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HBT Study in PHOBOS. Willis T. Lin Dept. of Physics National Central University Chung-Li, TAIWAN. The PHOBOS Group. Argonne National Laboratory, USA Brookhaven National Laboratory, USA Institute of Nuclear Physics, Krakow, Poland Massachusetts Institute of Technology, USA
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HBT Study in PHOBOS Willis T. Lin Dept. of Physics National Central University Chung-Li, TAIWAN
The PHOBOS Group 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
PHOBOS PUBLICATION • • 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 GeVSubmitted 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 RHICNucl. Instr. Meth. A461, 143-149 (2001) • Array of Scintillator Counters for PHOBOS at RHICNucl. Instr. Meth. A474, 38-45 (2001)
RHIC Highest energy density ever produced in laboratory Species : pp, AuAu 12 June: 1st Collisions @ sNN = 56 GeV 24 June: 1st Collisions @ sNN = 130 GeV 5 Sep : end of first Au-Au Physics run 13 Sep : 1st polarized protons in RHIC 2001 : Looking for 1st Collisions @ sNN = 200 GeV Relativistic Heavy Ion Collider
RHIC • 3.83 km circumference • Two independent rings • Capable of colliding any nuclear species on any other species • Collision Energy :500 GeV for p-p200 GeV for Au-Au (per N-N collision) • Luminosity :Au-Au 2 x 1026 cm-2 s-1 • p-p : 2 x 1032 cm-2 s-1 (polarized) To understand fundamental features of the strong interaction : How does nuclear matter “melt” ? Where does the proton get its spin ?
PHOBOS Detector 96000 Silicon Pad channels Paddle Trigger Counter TOF Cerenkov Octagon+Vertex Ring Counters • 4p Multiplicity Array • - Octagon, Vertex & Ring Counters • Mid-rapidity Spectrometer • TOF wall for high-momentum PID • Triggering • Scintillator Paddles • Zero Degree Calorimeter Spectrometer
Silicon Everywhere Octagon Detector Ring Vertex Detector Silicon Pad Sensors Spectrometer Arm
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
Positive Paddles Negative Paddles ZDC N ZDC P Au Au PN PP x Events z Dt (ns) Event Selection Paddle Counters Coincidence (38 ns) between paddle counters
HBT Briefing – Two-Particle Correlation r1 x Source y r2 Probability amp. (plane wave) The probability to detect particles at r1 and r2
More Briefing Correlation function C2(k1,k2) can be defined: What can be measured are 1. 2. is the Fourier transformation particle density of source. : the distribution fn. of chaotic source
Pairs from same event HBT, TPA, Coulomb, FSI No Any Correlated Interactions Pairs from “mixed” event Extract HBT Correlation - Using Event Mixing Method Naively, assume density of the source is a Gaussian distribution
Qside Y-Axis Qlong Qout q P 1 K P 2 X-Axis Beam Axis Z-Axis Conventional Q Variables in LCMS LCMS or Pratt coor.
Relationship btw Rout and Rside Only if x-t correlations are small and we get
HBT Physics Motivation Au Source Size QGP Phase Hadron Phase Mixed Phase Au By definition HBT sensitive to distribution at hadron’s last scattering point a signature of QGP signalA tool to understand the space-time evolution in heavy-ion collisionTheories predicted a large and long-livedsource if QGP is created STAR PHENIX
Two Particle Acceptance @ High mt |Qlong| < 10 MeV , 0.8 <mt < 1 GeV 60 mr 20 mr PHOBOS TPA Cut ~ 25 mr
Two Particle Acceptance for “ideal case” • TPAC is parameterized by (Δθ,ΔYA) YA = 0 YA = 1 YA = 2 YA = 3 SpecP Only
Two Particle Acceptance for “ideal case” YA = 0 YA = 1 YA = 2 YA = 3 SpecN Only
Used Two Particle Acceptance Official Cut If the pair’s relative quantities (YA,θ) are located in the shadowed area, it won’t be employed in our analysis.
“E866” Approximate Coulomb Correction Full-Wave Coulomb Correction “Partial” Coulomb Correction Coulomb Correction Coulomb Correction Gamowλ = 1 Rinv = 5 fm λ = 1 Rinv = 10 fm Gamowλ = 1 Rinv = 5 fm λ = 0.5 Rinv = 5 fmλ = 0.1 Rinv = 5 fm Qinv (GeV/c) Qinv (GeV/c) Coulomb Correction We apply “partial” Coulomb correction officially Coulomb correction is only applied to mixed pairs
.05 cm vz .025 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 randomlyis exact three times of real pairs
Introduce HBT into MC (Ⅰ) Ideal comes from PYTHIA j NEW i NEW i OLD j OLD We can calculate the corresponding momentum shift Final momentum of particle i
Introduce HBT into MC (Ⅱ) MC Recon
Rout Rside Rlong R2out-long - - 0.540.02 5.80.2 5.10.4 6.80.3 4.91.7 ++ 0.570.03 5.80.2 4.90.4 7.30.3 4.51.9 Systematic error on radii of 1 fm, on of 0.06 PHOBOS HBT Results @ 200 GeV
HBT Excitation Function -- data
Summary of HBT from RHIC PRELIMINARY STAR error bars are not shown Rout / Rside KT (GeV/c)
3 Kt bins analysis (Rout) π-π- (Without error bar) PRELIMINARY
3 Kt bins analysis (Rside) π-π- (Without error bar) PRELIMINARY
3 Kt bins analysis (Rlong) π-π- (Without error bar) PRELIMINARY
3 Kt bins analysis (Rout/Rside) π-π- (Without error bar) PRELIMINARY
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 !
Predicted Rout/Rside Assume a first order phase transition from a thermalized QGP to a gas of hadrons S. Soff et al. nucl-th/0012085 v2 (2001)