1/20 Boris Tomášik: Fragmentation of the Fireball and its Signatures Boris Tomášik Univerzita Mateja Bela, Banská Bystrica, Slovakia Czech Technical University,

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1/20 Boris Tomášik: 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 Fragmentation of the Fireball and its Signatures

2/20 Boris Tomášik: Fragmentation of the Fireball and its Signatures Fragmentation: where and how to see it Fragmentation at 1 st order PT: spinodal decomposition at crossover: due to bulk viscosity How to see it? Look for differing rapidity distributions Look at rapidity correlations...

3/20 Boris Tomášik: Fragmentation of the Fireball and its Signatures Spinodal fragmentation at the phase transition p V Example: Van der Waals slow expansion: equilibrium trajectory fast expansion spinodal phase transition spinodal Example: linear sigma model coupled to quarks [O. Scavenius et al., Phys. Rev. D 63 (2001) ] What is fast? bubble nucleation rate < expansion rate

4/20 Boris Tomášik: Fragmentation of the Fireball and its Signatures 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

5/20 Boris Tomášik: Fragmentation of the Fireball and its Signatures Supercooling down to spinodal O. Scavenius et al., Phys. Rev. D 63 (2001) : compare nucleation rate with Hubble constant (1D)‏ likely to reach spinodal

6/20 Boris Tomášik: Fragmentation of the Fireball and its Signatures The size of droplets [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]

7/20 Boris Tomášik: Fragmentation of the Fireball and its Signatures Bulk viscosity near T c Bulk viscosity increases near T c : [K. Paech, S. Pratt, Phys. Rev. C 74 (2006) , D. Kharzeev, K. Tuchin, arxiv: [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:

8/20 Boris Tomášik: Fragmentation of the Fireball and its Signatures Bulk-viscosity-driven fragmentation (s)QGP expands easily Bulk viscosity singular at critical temperature System becomes rigid Inertia may win and fireball will fragment Fragments evaporate hadrons... and freeze-out

9/20 Boris Tomášik: Fragmentation of the Fireball and its Signatures “Sudden viscosity” => fragmentation Energy-momentum tensor energy density decrease rate fragment size: kinetic energy = dissipated energy where Almost universal size!

10/20 Boris Tomášik: Fragmentation of the Fireball and its Signatures Fragmentation and freeze-out: HBT puzzle Cooper-Frye from FO hypersurface < 0 Evaporation from droplets

11/20 Boris Tomášik: Fragmentation of the Fireball and its Signatures Droplets and rapidity distributions rapidity distribution in a single event y dN/dy y without droplets with droplets If we have droplets, each event will look differently

12/20 Boris Tomášik: Fragmentation of the Fireball and its Signatures The measure of difference between events Kolmogorov–Smirnov test: Are two empirical distributions generated from the same underlying probability distribution? y 0 1 D maximum distance D measures the difference of two empirical distributions

13/20 Boris Tomášik: Fragmentation of the Fireball and its Signatures Kolmogorov-Smirnov: theorems 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.

14/20 Boris Tomášik: Fragmentation of the Fireball and its Signatures Droplet generator QuaG MC generator of (momenta and positions of) particles BT: arXiv: [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

15/20 Boris Tomášik: Fragmentation of the Fireball and its Signatures Droplet generator: rapidity spectra T = 175 MeV, various droplet sizes, all particles from droplets No difference in distributions summed over all events!

16/20 Boris Tomášik: Fragmentation of the Fireball and its Signatures 2 fm 3 Droplet generator: all from droplets QQ QQ 20 fm 3 10 fm 3 average droplet volume 50 fm 3 Events are clearly different!

17/20 Boris Tomášik: Fragmentation of the Fireball and its Signatures Droplet generator: part from droplets from droplets 20% V = 10 fm 3 40% 60%80% Method is very sensitive: clusters are always seen

18/20 Boris Tomášik: Fragmentation of the Fireball and its Signatures Droplet generator: smeared rapidities V = 2 fm 3 V = 10 fm 3 V = 20 fm 3 V = 50 fm 3 Δy = 0.4 Clusters seen even for unprecise measurement

19/20 Boris Tomášik: Fragmentation of the Fireball and its Signatures Proton-proton rapidity correlations 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 weaken the signal b = 10fm 3 varying droplets percentage Simulation with resonances 100% from droplets

20/20 Boris Tomášik: Fragmentation of the Fireball and its Signatures Conclusions 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...