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WWND '07

THERMINATOR simulations and PHENIX images of a heavy tail of particle emission. √s. in =200GeV Au+Au collisions at RHIC. Róbert Vértesi. University of Debrecen KFKI RMKI. WWND '07. Outline. Introduction HBT and Bose-Einstein Correlation Gaussian Approximation

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WWND '07

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  1. THERMINATOR simulations and PHENIX images of a heavy tail of particle emission √s in =200GeV Au+Au collisions at RHIC Róbert Vértesi University of Debrecen KFKI RMKI WWND '07

  2. Outline • Introduction • HBT and Bose-Einstein Correlation • Gaussian Approximation • Coulomb effect, the Imaging method • PHENIX imaging • Heavy tail in p± emission source 200GeV Au+Au • Models and Simulation • Hadronic Rescattering Model • HRC and Anomalous diffusion • The Single Freezeout model • THERMINATOR simulations for PHENIX imaging • Answers and Questions Róbert Vértesi, WWND Feb 14 2007

  3. The HBT effect • History • „Interference between two different photons can never occur.” P. A. M. Dirac, The Principles of Quantum Mechanics, Oxford, 1930 • Robert Hanbury Brown and Richard Q. Twiss, (engineers, worked in radio astronomy) found correlation between photons from different sources. • „In fact to a surprising number of people the idea that the arrival of photons at two separated detectors can ever be correlated was not only heretical but patently absurd, and they told us so in no uncertain terms, in person, by letter, in print, and by publishing the results of laboratory experiments, which claimed to show that we were wrong …” • Astronomical usage • Intensity interferometry in radio astronomy • Angular diameter of a main sequence star measured Róbert Vértesi, WWND Feb 14 2007

  4. source S(x,k) x2 x1 Y1,2 k1 k2 detector Bose-Einstein Correlations • Two plane-waves: • Bosons: need for symmetrization • Spectrum: • S(x,k) is the source distribution • Two-particle spectrum (momentum-distribution): • Approximations: • Plane-wave, no multiparticle symmetrization, thermalization … Róbert Vértesi, WWND Feb 14 2007

  5. Source from Correlation • The invariantcorrelation function Depends on relative and average momenta • Uses Fourier-transformed form of the source • We can get the source from correlation! Róbert Vértesi, WWND Feb 14 2007

  6. Gaussian Approximation • If the source is approximated with Gaussian: • Then the correlation function is also Gaussian: • These radii are the so-called HBT radii • If transformed to the out-side-long system (not invariant) • Out: direction of the mean transverse momentum of the pair • Side: orthogonal to out • Long: beam direction • Not necessarily reflecting the geometrical size Róbert Vértesi, WWND Feb 14 2007

  7. Coulomb Correction • Charged particles Coulomb interact • Equally charged pions repel each other • Core – Halo picture • Dense, hydro interacting core part • Rare halo with no interaction • Lévy assumption for the source • Iteration: • Kcoulomb is calculated analytically • C0 is fitted, R, l, a determined Róbert Vértesi, WWND Feb 14 2007

  8. Source Imaging • Instead of Craw(q) we compute S12 (r) • Transformed to 2-particle source function and relative position • Evaluated in a specific transverse momentum range • Numerically invert this equation • No analytical solution, hence systematic errors • But we do not need to make the source shape assumption • Final state interactions included as well as Coulomb interactions Róbert Vértesi, WWND Feb 14 2007

  9. Pion Images in PHENIX • RHIC Year 2 Au+Au 200GeV data S. S. Adler et. al. (PHENIX Collaboration) nucl-ex/0605032 “Evidence for a long-range component in the pion emission source in Au+Au collisions at √sNN=200 GeV” • Can we explain that? Róbert Vértesi, WWND Feb 14 2007

  10. Hadronic Rescattering Model • Simple but “clever” cascade model • Causality kept in all scatterings • Cross sections are momentum-dependent • Relation with data • Describes such indicators as spectra, v2, HBT • Both SPS and RHIC data • Common predictions with exact Hydro • Slopes of spectra saturate after ~20ns (as gradients dissolve, self-identical expansion) • Very insensitive to initial conditions • Sensitive to PID (p, K, p) M. Csanad, T. Csorgo, M. Nagy hep-ph/0702032 Róbert Vértesi, WWND Feb 14 2007

  11. Hadronic Rescattering Code • Realized as Tom Humanic’s HRC simulator • Contains cascades of the most abundant hadrons • Neglect of electric charge Róbert Vértesi, WWND Feb 14 2007

  12. Central Au+Au 200 GeV p+p+ and p-p- source |y|< 0.5 0% < centrality< 20% 0.2 GeV/c < kT < 0.36 GeV/c Gauss HRC Pion S(r12) central low-kT Róbert Vértesi, WWND Feb 14 2007

  13. Peripheral 50% < centrality< 90% 0.2 GeV/c < kT < 0.36 GeV/c |y|< 0.5 HRC Pion S(r12) peripheral and hi-kT • High kT 0% < centrality< 20% 0.48 GeV/c < kT < 0.6 GeV/c |y|< 0.5 Róbert Vértesi, WWND Feb 14 2007

  14. Anomalous diffusion • Normal diffusion (random walk): • Constant mean free path • Adding up distributions with finite E(x), var(x) • Central Limit Theorem says: Final distribution will be Gaussian • Anomalous diffusion: • Mean free path not time independent • Distribution of steps have non-finite E(x), var(x) • Gnedenko–Kolmogorov generalization of CLT: Result is Lévy distribution That’s what we have in the rescattering model • Rescattering in a cooling, expanding system • Changing density, x-sections  changing free path Róbert Vértesi, WWND Feb 14 2007

  15. The Single Freezeout Model • Freeze-out • Thermal and chemical equilibrium is reached at the same time. • Particle phase-space densities follow FD of BE distributions. • Universal thermodynamical parameters present (T, mI3,mB , mS) • Occurs on a surface of a hyper-ellipsoid • Particles from freezeout are called Primordial • Later evolution • Resonance decay cascades • Products move along freely Róbert Vértesi, WWND Feb 14 2007

  16. THERMINATOR • A Thermal Heavy Ion Generator A. Kisiel, T. Tałuć, W. Broniowski, W. Florkowski • Based on the Cracow Single Freezeout Model • Handles many (385) resonances • No rescattering implemented • 2- and 3-body decays • Applied on PHENIX data • Parameters rmax and t were tuned to reproduce each centrality class of 5 to 10% • More classes combined to describe regimes in data Róbert Vértesi, WWND Feb 14 2007

  17. Parameters • Thermodinamical parameters T0 = 165 MeV mI3 = -0.9 MeV mB = 6.9 MeV mS = 28.5 MeV • Geometrical parameters • Parameters are tuned for STAR data • Describing PHENIX properly needs further work, but possible Róbert Vértesi, WWND Feb 14 2007

  18. Particle Spectra • Hadron spectra reasonable • Rapidity distribution flat Rapidity distribution PT spectra color codes: K+/-p+/- p+/- primordial (open) final state (closed) Róbert Vértesi, WWND Feb 14 2007

  19. Central Au+Au 200 GeV p+p+ and p-p- source |y|< 0.5 0% < centrality< 20% 0.2 GeV/c < kT < 0.36 GeV/c Pion S(r12) central low-kT Róbert Vértesi, WWND Feb 14 2007

  20. Peripheral 50% < centrality< 90% 0.2 GeV/c < kT < 0.36 GeV/c |y|< 0.5 Pion S(r12) peripheral and hi-kT • High kT 0% < centrality< 20% 0.48 GeV/c < kT < 0.6 GeV/c |y|< 0.5 Róbert Vértesi, WWND Feb 14 2007

  21. all core primordial resonances G>150MeV resonances G>120MeV resonances no core Core investigation for r0 • Remarks • Slope not depending much on the source of pions • r0 shape best reproduced when resonances only Róbert Vértesi, WWND Feb 14 2007

  22. What have we learned? • Data and THERMINATOR • Good description of tails for lower- kT events • Predicts more tail in high kT • Fails for r0 • No rescattering but Long-range tail… Why? • Gauss source containing a parameter that changes in time lead to power-law tail • “continouos” distribution of lifetimes, increasing mean • High number of resonances can provide a similar mechanism to anomalous diffusion • Bialas, Acta Phys. Polon. B 23, 561 (1992). • Measured in e++e-, p+p, h+p Róbert Vértesi, WWND Feb 14 2007

  23. Summary • We have seen that long range tails can be reproduced by different simple models • Rescattering is a kinematic explatation, but not the only one • More effects can lead to them, with the same basic principle behind • There are predictions for power-law exponents of individual particles in both models. Kaon is tale-telling. • Both models overpredict for higher-kT region • It can be a tuning problem, or a clue that we need both features at the same time to explain the tail • Or can mean we miss the point Róbert Vértesi, WWND Feb 14 2007

  24. That’s it! … Backup slides follow Thank you for your attention

  25. Centrality Dependence in TH. Centrality dependent behavior of Therminator simulated S(r12) . Therminator centralities of 0-5% (upper left), 10-20% (upper center) and 30-40% (upper right) are compared to PHENIX central (0-20%), while 40-50% (lower left), 50-60% (lower center) and 70-80% (lower right) to PHENIX peripheral (50-90%). Data and MC: 200 MeV < kT < 360 MeV, |y| < 0.5 GeV/c Róbert Vértesi, WWND Feb 14 2007

  26. Tail dependencies in HRC • Weakly depends on centrality • Weakly depends on PT • Strongly depends on PID • Determined by s(p) shapes Róbert Vértesi, WWND Feb 14 2007

  27. Physics motivation • Predictions for Rout /Rside: • S. Pratt: For strong first order phase transition Rout»Rside • Gyulassy: Prediction for RHIC: Rout»Rside, sign for QGP • Hydro, parton cascade: Rout Rside • Exact hydro result: • Thermal and geometrical radii determine correlation radii Correlation radii Geometrical radii Thermal radii Róbert Vértesi, WWND Feb 14 2007

  28. Problems and solutions • Cut on spatial separation: information may be lost • Correction via Monte Carlo simulation • There is a correlation due to Coulomb-interaction • Two-body Coulomb-problems is solved, so: • What if the source is not Gaussian? • Just fit with a more general function, eg. Levy • There are other methods, but time limitations also… Róbert Vértesi, WWND Feb 14 2007

  29. Fcoul qinv Core-halo picture • Particles in the core Coulomb-interact • Rare halo, no Coulomb interaction • Coulomb-correction is to bedone only for the core part • Sinyukov’s fitting method: • w=l/l’ accounts for smearing due to finite momentum resolution • This can be calculated via MC simulations… • There are more advanced techniques… Róbert Vértesi, WWND Feb 14 2007

  30. Full Coulomb No Coulomb Sinyukov’s fit: w=1 50% Coulomb Sinyukov’s fit: w from MC π π π π + + - - kt (GeV/c) kt (GeV/c) kt (GeV/c) kt (GeV/c) kt (GeV/c) kt (GeV/c) kt (GeV/c) kt (GeV/c) Result of Coulomb-correction • Let us look at how the results vary Róbert Vértesi, WWND Feb 14 2007

  31. Interesting new directions • Azimuthally sensitive HBT (STAR, PHENIX) • Source imaging (PHENIX) • Multiparticle correlations (STAR, PHENIX) • Non-identical correlations (STAR) • Rapidity dependent HBT (PHOBOS) • Photon HBT (STAR) • Non-Gaussian features S. Hegyi, T. Csörgő, W. A. Zajc, L3, STAR, ... • Pion lasers S. Pratt, Q.H. Zhang, J. Zimányi, U. Heinz, Yu. Sinyukov... • Mass-modification, squeezing M. Asakawa, T. Csörgő, M. Gyulassy, Y. Hama, S. Padula, ... • Search for axial UA(1) symmetry restoration using l(pt) S. Vance, T. Csörgő, D. Kharzeev Róbert Vértesi, WWND Feb 14 2007

  32. Core – Halo in the SFM • Pions are grouped after the range in source • Core : if it is • either primordial • or coming from a short-living resonance (G<Gw(782)) • Omega : a decay product of w(782) • Halo : product of a long-living resonance (G<Gw(782)) • Paired into correlation classes Róbert Vértesi, WWND Feb 14 2007

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