1. Simulations on the Event-by-event Fluctuations of the Particle Yield Ratios D. Kresan, V. Friese GSI, Darmstadt, Germany Correlations and Fluctuations in Relativistic Nuclear Collisions Arcetri, Florence July 7-9 2006

2. July 7 2006 D. Kresan Correlations and Fluctuations Workshop, Florence2 Outline Motivation Definition of dynamical fluctuations NA49 results vs. UrQMD – previous studies and consistency UrQMD studies –single particle ratios (K + over pi + /  and vice versa) –acceptance effects –resonance decay influence –hadronic cascades Toy model simulations (K* and  decay)

3. July 7 2006 D. Kresan Correlations and Fluctuations Workshop, Florence3 Motivation E-b-e fluctuations of the particle yield ratio are proposed as the signature for the critical endpoint But influence of acceptance, resonance decays and hadronic cascades on e-b-e fluctuations remains to be studied Model to start from – UrQMD. Has both resonances and re-scattering

4. July 7 2006 D. Kresan Correlations and Fluctuations Workshop, Florence4 Dynamical Fluctuations Measure the particle yields ratio in an event : K/  Relative width of distribution :  = RMS / MEAN  data 2 =  fin 2 +  exp 2 +  dyn 2 background Event mixing: no two tracks coming from one real event  mixed  dyn 2 =  data 2   mixed 2

5. July 7 2006 D. Kresan Correlations and Fluctuations Workshop, Florence5 NA 49 Measurements vs. UrQMD C.Roland @ QM 2004

6. July 7 2006 D. Kresan Correlations and Fluctuations Workshop, Florence6 Acceptance Effects – forward rapidity 44 y > y cm

7. July 7 2006 D. Kresan Correlations and Fluctuations Workshop, Florence7 Acceptance Effects – momentum cut (PID) 44 y > y cm p lab >3GeV/c Possible reasons for differences: 1.Different UrQMD versions ? 2.Different acceptance conditions (acceptance filter vs. simplified cuts)

8. July 7 2006 D. Kresan Correlations and Fluctuations Workshop, Florence8 UrQMD Results central Au+Au at 25 AGeV 44 real

9. July 7 2006 D. Kresan Correlations and Fluctuations Workshop, Florence9 Acceptance Effects  dyn (%)44 y > y cm y>y cm && p lab >3 GeV/c K/  2.6  0.22.2  0.63.4  0.6 p/  -5.51  0.04-6.14  0.08-7.0  0.1 K+/+K+/+ -6.2  0.1-7.0  0.3-6.1  0.5 K+/K+/ -7.9  0.1-9.0  0.2-8.6  0.3 K/+K/+ -8.9  0.3-9.3  0.6-10.7  0.7 K/K/ -7.5  0.3-7.2  0.8-6.7  1.2 central Au+Au at 25 AGeV by UrQMD Acceptance effect is present but not dramatic

10. July 7 2006 D. Kresan Correlations and Fluctuations Workshop, Florence10 Sources of Kaons in UrQMD 1.3 Results of collision history analysis central Au+Au at 25 AGeV by UrQMD Majority of kaons come from the K* decay

11. July 7 2006 D. Kresan Correlations and Fluctuations Workshop, Florence11 K* Decay Suppressed central Au+Au at 25 AGeV by UrQMD real

12. July 7 2006 D. Kresan Correlations and Fluctuations Workshop, Florence12 Summary Table σ dyn Nominalno K* decay no  decay t = 5 fm/ct = 2 fm/c K/  2.6  0.36.7  0.21.3  0.56.4  0.112.0  0.1 p/  -5.52  0.04-5.59  0.04-5.51  0.04-5.48  0.04-2.68  0.1 K+/+K+/+ -6.2  0.1-3.6  0.6-6.3  0.1-3.9  0.2-4.2  0.6 K+/K+/ -8.0  0.1-6.3  0.3-8.2  0.1-6.3  0.1-8.1  0.3 K/+K/+ -8.7  0.3-8.1  0.3-8.8  0.3-7.3  0.3-7.8  0.6 K/K/ -7.0  0.4-6.6  0.4-7.3  0.4-5.8  0.3-4.7  0.9 σ dyn K* contribution  contribution t = 5 fm/ct = 2 fm/c K/  -6.2  0.32.3  0.5-5.8  0.211.7  0.1 p/  0.9  0.4-0.3  0.9-0.7  0.5-4.83  0.07 K+/+K+/+ -5.0  0.41.1  0.8-4.8  0.2-4.6  0.6 K+/K+/ -4.9  0.41.8  0.6-4.9  0.21  2 K/+K/+ -3.2  1.11.3  2.8-4.7  0.73.9  1.4 K/K/ -2.3  1.62.1  2.0-3.9  0.85  1

13. July 7 2006 D. Kresan Correlations and Fluctuations Workshop, Florence13 Resonances in Toy Model – K* K*(892) 0  K  Toy Model features: 1.Independent particle production with yields and kinematics from UrQMD 2.Fluctuations of Kaon number of various amplitude 3.Resonance decays 4.Chains of resonance decays = 41 = 363 Independently produced:

14. July 7 2006 D. Kresan Correlations and Fluctuations Workshop, Florence14 Resonances in Toy Model –   K+KK+K K0LK0SK0LK0S 00 0000 ++ = 41 = 363 Independently produced: analytical formula

15. July 7 2006 D. Kresan Correlations and Fluctuations Workshop, Florence15 Conclusion Our results of UrQMD simulations are consistent with ones obtained by C.Roland Acceptance has effect on resulting fluctuations K* decay is not the only source of correlations Positive fluctuations of the (K + +K  )/(  + +   ) ratio in UrQMD are mainly due to  decay Possibly charge conservation ??? Interpretation of this observable is feasible ONLY IF yields (and phase space distr.) of all resonances and daughter particles are known