Ivan Melo, Mikuláš Gintner Žilina in collaboration with

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Presentation transcript:

Event-by-event fluctuations as a sign of 1st order Quark-Hadron phase transition Ivan Melo, Mikuláš Gintner Žilina in collaboration with Boris Tomášik (Banská Bystrica) Samuel Koróny (Banská Bystrica) FÚ ČAV Praha, Jun 14, 2007 k

Where is the 1st order phase transition? SPS? RHIC

Spinodal fragmentation at phase transition Example: linear sigma model coupled to quarks [O. Scavenius et al., Phys. Rev. D 63 (2001) 116003] spinodal phase transition What is fast? bubble nucleation rate < expansion rate

Supercooling down to spinodal O. Scavenius et al., Phys. Rev. D 63 (2001) 116003: compare nucleation rate with Hubble constant (1D) likely to reach spinodal

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

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

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 events generated from the same distribution, Q's (Q=1-H)will be distributed uniformly.

KS test on simulated events * artificial 'events' coming from uniform or half-normal distribution * simulated events from heavy ion collisions with no quark-gluon plasma (UrQMD) * simulated events from droplet generator

KS-test on generated distributions - random data generated according to half-normal distribution - peak close to Q = 1 (“too similar” events) WHY? Q - we use asymptotic formula valid for very large n results improve with larger n and/or correction terms - we have limited number of significant figures Does it matter in other e-by-e studies?

UrQMD for Pb+Pb at 158 AGeV, b=0, 523 events (Marcus Bleicher) KS-test on UrQMD UrQMD for Pb+Pb at 158 AGeV, b=0, 523 events (Marcus Bleicher) ... similar events

Droplet generator (B. Tomášik) MC generator of (momenta and positions of) particles 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 with tunable params. rapidity distribution: uniform or Gaussian possible OSCAR output

Droplet generator: rapidity spectra T = 175 MeV, various droplet sizes, all particles from droplets No difference in distributions summed over all events!

Droplet generator: all from droplets average droplet volume 50 fm3 20 fm3 Q Q Events are clearly different! 10 fm3 Q Q

Droplet generator: part from droplets V = 10 fm3

Conclusions a method to point out any differences between individual events apply the method to data from NA49 in most central data: droplets would appear when we reach the phase transition line Droplets hee

Bubble nucleation rate 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

The size of droplets Minimize thermodynamic potential per volume where [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]