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Particle Correlation Measurements from

Particle Correlation Measurements from. Stephen C. Johnson – Lawrence Livermore National Lab for the PHENIX Collaboration. HBT results presented here: submitted to PRL: 16 Jan `02 nucl-ex/0201008. R. 2. r. 1. q. The Physics of Hanbury-Brown Twiss. r 1 , p 1. S(r).

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Particle Correlation Measurements from

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  1. Particle Correlation Measurements from Stephen C. Johnson – Lawrence Livermore National Lab for the PHENIX Collaboration HBT results presented here: submitted to PRL: 16 Jan `02 nucl-ex/0201008

  2. R 2 r 1 q The Physics of Hanbury-Brown Twiss r1, p1 S(r) • Consider a source S(r) of identical bosons (g or p) whose wave functions can be described as plane waves. • Assume: • Production amplitudes independent of momentum • Mutually incoherent x r2, p2 y Amplitude for this diagram: Corresponding normalized probability:

  3. S(x,p) Some details: Pairs from same event In principle: In practice: • One dimension works fine when measuring stars: • Static • Isotropic emission (no position momentum correlations) • Heavy Ion Collisions are anything but • Consider a more complicated source • S() – effective single particle Wigner phase space density • Often replaced by a classical phase-space density in practical calculations • Note: due to mass shell constraints, the function is non-invertible (model assumptions). Pairs from ‘mixed’ events

  4. k q qlong qout Kinematic Variables • Currently the field tends to consider projections of the momentum difference into: • qlong, qside, qout • qlong Rlong ~longitudinal extent • qside/qout Rside/Rout ~transverse extent qside qlong qout

  5. Rside Rout HBT and the QGP • “Naïve” picture: • Rout2=Rside2+(bpairt)2 • Concrete predictions are few: • Pratt PRD 1314 (`86): fireball and EOS  t ~ 90 fm/c • Bertsch NPA 173 (89) QGP + cascade  t ~ 12 fm/c • Hydro calculation of Rischke & Gyulassy expects Rout/Rside ~ 2->4 @ kt = 350 MeV. • Result robust to Tfreeze, dQ/dH, 1st order vs. rapid cross-over. • Response: can hadronic rescattering mask this prediction?

  6. One step closer • Soff, Bass, Dumitru (PRL 86) • Couple microscopic transport to hydro with phase transition • Still expect Rout/Rside>1  measurements at high kt are very interesting. • Note: • Hydro: Ro/Rs(200)<Ro/Rs(160) • Longer time at phase transition • Transport: Ro/Rs(200)>Ro/Rs(160) • Longer time rescattering

  7. PHENIX – Year 1 Configuration • Both arms provide hadron PID (contrary to popular belief) • East: • DC + TOF (~100 ps) • p/K separation to 2 GeV/c • West: • DC + PbSc (~600 ps) • p/K separation to 1 GeV/c • B-field + geometry limits lower kt bound to 200 MeV. I use ‘electron’ acceptance for this hadron analysis

  8. Centrality definition and sample • This data sample uses the 30% most central collisions • <centpairs> = 10% • 493k events • After all analysis cuts: • 3.1M p+ pairs • 3.3M p- pairs BBC ZDC

  9. Pair acceptance and corrections • p definition  <1.5s from p peak && >2.5s from K peak • Require pairs from mixed events to have reconstructed vertices within 1cm • Acceptance varies as a function of vertex position • Remove pairs within 2cm in drift chamber • Ghosting • Remove tracks with EMC clusters within 12cm of each other in both real and mixed sample • Shower + tower size in EMC • Correct for two track inefficiencies at low relative f in the drift chamber. • Full Coulomb Correction modified for momentum smearing • Partial correction changes radii results marginally • Residual correlations in event mixed background  <2% error • Momentum smearing correction to correlation function Systematic Errors: Rlong & Rside: 8% Rout: 4.5%

  10. Results: Assume T = 125 MeV, bf = .69/hf=.85 From fits to singles spectra in centrality region 5-15% (J. Burward-Hoy) • Theoretical hydro-inspired fits. • Chapman, Nix, Heinz PRC 52, 2694 • Wiedemann, Scotto, Heinz PRC 53, 918 • However, hydro calculations predict Ro than data, Rs, smaller. • Much larger than comparable 1D RMS Au radius of 3.07fm • kt dependence suggest larger bf/T (hf/T) than fits to singles Systematic Errors: Rlong & Rside: 8% Rout: 4.5%

  11. Compared to STAR • Well described by hydro model if consider datasets separately. • But they indicate a much higher flow/temp ratio when taken together • Need to be careful about systematics between different measures. • Both experiments should be able to sort this out in the next dataset. • Inconsistent with models of QGP that include an hadronic rescattering phase. Soff, Bass, Dumitru (PRL 86)

  12. Energy dependence … M. Lisa et al., PRL 84, 2798 (2000) R. Soltz et al., to be sub PRC C. Adler et al., PRL 87, 082301 I.G. Bearden et al., EJP C18, 317 (2000) • Rout and Rside are energy independent within error bars. • Smooth energy dependence in Rlong • No immediate indication of very different physics • Fit Rlong to: • AGS: A = 2.19 +/- .05 • SPS: A = 2.90 +/- .10 • RHIC: A = 3.32 +/- .03 A = t0T in 1st order T/mT calculation t0 = average freeze-out proper time

  13. Even an experimentalist can’t predict this • “A prognostication” • Local PHENIX HBT expert keeps his predictions on the web. • Zajc at Nucleus-Nucleus 97 showed this slide • Extrapolation to RHIC multiplicities? • (dN/dy)1/3 => R ~ 9 fm • (dN/dy) => R ~20 fm • Neither. • What is happening here? • ** ** To be fair: Bill’s radii predictions are way off. His guess at the charged particle multiplicity in the extrapolations…bang on

  14. R.A. Soltz E859 Si+Al/Si+Au/Au+Au Q & A • Q: Why are Rout and Rside ~identical over an order of magnitude of beam energy? • There is ample evidence at AGS and SPS of dependence of radii on # target+projectile nucleons • Even though the larger nuclei have larger flow the radii follow a simple scaling • Why no multiplicity/energy dependence? • Q: Flow higher at RHIC leads to smaller radii? • HBT results suggest high flow but spectra imply flow comparable to SPS ** • kt dependence of radii is similar for different energies (competing mechanisms that create similar bf/T?) • Q: Higher opacity at RHIC energies? • Why would opacity be higher at RHIC than at AGS? • pn->D->pn  pp->r->pp • And why would size and opacity effects identically cancel? • Red herring? – You can’t create opaque source with smaller lifetime. • Q: Why is it only changing in the longitudinal direction? • Some surprise among theorists that the difference is so small. • Is there a quantitative expectation of the Rlong dependence? ** To my knowledge no one has fit both SPS and RHIC results to same hydro model

  15. A taste of the future • For year-1 we wrote ~5 million min. bias events. • 1/2 million events in this analysis after all cuts • In the past run we wrote ~90 million min. bias events (+14 million rare event triggers) • Therefore, for the year-2 pion correlations: • easily 10 high statistics bins in kt from .2 to 1.0 GeV + a few bins from 1.0 to 2.0 GeV • Capability to exclude detailed theories • Systematic errors start to become the real problem • Beyond pions: • 1D proton and kaon correlations • Non-identical correlations (pK, pp, etc.) • p0 • maybe possible in year 2 … year 3? • Probe of very high kt. • anti-neutron correlations • Better than proton correlations  lack of coulomb. Ro,s,l kt

  16. The scientists that make me look good* *or at least better than I normally do

  17. Supporting slides:

  18. PHENIX Preliminary PHENIX Preliminary PHENIX Preliminary 118-126 MeV 0.71-0.73 PHENIX Preliminary Fitting the Single Particle Spectra:Jane Burward-Hoy (LLNL) 1/mt dN/dmt = A  f()  d mT K1( mT /Tfo cosh  ) I0( pT /Tfo sinh  ) • Linear velocity profile • Gaussian spatial distribution • Exclude pion resonance region • Exclude mt-m0>1.0 GeV

  19. Switching frames • Problem: radii extracted depend on the frame in which you measure • Historically we have used: • Qinv (1D pair rest frame) • Collision Center of Mass • AGS • LCMS (longitudinally co-moving frame) • Longitudinally boost invariant sources • SPS(?), RHIC • Jet frame • p-p collisions. • PCMS (pair center-of-mass – 3D version of Qinv) • … • What is the ‘correct’ frame?? (= the frame in which the source is not moving) • Can we bound it experimentally?

  20. Our source?? 2p HBT measurement is simultaneous in the PCMS frame p1 bpair p2 bsource Source Detector Pair rest frame != source rest frame What is the bsource? We don’t know, but we can bound it: >0 <bpair

  21. ‘side’ ‘out’ p1 p’1 bpair p2 p’2 unphysical LCMS vs. PCMS • LCMS • A Lorentz contracted measurement of the frame • PCMS • A measurement of the length of the train in the train frame True frame unphysical

  22. Fits to entire dataset (p-) LCMS PCMS* *PCMS = Pair Center of Mass System

  23. PCMS results • Rside and Rlong unchanged • And not plotted • RoutPCMS differs by <gpair> from RoutLCMS • Be careful about deducing a lifetime from Rout2=Rside2+(bpairt)2 • bpair=0

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