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Boris Tomášik Univerzita Mateja Bela, Banská Bystrica, Slovakia

Fragmentation of the Fireball and its Signatures. Boris Tomášik Univerzita Mateja Bela, Banská Bystrica, Slovakia Czech Technical University, Prague, Czech Republic in collaboration with Ivan Melo (University of Žilina) ‏ Giorgio Torrieri (Universität Frankfurt) ‏

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Boris Tomášik Univerzita Mateja Bela, Banská Bystrica, Slovakia

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  1. Boris Tomášik: Fragmentation of the Fireball and its Signatures Fragmentation of the Fireball and its Signatures • Boris Tomášik • Univerzita Mateja Bela, Banská Bystrica, Slovakia • Czech Technical University, Prague, Czech Republic • in collaboration with • Ivan Melo (University of Žilina)‏ • Giorgio Torrieri (Universität Frankfurt)‏ • Igor Mishustin (FIAS Frankfurt)‏ • Martin Schulc (FNSPE CTU Prague)‏ • Pavol Bartoš (UMB Banská Bystrica)‏ • Mikuláš Gintner (University of Žilina)‏ • Samuel Koróny (UMB Banská Bystrica)‏ • Dense Matter in Heavy Ion Collisions and Astrophysics • Dubna • July 2008

  2. Fragmentation at 1st order PT: spinodal decomposition at crossover: due to bulk viscosity How to see it? Look for differing rapidity distributions Look at rapidity correlations ... Fragmentation: where and how to see it Boris Tomášik: Fragmentation of the Fireball and its Signatures

  3. Spinodal fragmentation at the phase transition p Example: Van der Waals spinodal phase transition slow expansion: equilibrium trajectory fast expansion spinodal Example: linear sigma model coupled to quarks [O. Scavenius et al., Phys. Rev. D 63 (2001) 116003] What is fast? V bubble nucleation rate < expansion rate Boris Tomášik: Fragmentation of the Fireball and its Signatures

  4. eg. [L. Csernai, J. Kapusta: Phys. Rev. Lett. 69 (1992) 737] nucleation rate: difference in free energy: critical size bubble: at phase transition => must supercool Bubble nucleation rate Boris Tomášik: Fragmentation of the Fireball and its Signatures

  5. O. Scavenius et al., Phys. Rev. D 63 (2001) 116003: compare nucleation rate with Hubble constant (1D)‏ Supercooling down to spinodal likely to reach spinodal Boris Tomášik: Fragmentation of the Fireball and its Signatures

  6. [I.N. Mishustin, Phys. Rev. Lett. 82 (1998), 4779; Nucl. Phys. A681 (2001), 56c] Minimize thermodynamic potential per volume where this gives also [D.E. Grady, J.Appl.Phys. 53 (1982) 322] The size of droplets Boris Tomášik: Fragmentation of the Fireball and its Signatures

  7. Bulk viscosity increases near Tc: [K. Paech, S. Pratt, Phys. Rev. C 74 (2006) 014901, D. Kharzeev, K. Tuchin, arxiv:0705.4280 [hep-ph]. F.Karsch, D.Kharzeev, K.Tuchin, Phys. Lett. B 663 (2008) 217] Kubo formula for bulk viscosity: From lattice QCD, using low energy theorems: Bulk viscosity near Tc Boris Tomášik: Fragmentation of the Fireball and its Signatures

  8. (s)QGP expands easily Bulk viscosity singular atcritical temperature System becomes rigid Inertia may win and fireball will fragment Fragments evaporatehadrons Bulk-viscosity-driven fragmentation ... and freeze-out Boris Tomášik: Fragmentation of the Fireball and its Signatures

  9. Energy-momentum tensor energy density decrease rate fragment size: kinetic energy = dissipated energy where Almost universal size! “Sudden viscosity” => fragmentation Boris Tomášik: Fragmentation of the Fireball and its Signatures

  10. Fragmentation and freeze-out: HBT puzzle Evaporation from droplets Cooper-Frye from FO hypersurface <xt> < 0 Boris Tomášik: Fragmentation of the Fireball and its Signatures

  11. rapidity distribution in a single event Droplets and rapidity distributions dN/dy dN/dy y y without droplets with droplets If we have droplets, each event will look differently Boris Tomášik: Fragmentation of the Fireball and its Signatures

  12. Kolmogorov–Smirnov test: Are two empirical distributions generated from the same underlying probability distribution? The measure of difference between events 1 D measures the difference of two empirical distributions D maximum distance 0 y Boris Tomášik: Fragmentation of the Fireball and its Signatures

  13. How are the D's distributed? Smirnov (1944):If we have two sets of data generated from the same underlying distribution, then D's are distributed according to This is independent from the underlying distribution! For each t=D we can calculate For events generated from the same distribution, Q's will be distributed uniformly. Kolmogorov-Smirnov: theorems Boris Tomášik: Fragmentation of the Fireball and its Signatures

  14. MC generator of (momenta and positions of) particles BT: arXiv:0806.4770 [nucl-th] some particles are emitted from droplets (clusters) droplets are generated from a blast-wave source (tunable parameters) droplets decay exponentially in time (tunable time, T) tunable size of droplets: Gamma-distributed or fixed no overlap of droplets also directly emitted particles (tunable amount) chemical composition: equilibrium, resonances rapidity distribution: uniform or Gaussian possible OSCAR output Droplet generator QuaG Boris Tomášik: Fragmentation of the Fireball and its Signatures

  15. T = 175 MeV, various droplet sizes, all particles from droplets Droplet generator: rapidity spectra No difference in distributions summed over all events! Boris Tomášik: Fragmentation of the Fireball and its Signatures

  16. Events are clearly different! Droplet generator: all from droplets average droplet volume 50 fm3 20 fm3 Q Q 2 fm3 10 fm3 Q Q Boris Tomášik: Fragmentation of the Fireball and its Signatures

  17. Method is very sensitive: clusters are always seen Droplet generator: part from droplets from droplets 20% 40% V = 10 fm3 60% 80% Boris Tomášik: Fragmentation of the Fireball and its Signatures

  18. Droplet generator: smeared rapidities V = 2 fm3 V = 10 fm3 Δy = 0.4 • Clusters seen even for unprecise measurement V = 50 fm3 V = 20 fm3 Boris Tomášik: Fragmentation of the Fireball and its Signatures

  19. Motivation: S. Pratt, PRC 49 (1994) 2722; J. Randrup, Heavy Ion Phys. 22 (2005) 69 Only correlations due to droplets included RHIC settings, STAR acceptance Resonances weakenthe signal Proton-proton rapidity correlations b = 10fm3 varying droplets percentage Simulation with resonances 100% from droplets Boris Tomášik: Fragmentation of the Fireball and its Signatures

  20. Fragmentation of the fireball: due to spinodal decomposition (lower energies) bulk-viscosity driven Fragments can be seen: KS method – different rapidity distributions Femtoscopy Rapidity correlations Fluctuations ... Conclusions Boris Tomášik: Fragmentation of the Fireball and its Signatures

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