1. Quark/hadron phase transition and fluctuations of rapidity distributions
Ivan Melo (Žilina)
in collaboration with
Boris Tomášik (Banská Bystrica)
Mikuláš Gintner (Žilina)
Samuel Koróny (Banská Bystrica)

4. QCD phase diagram
SPS?
SPS?
RHIC
RHIC

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

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

7. rapidity distribution in a single event
dN/dy
dN/dy y y
No droplets
Droplets
If we have droplets, each event will look differently

8. 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

9. 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.

10. KS test on simulated events
* toy 'events' coming from Gauss or
uniform distribution
* events from droplet generator
(B. Tomášik)

11. KS-test on toy events random data: half events generated
according to Gauss (1,0.1) and half according to Gauss(2,0.1)
distribution
we apply KS test to
random pairs of events Q
pairs at Q=0: events come from opposite distributions
pairs uniformly distributed: events come from the same
Gauss distribution

12. KS-test on toy events (continued)
random data: half events generated
according to Gauss(1.99,0.1) and
half according to
Gauss(2,0.1)
distribution Q
- peak close to Q = 1 (“too similar” events)
- 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

15. Toy droplets: correlations and nonstatistical fluctuations

16. Toy droplets: decreasing number of droplets

17. Droplet generator (B. Tomášik)
MC generator of (momenta and positions of) particles emitted from a fragmented fireball
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
no overlap of droplets
also directly emitted particles (tunable amount)
chemical composition: equilibrium with tunable params.
rapidity distribution: uniform or Gaussian

18. Generator simulates droplets at SPS

19. Introducing resonances into generator

20. Study of different particle species (no droplets)

21. Conclusions
Droplets lead to event-by-event fluctuations of rapidity distributions
KS test is a sensitive tool to study these fluctuations
Apply the method to data from NA49
Droplets hee

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

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

25. 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

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