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Correlation Functions: Getting Into Shape D.Brown, P.Danielewicz, S.Petriconi and S.Pratt

Correlation Functions: Getting Into Shape D.Brown, P.Danielewicz, S.Petriconi and S.Pratt. Probability 2 particles of same v are separated by r. Main Goal: Determine S. Measure C(q x ,q y ,q z ). Visualizing S. S P (r) = distribution of relative coordinates. Visualizing S.

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Correlation Functions: Getting Into Shape D.Brown, P.Danielewicz, S.Petriconi and S.Pratt

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  1. Correlation Functions:Getting Into Shape D.Brown, P.Danielewicz, S.Petriconi and S.Pratt Scott Pratt Michigan State University

  2. Probability 2 particles of same v are separated by r Main Goal: Determine S • Measure C(qx,qy,qz) Scott Pratt Michigan State University

  3. Visualizing S SP(r) = distribution of relative coordinates Scott Pratt Michigan State University

  4. Visualizing S Scott Pratt Michigan State University

  5. Lifetimes fromHBT Scott Pratt Michigan State University

  6. Frightening Results from RHIC • Hydro overpredicts: • Rside by 0% • Rbeam by ~ 50% • Rout by ~ 50% HYDRO+URQMD Scott Pratt Michigan State University

  7.    STAR      Simple Boltzmann Calculation (GROMIT)T. Humanic, AMPT, D. Molnar, S.P. • Underpredicts R ! • Underpredicts t ! • Slightly overpredicts Dt Scott Pratt Michigan State University

  8. Frightening results from RHIC • Suggests NO LATENT HEAT • Not so many extra degrees of freedom • Incompatible with Lattice EOS • Hard-EOS cascade does better (AMPT….) • Still has problems with Rside • Independent measurement would help Scott Pratt Michigan State University

  9. Can one determine Rout/Rlong/Rsidewith other classes of correlations? • Classical Coulomb IMF-IMF CorrelationsKim et al, PRC, (92) • Lednicky q+/q- correlations Scott Pratt Michigan State University

  10. Coulomb correlations Classically, determined by trajectories Q Scott Pratt Michigan State University

  11. Coulomb correlations Scott Pratt Michigan State University

  12. Approaches unity as 1/q2 Classical Coulomb correlations Scott Pratt Michigan State University

  13. pK+ correlations Rout=8 fm, Rside = Rbeam = 4 fm Classical approximation works well for Q > 50 MeV/c Scott Pratt Michigan State University

  14. Ratio ~ (Rout/Rside)2 Independent of Qinv for large Q pK+ correlations Rout=8 fm, Rside = Rbeam = 4 fm Scott Pratt Michigan State University

  15. Coulomb correlations • Sensitive to shape / lifetime !!! • Difficulty: Correlation in tails ~ 1% • Residual interactions can be subtracted away Scott Pratt Michigan State University

  16. For r outside interaction range , Strong interactions Everything determined by phase shifts Scott Pratt Michigan State University

  17. For r < , Density of States Constraint: Gives: Also determined by phase shifts Strong interactions Scott Pratt Michigan State University

  18. Positive for qside Negative for qout pp+ correlations Rout=8 fm, Rside = Rbeam = 4 fm Scott Pratt Michigan State University

  19. Reduces to 1-d problems! Danielewicz and Brown Angular Moments Defining, Using identities for Ylms, Scott Pratt Michigan State University

  20. L=0 • L=1, M=1 • L=2, M=0,2 • L=3, M=1,3 Angle-integrated shape Moments Lednicky offsets Shape (Rout/Rside, Rlong/Rside) Boomerang distortion Scott Pratt Michigan State University

  21. Blast Wave Moments • (z  -z) CL+M=even(q) = 0 • (y -y) Imag CL,M = 0 Scott Pratt Michigan State University

  22. Cartesian Harmonics Scott Pratt Michigan State University

  23. Cartesian Harmonics Scott Pratt Michigan State University

  24. Expansions… Advantage: More intuitive Scott Pratt Michigan State University

  25. Conclusions Strong and Coulomb provide 3-d resolving power • Resonances : f, K*, D, X* … • Small Qinv : pK, pp, pp, … • Moment analyses are POWERFUL • Reduces to 1-d problems for each L,M • Cartesian moments Scott Pratt Michigan State University

  26. CorAL, version 1.0aaaCorrelation Analysis LibraryDave Brown, Mike Heffner, Scott Pratt • Calculate |f(q,r)|2 • (pp, pp, pp, pn, nn, pK, pK, pL, LL, pS, …) • Correlations from models • Gaussian, Blast Wave, OSCAR files… • Fitting capability • Imaging capability • Integrated YLm and Cartesian moment analyses • Available Summer 2005 Scott Pratt Michigan State University

  27. Strong interactions One can integrate analytically, Scott Pratt Michigan State University

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