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The HBT Puzzle at RHIC

The HBT Puzzle at RHIC. 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 !. Foundation of HBT.

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The HBT Puzzle at RHIC

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

  2. 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 ! SCOTT PRATT MICHIGAN STATE UNIVERSITY

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

  4. Review some vocabulary Rbeam : parallel to beam Rout:  to beam, & parallel to Ppair Rside:  to beam, &  to Ppair SCOTT PRATT MICHIGAN STATE UNIVERSITY

  5. Lifetime and Pressure SCOTT PRATT MICHIGAN STATE UNIVERSITY

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

  7.    STAR      GROMITSimple hadronic Boltzmann • Underpredicts R ! • Underpredicts t ! • Slightly overpredicts Dt Similar results: Molnar,Humanic, AMPT … SCOTT PRATT MICHIGAN STATE UNIVERSITY

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

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

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

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

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

  13. Bad Theory?? • Higher-order symmetrization S.P. PLB(93) Only important at q>200, where fmax >1 Permutation cycle Cutting cycle diagram yields Gm(p1,p2) SCOTT PRATT MICHIGAN STATE UNIVERSITY

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

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

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

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

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

  19. Ultra-Stiff Equation of State? No Latent Heat • Not melting vacuum?? • Still difficult to get large Rside and small Rout & Rlong SCOTT PRATT MICHIGAN STATE UNIVERSITY

  20. For r outside interaction range , Phase shifts determine y(even for small r) Alternate Measurement of Rout/Rlong/Rside S.P. and S.Petriconi, PRC(2003) Any cos(qqr) dependence in |f(q,r,cosq)|2 provides leverage for determining shape SCOTT PRATT MICHIGAN STATE UNIVERSITY

  21. pK+ correlations Rout=8 fm, Rside = Rbeam = 4 fm ~1-(me2/q2)<1/r> Classical approximation works well for Q > 75 MeV/c SCOTT PRATT MICHIGAN STATE UNIVERSITY

  22. Ratio ~ (Rout/Rside)2 Independent of Qinv for large Q pK+ correlations Rout=8 fm, Rside = Rbeam = 4 fm SCOTT PRATT MICHIGAN STATE UNIVERSITY

  23. Positive for qside Negative for qout pp+ correlations Rout=8 fm, Rside = Rbeam = 4 fm SCOTT PRATT MICHIGAN STATE UNIVERSITY

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

  25. 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

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

  27. 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 SCOTT PRATT MICHIGAN STATE UNIVERSITY

  28. SUMMARY • Some correlation candidates: • q < 25 MeV/c (HBT, and scattering length)p p,KK,pp,pK-,pL,K+K-,KsKs,KKs,LL • 25 < q < 75 MeV/c (Coulomb tails)p p,KK,pp,pK+,p+p • Sharp resonancesf(K+K-),D(pp),r(p+p-),K*(Kp),X*(Xp),S*(Lp),5Li(pa) • Coalescenced(pp),L1405(pK) SCOTT PRATT MICHIGAN STATE UNIVERSITY

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