Boris Tomášik: Identifying f
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Identifying f ireball fragmentation with the Kolmogorov-Smirnov test. Boris Tomášik Univerzita Mateja Bela, Banská Bystrica, Slovakia Czech Technical University, Prague, Czech Republic NICA Round Table Workshop September 10 , 2009. rapidity distribution in a single event.

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Boris Tomášik Univerzita Mateja Bela, Banská Bystrica, Slovakia

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Boris tom ik univerzita mateja bela bansk bystrica slovakia

Boris Tomášik: Identifying fireball fragmentation with the Kolmogorov-Smirnov test

Identifying fireball fragmentation

with the Kolmogorov-Smirnov test

  • Boris Tomášik

  • Univerzita Mateja Bela, Banská Bystrica, Slovakia

  • Czech Technical University, Prague, Czech Republic

  • NICA Round Table Workshop

  • September 10, 2009


Rapidity distribution in a single event

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: Identifying fireball fragmentation with the Kolmogorov-Smirnov test


The measure of difference between events

Kolmogorov–Smirnov test (general intro):

Are two empirical distributions generated from the same underlying probability distribution? (null hypothesis)

The measure of difference between events

1

D measures the

difference of two

empirical distributions

D

maximum

distance

0

y

Boris Tomášik: Identifying fireball fragmentation with the Kolmogorov-Smirnov test


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.

Kolmogorov-Smirnov: theorems

Boris Tomášik: Identifying fireball fragmentation with the Kolmogorov-Smirnov test


Null hypothesis

All events within the selected centrality class are evolve according to the same scenario and the bulk evolves smoothly from the beginning to the freeze out.

(Like in hydrodynamic simulation.)

Null hypothesis

Boris Tomášik: Identifying fireball fragmentation with the Kolmogorov-Smirnov test


Dr oplet and h a dron g enerat o r for n uclear collisions

DRAGON:

MC generator of (momenta and positions of) particles

[BT: Computer Physics Communications 180 (2009) 1642, arXiv:0806.4770 [nucl-th]]

some particles are emitted from droplets (clusters)

if no droplet formation is assumed, then similar to THERMINATOR

droplets are generated from a blast-wave source (tunable parameters)

tunable size of droplets: Gamma-distributed or fixed

droplets decay exponentially in time (tunable time, T)

no overlap of droplets

also directly emitted particles (tunable amount)

chemical composition: equilibrium, resonances

rapidity distribution: uniform or Gaussian

possible OSCAR output

DRoplet and hAdron GeneratOr for Nuclear collisions

Boris Tomášik: Identifying fireball fragmentation with the Kolmogorov-Smirnov test


Results from simulation q histograms

Results from simulation: Q histograms

RHIC simulation

(but similar for NICA with droplets)

Droplets with average volume 5 fm3

All hadrons are produced by droplets

Small signal also with no droplets due to

resonance decays

With identified species problems with

small multiplicity

droplets

no droplets

droplets

droplets

no droplets

no droplets

Boris Tomášik: Identifying fireball fragmentation with the Kolmogorov-Smirnov test


Different sizes of droplets and droplet abundance

Different sizes of droplets and droplet abundance

The peak at Q = 0 is visible

… down to average droplet size

of 2.5 fm3

… also if not all hadrons come from

the droplets

Boris Tomášik: Identifying fireball fragmentation with the Kolmogorov-Smirnov test


The effect of momentum conservation

The effect of momentum conservation

  • Toy model simulation:

  • N subsystems – momentum is exactly 0 within each subsystem

  • This leads to a dip in the Q histogram at small Q

  • This generates a histogram which looks as if the events were correlated with each other

with resonance

decays

y cut

  • NB: other effects which

  • may influence the KS test:

  • string fragmentation (weaker than droplets)

  • jets (high pt)

  • quantum correlations (how to simulate them)

stable

Boris Tomášik: Identifying fireball fragmentation with the Kolmogorov-Smirnov test


Summary

The Kolmogorov-Smirnov test can be used to compare rapidity distributions event-by-event in order to identify non-statistical differences between the events

Try KS test – if it gives no effect, then all events are the same and we have one piece of bulk matter (null hypothesis)

Advantage of the KS test is no bias on any moment of the rapidity distribution.

Fireball fragmentation would lead to a clear signal with this technique

Other effects on the KS test to be examined

Summary

Boris Tomášik: Identifying fireball fragmentation with the Kolmogorov-Smirnov test


Backup exact formulas for q

Backup: exact formulas for Q

Boris Tomášik: Identifying fireball fragmentation with the Kolmogorov-Smirnov test


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