2. Róbert Vértesi, WWND Feb 14 2007 2 / 23 Outline Introduction –HBT and Bose-Einstein Correlation –Gaussian Approximation –Coulomb effect, the Imaging method PHENIX imaging –Heavy tail in   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

3. Róbert Vértesi, WWND Feb 14 2007 3 / 23 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

4. Róbert Vértesi, WWND Feb 14 2007 4 / 23 Bose-Einstein Correlations Two plane-waves: Spectrum: S(x,k) is the source distribution Bosons: need for symmetrization Two-particle spectrum (momentum-distribution): k1k1 k2k2 x1x1 x2x2  1,2 S(x,k) source detector Approximations: Plane-wave, no multiparticle symmetrization, thermalization …

5. Róbert Vértesi, WWND Feb 14 2007 5 / 23 Source from Correlation The invariant correlation function Depends on relative and average momenta Uses Fourier-transformed form of the source We can get the source from correlation!

6. Róbert Vértesi, WWND Feb 14 2007 6 / 23 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

7. Róbert Vértesi, WWND Feb 14 2007 7 / 23 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: 1.K coulomb is calculated analytically 2.C 0 is fitted, R,  determined Coulomb Correction

8. Róbert Vértesi, WWND Feb 14 2007 8 / 23 Source Imaging Instead of C raw (q) we compute S 12 (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

9. Róbert Vértesi, WWND Feb 14 2007 9 / 23 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 √ s NN =200 GeV” Can we explain that?

10. Róbert Vértesi, WWND Feb 14 2007 10 / 23 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 ( , K, p) M. Csanad, T. Csorgo, M. Nagy hep-ph/0702032

11. Róbert Vértesi, WWND Feb 14 2007 11 / 23 Hadronic Rescattering Code Realized as Tom Humanic’s HRC simulator –Contains cascades of the most abundant hadrons Particle  [MeV] Classification  152 Core: h/  < 4 fm  120 ** 50  8.4  h/  = 23.5 fm  0.00012 Halo: h/  > 40 fm ’’ 0.200  4.4  2.5x10 -2 Neglect of electric charge

12. Róbert Vértesi, WWND Feb 14 2007 12 / 23 HRC Pion S(r 12 ) central low-k T Central Au+Au 200 GeV     and     source |y|< 0.5 0% < centrality< 20% 0.2 GeV/c < k T < 0.36 GeV/c Gauss

13. Róbert Vértesi, WWND Feb 14 2007 13 / 23 HRC Pion S(r 12 ) peripheral and hi-k T Peripheral 50% < centrality< 90% 0.2 GeV/c < k T < 0.36 GeV/c |y|< 0.5 High k T 0% < centrality< 20% 0.48 GeV/c < k T < 0.6 GeV/c |y|< 0.5

14. Róbert Vértesi, WWND Feb 14 2007 14 / 23 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

15. Róbert Vértesi, WWND Feb 14 2007 15 / 23 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,  I3,  B,  S ) –Occurs on a surface of a hyper-ellipsoid –Particles from freezeout are called Primordial Later evolution –Resonance decay cascades –Products move along freely

16. Róbert Vértesi, WWND Feb 14 2007 16 / 23 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  max and  were tuned to reproduce each centrality class of 5 to 10% –More classes combined to describe regimes in data

17. Róbert Vértesi, WWND Feb 14 2007 17 / 23 Parameters Thermodinamical parameters T 0 = 165 MeV  I3 = -0.9 MeV  B = 6.9 MeV  S = 28.5 MeV Geometrical parameters Parameters are tuned for STAR data –Describing PHENIX properly needs further work, but possible Centrality (%)  max  SimulatedData regime 0 – 5 0 – 20 7.749.74 5 – 107.188.69 10 – 206.448.12 20 – 30 – 5.577.24 30 – 404.636.07 40 – 503.916.38 50 – 6050 – 803.256.19 70 – 804.035.48

18. Róbert Vértesi, WWND Feb 14 2007 18 / 23 Particle Spectra Hadron spectra reasonable Rapidity distribution flat positive hadronsnegative hadronspositive hadronsnegative hadrons central eventsperipheral events Rapidity distribution P T spectra color codes: K    p+/- primordial (open) final state (closed)

19. Róbert Vértesi, WWND Feb 14 2007 19 / 23 Pion S(r 12 ) central low-k T Central Au+Au 200 GeV     and     source |y|< 0.5 0% < centrality< 20% 0.2 GeV/c < k T < 0.36 GeV/c

20. Róbert Vértesi, WWND Feb 14 2007 20 / 23 Pion S(r 12 ) peripheral and hi-k T Peripheral 50% < centrality< 90% 0.2 GeV/c < k T < 0.36 GeV/c |y|< 0.5 High k T 0% < centrality< 20% 0.48 GeV/c < k T < 0.6 GeV/c |y|< 0.5

21. Róbert Vértesi, WWND Feb 14 2007 21 / 23 Core investigation for r  0 primordialall coreresonances  >150MeV resonances  >120MeV resonances no core Remarks –Slope not depending much on the source of pions –r  0 shape best reproduced when resonances only

22. Róbert Vértesi, WWND Feb 14 2007 22 / 23 What have we learned? Data and THERMINATOR –Good description of tails for lower- k T events –Predicts more tail in high k T –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 A.Bialas, Acta Phys. Polon. B 23, 561 (1992). –Measured in e + +e , p+p, h+p

23. Róbert Vértesi, WWND Feb 14 2007 23 / 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-k T 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

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

25. Róbert Vértesi, WWND Feb 14 2007 25 / 23 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

26. Róbert Vértesi, WWND Feb 14 2007 26 / 23 Tail dependencies in HRC Weakly depends on centrality Weakly depends on P T Strongly depends on PID –Determined by  (p) shapes

27. Róbert Vértesi, WWND Feb 14 2007 27 / 23 Physics motivation Predictions for R out / R side : –S. Pratt: For strong first order phase transition R out »R side –Gyulassy: Prediction for RHIC: R out » R side, sign for QGP –Hydro, parton cascade: R out  R side Exact hydro result: –Thermal and geometrical radii determine correlation radii Correlation radii Geometrical radii Thermal radii

28. Róbert Vértesi, WWND Feb 14 2007 28 / 23 Problems and solutions What if the source is not Gaussian? –Just fit with a more general function, eg. Levy –There are other methods, but time limitations also… 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:

29. Róbert Vértesi, WWND Feb 14 2007 29 / 23 Core-halo picture Particles in the core Coulomb-interact Rare halo, no Coulomb interaction q inv F coul  / ’ accounts for smearing due to finite momentum resolution –This can be calculated via MC simulations… There are more advanced techniques… Coulomb-correction is to be done only for the core part Sinyukov’s fitting method:

30. Róbert Vértesi, WWND Feb 14 2007 30 / 23 Result of Coulomb-correction Let us look at how the results vary π + π + π - π - Full CoulombNo Coulomb k t (GeV/c) Sinyukov’s fit: w=1 50% Coulomb k t (GeV/c) Sinyukov’s fit: w from MC

31. Róbert Vértesi, WWND Feb 14 2007 31 / 23 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 ( p t ) S. Vance, T. Csörgő, D. Kharzeev

32. Róbert Vértesi, WWND Feb 14 2007 32 / 23 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 (   ) –Omega : a decay product of  (782) –Halo : product of a long-living resonance (   ) Paired into correlation classes 0.core – core 1.core – omega 2.core – halo 3. omega – omega 4. omega – halo 5. halo – halo