulomb and strong interactions Code by R.Lednicky Phys. Rev. Lett. 91 (2003) 262302

19. 18 Gaussian fit parameter Two parameter fit Width Related to both particle source size Offset Calculate offsets from models 130 GeV Compilation by A. Kisiel (QM04) 200 GeV STAR preliminary

20. 19 The dark side of the story Large systematic errors Purity correction No to absorb it Gaussian shape Not so well known interaction Wait, this is not so bad Solution: look at relative variations varying pt varying centrality But baseline problem Baseline issues Possibly due to event by event variation of spectra slope introduce  Study system with large statistical errors …

21. 20 Ξ* unlike-sign particles like-sign particles __ R from pi -pi.... R*0.75 --- R*1.25 ✗ Coulomb and strong interaction effects visible. ✗ Ξ* peak is very sensitive to the source size, while Coulomb not as much. Rout=10fm, Rside=5.5fm, Rlong=6.9 fm RQMD simulation  -  correlation functions Analysis by Petr Chaloupka

22. 21 Testing different hypothesis STAR preliminary  source size <<  source size  source size =  source size 10 fm offset included in both calculations

23. 22 Wait until QM05 for more on  Moving on to baryon-baryon correlation

24. 23 p- , pbar- , p-  bar, pbar-  bar STAR preliminary Analysis by Gael Renault and Richard Lednicky

25. 24 Fit and extract source size STAR preliminary

26. 25 From correlation functions to source size Known scatt lengths Unknown scattering length Fit scattering lengths Problem: 2 different radii! STAR preliminary

27. 26 Purity and residual correlation 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(   )-  …

28. 27 Problem: 2 different radii

29. 28 The pbar-  scattering lengths Annihilation Repulsive interaction (negative) STAR preliminary

30. 29 High precision  -  scattering lengths High statistics Coulomb dominated But calculable Purity measured by HBT Source measured by HBT Can we keep the systematic errors under control? Key crosscheck: source size and purity vary with p T range and centrality but scatt lengths do NOT Source ++ -- --  Measured by HBT Uncorrelated pion Fraction from HBT

31. 30 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

32. 31 Calculate correlation function using HBT radii and purity Theory predication Scattering lengths driven to large value away from theory and E865 Calculations systematically Below data Analysis by Michal Bystersky (Prague) STAR preliminary

33. 32 Twicking the chi2 map to estimate our sensitivity 1, 2 and 3  contours Rescale purity and size and refit From ~250k central events Looks like we will use all the statistics we can get STAR preliminary

34. 33 Summary From flow to strong interaction Non-id correlation probe a unique feature of flow Space-time offset between sources of different particle species Nice qualitative results from  -K,  -p, K-p Systematic errors being worked out Blast Wave agree with data qualitatively Baryon-baryon correlation are promising But hard because of large feeddown Residual correlations Measure unknown scattering lengths  very promising Wait until QM05 Attempt to measure p-p scattering lengths with high precision New window onto the strong interaction

35. 34 Back up

36. 35 Hanna Gos (Warsaw/Nantes) proton - antiproton proton - proton 2 k* (GeV/c)