Fireball fragmentation overview of observables Boris Tomik Univerzita

Fireball fragmentation: overview of observables Boris Tomášik Univerzita Mateja Bela, Banská Bystrica, Slovakia Czech Technical University, Prague, Czech Republic collaborators: Ivan Melo (Žilina), Giorgio Torrieri (Frankfurt) Igor Mishustin (Frankfurt), Martin Schulc (Prague, FNSPE) Paul Chung (Řež/Prague), Sascha Vogel (Frankfurt) Marcus Bleicher (Frankfurt), Samuel Koróny (Banská Bystrica) Mikuláš Gintner (Žilina) Zimányi RHIC Winter School Budapest, December 3, 2009 1

Outline 1. Fragmentation of the fireball – why and when? 2. DRAGON: MC tool for studying observables 3. Observables 1: Kolmogorov-Smirnov (KS) test 4. Observables 2: rapidity correlations 5. Observables 3: imaging 6. Outlook: other observables 7. DRAGON upgrade 2

Fragmentation of the fireball: why and when At the phase transition Case 1: first order phase transition ry : ion jecto ns pa tra ex m w riu slo uilib eq ion ans may be relevant for nuclear collisions observed in multifragmentation exp Scenario possible if nucleation rate < expansion rate fast Rapid passage through the phase transition leads to spinodal decomposition (known also in classical physics) Example: van der Waals isotherm p spinodal V 3

Fragmentation at the cross-over? Spinodal fragmentation scenario is irrelevant at RHIC and LHC. Case 2: Rapid cross-over The bulk viscosity suddenly grows near Tc [K. Paech, S. Pratt, Phys. Rev. C 74 (2006) 014901, D. Kharzeev, K. Tuchin, JHEP 0809: 093 (2008). F. Karsch, D. Kharzeev, K. Tuchin, Phys. Lett. B 663 (2008) 217 H. B. Meyer, Phys. Rev. Lett. 100 (2008) 162001 U. Gürsoy, E. Kiritsis et al. , ar. Xiv: 0906. 1890 v 1 [hep-ph]] 4

The bulk viscosity close to Tc D. Kharzeev, K. Tuchin JHEP 0809: 093 (2008) H. B. Meyer PRL 100 162001 U. Gürsoy, E. Kiritsis et al. ar. Xiv: 0906. 1890 v 1 [hep-ph] 5

Bulk-viscosity-driven fragmentation. . . and freeze-out (s)QGP expands easily Bulk viscosity singular at critical temperature System becomes rigid Inertia may win and fireball will fragment Fragments evaporate hadrons 6

Cavitation = fragmentation Bulk viscosity diminishes the pressure 7

The size of fragments Energy-momentum tensor (only bulk viscosity) Energy density decrease rate Fragment size: kinetic energy = dissipated energy with 8

DRAGON: MC tool for studying observables DRoplet and h. Adron Generat. Or for Nuclear collisions MC generator of (momenta and positions of) particles [BT: Computer Physics Communications 180 (2009) 1642, ar. Xiv: 0806. 4770 [nucl-th]] some particles are emitted from droplets and some directly if no droplet formation is assumed, then similar to THERMINATOR droplets are generated from a blast-wave source (tunable parameters) also non-central fireballs: asymmetry in transverse flow and shape chemical composition: equilibrium resonance decays included tunable size of droplets: Gamma-distributed or fixed droplets decay exponentially in time (tunable time) rapidity distribution: uniform or Gaussian possible OSCAR output 9

Fragmentation: clustering of momenta Fragmentation = (cavitation, granularity, droplet formation…) momentum space position space Clustering in space leads to clustering in momentum space (but the latter is blurred by temperature) no droplets, T = 170 Me. V droplets, T = 10 Me. V 10

Observables E-by-e fluctuations of rapidity distributions rapidity correlations of protons [Melo et al. , Phys. Rev. C 80 (2009) 024904] -> talk Ivan Melo on Wednesday [S. Pratt, Phys. Rev. C 49 (1994) 2722, J. Randrup, Heavy Ion Phys. 22 (2005) 69] imaging femtoscopy [Z. T. Yang et al. , J. Phys. G 36 (2008) 015113] [G. Torrieri, B. Tomášik, I. N. Mishustin, Phys. Rev. C 77 (2008) 034903] mean pt fluctuations angular correlations [Broniowski et al. Phys. Lett. B 635 (2006) 290] [PHOBOS collaboration, ar. Xiv: 0812. 1172 [nucl-ex] ] multiplicity fluctuations [PHENIX, Phys. Rev. C 78 (2008) 044902, H. Heiselberg, Phys. Rep. 351 (2001) 161] elliptic flow (fluctuations). . . Boris Tomášik: Fireball fragmentation – overview of observables

Droplets and rapidity distributions rapidity distribution in a single event d. N/dy without droplets y y with droplets If we have droplets, each event will look differently 12

The measure of difference between events Kolmogorov–Smirnov test (general intro): Are two empirical distributions generated from the same underlying probability distribution? 1 D maximum distance 0 D measures the difference of two empirical distributions y 13

Results from simulation: Q histograms RHIC simulation Droplets with average volume 5 fm 3 All hadrons are produced by droplets Small signal also in events with no droplets due to correlations from resonance decays droplets With identified species problems with small multiplicity no droplets 14

Image of a fragmented fireball imaging gives the pair distribution function There are two scales in the image droplet size a homogeneity length R see also Z. T. Yang et al. : J. Phys G 36 (2009) 015113 15

Benchmark: comparison to THERMINATOR: blast wave freeze-out time does not depend on tranverse position Same choice of parameters in DRAGON PERFECT MATCH OF MODELS! Data: PHENIX, PRL 100 (2008) 232301 16

Image of the fragmented source Comparison of sources with and without droplets - small peak from the droplets - tail from the resonance decays on average 12. 1 hadrons per droplet PHOBOS: 6 -8 hadrons in cluster from correlations in eta-phi -> not much room for larger droplets no room for broad droplet peak 17

Anatomy of the image two-source structure: (resonances included) pairs from same droplet pairs from different droplet 18

Rapidity correlations Hadrons coming from the same droplet have similar rapidities and will be correlated Temperature smears the rapidities – most for light hadrons => use heavy and abundant species – protons See also [S. Pratt, Phys. Rev. C 49 (1994) 2722, J. Randrup, Heavy Ion Phys. 22 (2005) 69] 19

Correlation function Compare distribution in relative rapidity for pairs from the same event and from different events For Gaussian emitters note 20

Rapidity correlations: selected results [Martin Schulc, diploma thesis, FNSPE, Czech Technical University] RHIC simulation with droplets Average volume of droplets 25 fm 3, all hadrons from droplets The influence of freeze-out temperature 110 130 150 170 Me. V 21

Influence of resonance decays [Martin Schulc, diploma thesis, FNSPE, Czech Technical University] Resonances effectively lower the temperature (like in single particle spectra) Resonances not decayed Deltas not decayed All resonances decayed 22

Outlook: other observables Elliptic flow and its fluctuations [Filip Mohyla, Kateřina Hrdinová] Multiplicity fluctuations Rapidity-phi correlations … 23

Outlook: DRAGON upgrade Build in strict energy conservation into droplet decays [Michal Mereš, Ivan Melo] Optimize positioning of droplets 24

Summary Fragmentation is a realistic scenario for heavy ion collisions A tool for generating the final state: DRAGON Fragmentation is seen in - e-by-e fluctuations of rapidity distributions - imaging of hadron sources - proton rapidity correlations -… 25