Non-identical particle correlation at RHIC* From flow to strong interaction

1. Non-identical particle correlationat 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)

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 • p-K, p-p, K-p correlation functions • New analyses • p-X • Baryon-baryon correlations • p-p scattering lengths

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

4. “Hydro-like” parameterization Boltzman with Flow Flow: r(r) = (r0 +r2 cos(2fp)) r Grows linearly increasing r May vary with angle wrt event plane Parameters: T, r0 and r2 System geometry Elliptical box (fuzzy edges possible) Parameters: Rx (in-plane) and Ry (out-of-plane) Time Parameters: proper life time (t) and emission duration (Dt) Blast wave parameterization 2 To calculate: - Spectra = integral over space and momentum azimuthal angle - v2(pt) = average of cos(2fp)over space at a given pt - Hbt radii (pt) = standard deviations along out, side and long directions at a given pt

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

6. Au-Au 200 GeV Spectra T=106 ± 1 MeV <bInPlane> = 0.571 ± 0.004 c <bOutOfPlane> = 0.540 ± 0.004 c RInPlane = 11.1 ± 0.2 fm ROutOfPlane = 12.1 ± 0.2 fm Life time (t) = 8.4 ± 0.2 fm/c Emission duration = 1.9 ± 0.2 fm/c c2/dof = 120 / 86 v2 HBT Same thing from data available at QM04

7. KT Rout Rside Blast wave and space-time PT=160 MeV/c PT=380 MeV/c Rside Rout Rside Rout Dt Time Rlong Sketch by Scott Pratt

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

9. pion Looking at different particles Distribution of emission points at a given emission momentum. Particles are correlated when their velocities are similar. Keep velocity constant: - Left, bx = 0.73c, by = 0 - Right, bx = 0.91c, by = 0 Dash lines: average emission Radius.  <Rx(p)> < <rx(K)> < <Rx(p)> px = 0.3 GeV/c px = 0.15 GeV/c Kaon px = 0.53 GeV/c px = 1.07 GeV/c Proton px = 1.01 GeV/c px = 2.02 GeV/c

10. Blast wave and time shift hspread for pions and kaons emitted at mid-rapidity Time Note: our Blast Wave freeze-out at constant t2 = (t2-z2) t = t cosh(h)  <t(p)> > <t(K)>

11. 2 free parameters in the Gaussian approximation Width of the distribution in pair rest frame Offset of the distribution from zero Boosting to pair rest frame where the action takes place Separation between particle 1 and 2 and Boost to pair Rest frame Particle 1 source Particle 2 Source Dr*out = gT (Drout – bTDt)

12. Parameters from best fit to central Au-Au @ 130 GeV No tuning Legend Dot = -gbDt Dash = gDrout Plain = Dr*out Offsets p-K p-p K-p

13. 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 A) faster particle flying away • Effective interaction time shorter • Weaker correlation B) faster particle catching up • Effective interaction time larger • Stronger correlation Measuring offset by kinematic selection R.Lednicky, V. Lyuboshitz, B. Erazmus, D. Nouais, Phys.Lett. B 373 (1996) 30.

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

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

16. 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 p-K correlation at 130 GeV Phys. Rev. Lett. 91 (2003) 262302

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

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

19. Large systematic errors Purity correction No l 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 The dark side of the story • Study system with large statistical errors …

20. unlike-sign particles RQMD simulation __ R from pi -pi .... R*0.75 --- R*1.25 Ξ* like-sign particles p-X correlation functions • 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 Analysis by Petr Chaloupka

21. Testing different hypothesis X source size << p source size X source size = p source size 10 fm offset included in both calculations STAR preliminary

22. Wait until QM05 for more on p-X Moving on to baryon-baryon correlation

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

24. Fit and extract source size STAR preliminary

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

26. Purity and residual correlation • 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 …

27. Problem: 2 different radii

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

29. 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 pT range and centrality but scatt lengths do NOT High precision p-p scattering lengths p+ Source L p- p- Uncorrelated pion Fraction l from HBT Measured by HBT

30. 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

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

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

33. Non-id correlation probe a unique feature of flow Space-time offset between sources of different particle species Nice qualitative results from p-K, p-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 p-X very promising Wait until QM05 Attempt to measure p-p scattering lengths with high precision New window onto the strong interaction SummaryFrom flow to strong interaction

34. Back up

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