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Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition

Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition. RHIC Physics, HBT and RHIC HBT Puzzle Formalism Quantum mech. treatment of optical potential, U (Chiral symmetry) Reproducing data, wave function Summary. Gerald Miller and John Cramer, UW. The RHIC HBT Puzzle .

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Quantum Opacity, RHIC HBT Puzzle , and the Chiral Phase Transition

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  1. Quantum Opacity, RHIC HBT Puzzle, and the Chiral Phase Transition • RHIC Physics, HBT and RHIC HBT Puzzle • Formalism • Quantum mech. treatment of optical potential, U (Chiral symmetry) • Reproducing data, wave function • Summary Gerald Miller and John Cramer, UW

  2. The RHIC HBT Puzzle Data from the first five years of RHIC Some evidence supports the presence of QGP formed in early stages of Au+Au collisions: • Relativistic hydrodynamics describes the low and medium energy dynamic collision products • Elliptic flow data implies very high initial pressure and collectivity • Most energetic pions, produced early, strongly suppressed • Strong suppression of back-to-back jets. • D Au vs Au Au, central vs peripheral • Hydrodynamics works BUT NOT FOR HBT

  3. Rlong qside qout Rside qlong Rout HBT- 2 particle interferometry p1 p2 q=p1-p2 p2 q + p2 p1 Quantum mechanical interference-space time separation of source K=(p1+p2)/2 Hydrodynamics predicts big RO/RS, Data RO/RS about 1 HBT puzzle C(q,K) =s(p1,p2)/(s(p1)s(p2))-1 ~ λ(1-q2L R2L-q2S R2S –q2O R2O )

  4. Time extent of source R2o >>R2s • j=w1t1 +w2 t2 Expect R2o >>R2s

  5. Rs =Ro A highlight from this week Burt Holzman, PHOBOS

  6. Old Formalism  source current density =J Chaotic sources, Shuryak ‘74 S0~<J J*> σ(p1)

  7. Source Properties hydrodynamics inspired source function of Wiedemann Heinz et al Bjorken tube model-boost invariant S0(x,K) ~freeze out surface but π emission allowed everywhere ρ(b) medium density radial flow

  8. Overview of Our Model • Allow pions to be emitted anywhere in medium, not only at freeze-out surface • Pions interact with the matter on their way out. • Pion absorption implemented via imaginary part of optical potential. • Real part of optical must exist, acts as mass and velocity change of pions due to chiral-symmetry breaking as they pass from the hot, dense collision medium to the outside vacuum

  9. Formalism • Pions interact U with dense medium Gyulassy et al ‘79 is distorted (not plane) wave  DWEF- distorted wave emission function

  10. Wave Equation Solutions Matter is infinitely long Bjorken tube and azimuthal symmetry, wave functions factorize: 3D ® 2D(distorted)´1D(plane) We solve the reduced Klein-Gordon wave equation for yp: Partial wave expansion ! ordinary diff eq

  11. Son & Stephanov 2002 v2, v2 m2p (T) approach 0 near T = Tc =ω2-m2π Both terms of U are negative (attractive)

  12. Fit STAR Data 6 source, 3 optical potential parameters Fit central STAR data at ÖsNN=200 GeV reproduce Ro, Rs, Rl reproduce dNp/dy (both magnitude and shape) 8 momentum values (i.e., 32 data points)

  13. Fit to 200 GeV Au+Au Radii U=0 Re U=0

  14. Potential Effects

  15. 200 GeV Au+Au Spectrum U=0 noBE no flow

  16. Meaning of the Parameters • Temperature: 193 MeV fixed at phase transition temperature S. Katz, QM05 • Transverse flow rapidity: 1.5 ®vmax=0.85 c, vav=0.6 c • Pion emission between 6.2 fm/c and 11 fm/c ® soft EOS . • WS radius: 11.8 fm = R (Au) + 4.4 fm > R @ SPS • Re(U): 0.14 + 0.85 p2®deep well ® strong attraction. • Im(U): 0.12 p2® lmfp » 8 fm @ KT=1 fm-1 ® strong absorption ® high density • Pion chemical potential: mp= mass(p) Consistent with CHIRAL PHASE TRANSITION!

  17. Wave Functions |y(q, b)|2 r(b) DWEF(Full) EikonalApprox. DWEF(Im Pot only) KT= 100 MeV/c KT= 250 MeV/c KT= 600 MeV/c

  18. Centrality & Nuclear Dependence Cu+Cu Au+Au Cu+Cu Centrality: 0-10% 10-20% 20-30% 30-40% 40-50% 50-60% Au+Au Centrality: 0-5% 5-10% 10-20% 20-30% 30-50% 50-80% Rout Rout Rside Rside Rlong Rlong

  19. Summary • Quantum mechanics solves technical problems of applying opacity to HBT. • Excellent fits ÖsNN=200 GeV data: three radii, pT spectrum. • Fit parameters: indicate strong collective flow, significant opacity, and huge attraction. Describe pion emission in hot, highly dense matter (a soft pion equation of state) . • Replace the RHIC HBT Puzzle with evidence for a chiral phase transition. In most scenarios, the QGP phase transition is accompanied by chiral phase transition at about same critical temperature. • Phys.Rev.Lett.94:102302,2005, nucl-th/0507004 The End

  20. SPARES FOLLOW

  21. For details see: Phys.Rev.Lett.94:102302,2005and a newer preprint: nucl-th/0507004, submitted PRC The End

  22. Source Properties (“hydrodynamics inspired” source function of Heinz & collaborators) (medium density) (Bose-Einstein thermal function) S0(x,K) ~freeze out surface

  23. Correlation/Gaussian Fit

  24. Eikonal Magnitude of wave function l b  b/R RO = R/4.48 HV

  25. Correlation Functions

  26. 9 Fits: 200 GeV/A Au+Au

  27. c2 vs. Temp for 9 Fits

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