1. The HBT Puzzle at RHIC Scott Pratt, Michigan State University

2. SCOTT PRATT MICHIGAN STATE UNIVERSITY OUTLINE Brief review What is the HBT Puzzle? Can we blame theorists? Can we blame experimentalists? Are we leaving something out of the dynamics? New “HBT” Methods Seize the moments !

3. SCOTT PRATT MICHIGAN STATE UNIVERSITY Foundation of HBT GOAL of HBT: Invert C(v,q) to obtain g(v,r) g(v,r) samples relative positions

4. SCOTT PRATT MICHIGAN STATE UNIVERSITY Review some vocabulary R beam : parallel to beam R out :  to beam, & parallel to P pair R side :  to beam, &  to P pair

5. SCOTT PRATT MICHIGAN STATE UNIVERSITY Lifetime and Pressure

6. SCOTT PRATT MICHIGAN STATE UNIVERSITY HYDRO and RQMD Compared to STAR: R beam 80% too large R side 10% too large R out 40% too large D. Teaney (EOS has phase transition) Similar conclusions: P. Kolb, P. Huovinen, A.Dumitru, S.Soff and S. Bass          STAR

7. SCOTT PRATT MICHIGAN STATE UNIVERSITY GROMIT Simple hadronic Boltzmann Underpredicts R  ! Underpredicts  ! Slightly overpredicts           STAR Similar results: Molnar, Humanic, AMPT …

8. SCOTT PRATT MICHIGAN STATE UNIVERSITY Blast Wave Parameters Unphysical acceleration??? F.Retiere,M.Lisa…

9. SCOTT PRATT MICHIGAN STATE UNIVERSITY Essence of the RHIC puzzle How can the fireball grow from R=6 fm to R=13 fm in ~ 10 fm/c ?

10. SCOTT PRATT MICHIGAN STATE UNIVERSITY Solving the RHIC HBT Puzzle Bad Experimental Analysis? Bad theory? Is something missing from hydro treatments? Could EOS be ultra stiff? Alternate Measurement of R out /R long /R side

11. SCOTT PRATT MICHIGAN STATE UNIVERSITY Bad Experimental Analysis?? 1.Experimental Resolution Tested with MC Experiments are consistent 2.Coulomb “Correction” Originally done incorrectly, but only 10% effect

12. SCOTT PRATT MICHIGAN STATE UNIVERSITY Bad Theory?? 1.Higher-order symmetrization 2.Independent emission 3.Equal-time approximation 4.Smoothness 5.Interact only two-at-a-time Based on 5 approximations

13. SCOTT PRATT MICHIGAN STATE UNIVERSITY Bad Theory?? 1.Higher-order symmetrization S.P. PLB(93) Only important at q>200, where f max >1 Permutation cycle Cutting cycle diagram yields G m (p 1,p 2 )

14. SCOTT PRATT MICHIGAN STATE UNIVERSITY Bad Theory?? 2. Independent emission Should be good for large sources at moderate p t Coherent sources?? (unlikely to extend over large V)

15. SCOTT PRATT MICHIGAN STATE UNIVERSITY Bad Theory?? 3. Equal-time approximation Not an issue for pure HBT or classical Coulomb

16. SCOTT PRATT MICHIGAN STATE UNIVERSITY Bad Theory?? 4. Smoothness Not necessary for Coulomb trajectories Not an issue for pure HBT with large sources S.P., PRC(2000)

17. SCOTT PRATT MICHIGAN STATE UNIVERSITY Bad Theory?? 5. Interact only two-at-a-time Assumes “Hard” Interactions with 3rd body Mean Field effects cancel in Glauber approximation R.Lednicky et al., PLB(96)

18. SCOTT PRATT MICHIGAN STATE UNIVERSITY Shortcomings of Hydro Treatments 1.Lack of viscosity Underpredicts transverse acceleration Underpredicts lifetime (v therm,z would shrink) 2.Assume boost invariance Should cut off tails of source at large z Neglects longitudinal acceleration 3.“Emissivity” between phases Shock wave treatments assume maximum burn rate 4.Neglect mass shifts Underpredicts phase space density Help explain small  Help explain small Help explain small size

19. SCOTT PRATT MICHIGAN STATE UNIVERSITY Ultra-Stiff Equation of State? No Latent Heat Not melting vacuum?? Still difficult to get large R side and small R out & R long

20. SCOTT PRATT MICHIGAN STATE UNIVERSITY Alternate Measurement of R out /R long /R side Any cos(  qr ) dependence in |  (q,r,cos  )| 2 provides leverage for determining shape For r outside interaction range , S.P. and S.Petriconi, PRC(2003) Phase shifts determine  (even for small r)

21. SCOTT PRATT MICHIGAN STATE UNIVERSITY pK + correlations R out =8 fm, R side = R beam = 4 fm Classical approximation works well for Q > 75 MeV/c ~1-(  e 2 /q 2 )

22. SCOTT PRATT MICHIGAN STATE UNIVERSITY pK + correlations R out =8 fm, R side = R beam = 4 fm Ratio ~ (R out /R side ) 2 Independent of Q inv for large Q

23. SCOTT PRATT MICHIGAN STATE UNIVERSITY p  + correlations R out =8 fm, R side = R beam = 4 fm Positive for q side Negative for q out

24. SCOTT PRATT MICHIGAN STATE UNIVERSITY Moments Standard formalism: Defining, Using identities for Y lm s, Simple correspondence! Danielewicz and Brown

25. SCOTT PRATT MICHIGAN STATE UNIVERSITY Moments L=0 L=1, M=1 L=2, M=0,2 L=3, M=1,3 Angle-integrated shape Lednicky offsets Shape (R out /R side, R long /R side ) Boomerang distortion

26. SCOTT PRATT MICHIGAN STATE UNIVERSITY Blast Wave Moments (z  -z) C L+M=even (q) = 0 (y  -y) Imag C L,M = 0 PRELIMINARY

27. SCOTT PRATT MICHIGAN STATE UNIVERSITY SUMMARY HBT Puzzle remains elusive Theorists must: –Finish checking validity of HBT formalism –Add features to “hydro” treatments (viscosity, emissivity, non-Bjorken IC) –Further investigate non-idenctical particles Experimentalists should: –Finish analyses of KK interferometry –Perform shape analyses with non-identical particles

28. SCOTT PRATT MICHIGAN STATE UNIVERSITY SUMMARY Some correlation candidates: –q < 25 MeV/c (HBT, and scattering length)    ,K  K ,pp,pK -,p ,K  K ,K s K s,K  K s,  –25 < q < 75 MeV/c (Coulomb tails)    ,K  K ,pp,pK +,   p –Sharp resonances  (K + K - ),  (p  ),  (     ),K*(K  ),  *(  p),  *(  ), 5 Li(p  ) –Coalescence d(pp),  1405 (pK)