Correlation Functions Getting Into Shape D Brown P

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

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

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

Visualizing S Scott Pratt Michigan State University

Lifetimes from HBT Scott Pratt Michigan State University

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

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

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

Can one determine Rout/Rlong/Rside with other classes of correlations? • Classical Coulomb IMF-IMF Correlations Kim et al, PRC, (92) • Lednicky q+/q- correlations Scott Pratt Michigan State University

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

Coulomb correlations Scott Pratt Michigan State University

Classical Coulomb correlations Scott Pratt 2 Approaches unity as. Michigan 1/q State University

p. K+ correlations Rout=8 fm, Rside = Rbeam = 4 fm Classical approximation works well for Q > 50 Me. V/c Scott Pratt Michigan State University

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

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

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

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

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

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

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

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

Cartesian Harmonics Scott Pratt Michigan State University

Cartesian Harmonics Scott Pratt Michigan State University

Expansions… Advantage: More intuitive Scott Pratt Michigan State University

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

Cor. AL, version 1. 0 aaa Correlation Analysis Library Dave Brown, Mike Heffner, Scott Pratt • Calculate |f(q, r)|2 – (pp, pp, pn, nn, p. K, p. L, LL, p. S, …) • 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

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