1. HBT Study in PHOBOS Willis T. Lin Dept. of Physics National Central University Chung-Li, TAIWAN

2. Argonne National Laboratory, USA Brookhaven National Laboratory, USA Institute of Nuclear Physics, Krakow, Poland Massachusetts Institute of Technology, USA National Central University, Taiwan University of Rochester, USA University of Illinois at Chicago, USA University of Maryland, USA The PHOBOS Group

3. Physics Results –Charged particle multiplicity near mid-rapidity in central Au+Au collisions at 56 and 130 GeV Phys. Rev. Lett. 85, 3100 (2000) –Ratios of charged antiparticles-to-particles near mid-rapidity in Au+Au collisions at 130 GeV Phys. Rev. Lett. 87, 102301 (2001) –Charged-particle pseudorapidity density distributions from Au+Au collisions at 130 GeV Phys. Rev. Lett. 87, 102303 (2001) –Energy dependence of particle multiplicities near mid-rapidity in central Au+Au collisions Phys. Rev. Lett 88, 22302 (2002) –Centrality Dependence of Charged Particle Multiplicity at |η|<1 in Au+Au Collisions at 130 GeV Phys. Rev. C 65, 031901R (2002) –Centrality Dependence of Charged Particle Multiplicity at |η|<1 in Au+Au Collisions at 130 and 200 GeV Phys. Rev. C 65, 061901R (2002) –Pseudorapidity and centrality dependence of the collective flow of charged particles in Au+Au collisions at 130 GeV Submitted to Phys. Rev. Lett. (2002) –Ratios of charged antiparticles to particles near mid-rapidity in Au+Au collisions at 200 GeV Submitted to Phys. Rev. C (2002) –The significance of the fragmentation region in ultrarelativistic heavy ion collisions Submitted to Phys. Rev. Lett. (2002) Technical –Silicon Pad Detectors for the PHOBOS Experiment at RHIC Nucl. Instr. Meth. A461, 143-149 (2001) –Array of Scintillator Counters for PHOBOS at RHIC Nucl. Instr. Meth. A474, 38-45 (2001) PHOBOS PUBLICATION

4. Relativistic Heavy Ion Collider RHIC –Highest energy density ever produced in laboratory –Species : pp, AuAu 12 June: 1 st Collisions @  s NN = 56 GeV 24 June: 1 st Collisions @  s NN = 130 GeV 5 Sep : end of first Au-Au Physics run 13 Sep : 1 st polarized protons in RHIC 2001 : Looking for 1 st Collisions @  s NN = 200 GeV

5. RHIC To understand fundamental features of the strong interaction :  How does nuclear matter “melt” ?  Where does the proton get its spin ? 3.83 km circumference Two independent rings Capable of colliding any nuclear species on any other species Collision Energy : 500 GeV for p-p 200 GeV for Au-Au (per N-N collision) Luminosity : Au-Au 2 x 10 26 cm -2 s -1 p-p : 2 x 10 32 cm -2 s -1 (polarized)

6. Ring Counters Paddle Trigger Counter Spectrometer TOF Octagon+Vertex PHOBOS Detector Cerenkov 4  Multiplicity Array - Octagon, Vertex & Ring Counters Mid-rapidity Spectrometer TOF wall for high-momentum PID Triggering -Scintillator Paddles - Zero Degree Calorimeter 96000 Silicon Pad channels

7. Silicon Everywhere Spectrometer Arm Ring Silicon Pad Sensors Vertex Detector Octagon Detector

8. no. of days Silicon Sensors Performance S/N ratios better than 10:1 design specification Larger pads & longer readouts  lower S/N ratio Ave. noise in entire detector setup stable over time

9.  t (ns) Events Negative Paddles Positive Paddles ZDC NZDC P Au x z PP PN Paddle Counters Coincidence (38 ns) between paddle counters Event Selection

10. PHOBOS Works

11. HBT Briefing – Two-Particle Correlation Source x y r1r1 r2r2 The probability to detect particles at r 1 and r 2 Probability amp. (plane wave)

12. More Briefing Correlation function C 2 (k 1,k 2 ) can be defined: What can be measured are is the Fourier transformation particle density of source. 1. 2. : the distribution fn. of chaotic source

13. Extract HBT Correlation - Using Event Mixing Method HBT, TPA, Coulomb, FSI No Any Correlated Interactions Pairs from same event Pairs from “mixed” event Naively, assume density of the source is a Gaussian distribution

14. Z-Axis Y-Axis X-Axis Beam Axis K P 1 P 2 q Conventional Q Variables in LCMS Q side Q long Q out LCMS or Pratt coor.

15. Relationship btw R out and R side Only if x-t correlations are small and we get

16. HBT Physics Motivation Au QGP Phase Mixed Phase Source Size Hadron Phase By definition HBT sensitive to distribution at hadron’s last scattering point a signature of QGP signal A tool to understand the space-time evolution in heavy-ion collision Theories predicted a large and long-lived source if QGP is created STAR PHENIX

17. Two Particle Acceptance @ High m t |Q long | < 10 MeV, 0.8 <m t < 1 GeV 20 mr60 mr PHOBOS TPA Cut ~ 25 mr

18. Two Particle Acceptance for “ideal case” TPAC is parameterized by (Δθ,ΔYA)  Y A = 0  Y A = 1  Y A = 2  Y A = 3 SpecP Only

19. Two Particle Acceptance for “ideal case” SpecN Only  Y A = 0  Y A = 1  Y A = 2  Y A = 3

20. Official Cut Used Two Particle Acceptance If the pair’s relative quantities (  Y A,  θ) are located in the shadowed area, it won’t be employed in our analysis.

21. Gamow λ = 1 R inv = 5 fm λ = 1 R inv = 10 fm Gamow λ = 1 R inv = 5 fm λ = 0.5 R inv = 5 fm λ = 0.1 R inv = 5 fm Coulomb Correction Qinv (GeV/c) Full-Wave Coulomb Correction “Partial” Coulomb Correction “E866” Approximate Coulomb Correction Coulomb Correction We apply “partial” Coulomb correction officially Coulomb correction is only applied to mixed pairs

22. vzvz.025 cm.05 cm.025 cm Event Mixing “Fixed classes “ : Chop up vertex space #Real / #Mixed pairs must be larger than 3 ! For each qualified domain, # of mixed pairs chosen randomly is exact three times of real pairs

23. Introduce HBT into MC ( Ⅰ ) Ideal comes from PYTHIA We can calculate the corresponding momentum shift i OLD j OLD i NEW j NEW Final momentum of particle i

24. Introduce HBT into MC ( Ⅱ ) MC Recon

25. Introduce HBT into MC ( Ⅲ )

26. PHOBOS HBT Results @ 200 GeV  - 0.54  0.025.8  0.25.1  0.46.8  0.3 R out R side R long ++++ 0.57  0.034.9  0.47.3  0.35.8  0.2 R 2 out-long 4.9  1.7 4.5  1.9 Systematic error on radii of 1 fm, on of 0.06

27.  -  - data HBT Excitation Function

28. Summary of HBT from RHIC K T (GeV/c) R out / R side STAR error bars are not shown PRELIMINARY

29. 3 Kt bins analysis (Rout) (Without error bar) π-π- PRELIMINARY

30. 3 Kt bins analysis (Rside) (Without error bar) π-π- PRELIMINARY

31. 3 Kt bins analysis (Rlong) (Without error bar) π-π- PRELIMINARY

32. 3 Kt bins analysis (Rout/Rside) (Without error bar) π-π- PRELIMINARY

33. Conclusion  HBT results are consistent between 130 and 200 GeV  RHIC Puzzle ! Most reasonable models still don’t agree well with RHIC HBT data  Don’t forget the x-t correlation term !  It’s possible a super-cooling source !

34. Predicted Rout/Rside S. Soff et al. nucl-th/0012085 v2 (2001) Assume a first order phase transition from a thermalized QGP to a gas of hadrons