1. Event characterization

2. Many important aspects of heavy-ion dynamics require the characterization and selection of events. Two main examples: 1.Determination of event centrality 2.Determination of reaction plane

3. Determination of the event centrality The classification of the events according to their centrality is one of the main tasks in the study of heavy ion reactions, from intermediate energy to ultrarelativistic collisions Most of the results obtained in HI collisions are studied as a function of the event centrality Usually some global property of the event is used to determine the centrality (global variables) However, there are several possible choices and many critical points related to detector limitations and theoretical models

4. Several observables may be related to the impact parameter in a nucleus-nucleus collision: Particle multiplicity Due to the violence of the collision, it is expected that at small impact parameters, the probability for the system to break up in more fragments is higher. Subsets of the multiplicity, such as the forward or backward multiplicity are sometimes considered. Total detected charge While a perfect detector gives a value of the total detected charge very close to the charge of the colliding nuclei, for a real detector some correlation exists between the detected charge and the impact parameter. Also in this case subsets (for instance the mid-rapidity charge) exist.

5. Total perpendicular momentum This is defined by the sum of perpendicular momenta of all detected particles. Average (or transverse) parallel velocity It is defined by the weighted average (over the masses) of the parallel (transverse) velocities. For a perfect detector this would give the C.M. velocity. Diagonal components of the quadrupole momentum tensor The shape of the momentum distribution of each event may be analyzed by the sphericity tensor. The eigenvalues give the axes of the ellipsoid momentum distribution, allowing to define 2 values: the eccentricity and the angle between the symmetry axis and the beam direction. The distribution of the events in this plane permits to sort out them into central, intermediate and peripheral collisions

6. Method: Generate events according to some realistic model Filter generated events through detector geometry, limitations and response Select well measured events, i.e. events which carry enough information to build the global variables of interest Study the correlation between simulated impact parameter and the value of the global variable Extract from filtered data the value of the reconstructed impact parameter and compare to the original value

7. An example from the MEDEA set-up in the study of pion production (F.Riggi et al., Zeit. Physik A344(1993)455) Detector structure: 180 BaF 2 modules arranged into 7 rings (24 detectors each + 1 ring with 12 detectors) 120 Phoswich detectors arranged into 5 rings 16 NE102 scintillators, arranged into 2 rings Solid angle=93% of 4 π

8. Detector limitations/1: Polar angle resolution: 1.25 ° Ring 1 Hodoscope 2.5 ° Ring 2 Hodoscope 2.0 ° Rings 1-5 Phoswich 7.5 ° Rings 1-8 BaF 2 Azimuthal angle resolution 22.5 ° Hodoscope 15 ° BaF 2 and Phoswich

11. Detector limitations/2: Particle identification BaF 2 : charge and mass for Z=1; for Z>1 Z=2 and A=4 assigned Phoswich: charge and mass for Z=1; for Z=2 A=4 assigned; for Z>2, Z=3 and A=6 assigned Hodoscope: charge identification up to Z=6; mass assigned as the most abundant isotope; for Z>6, Z=7 and A=14 assigned Velocity threshold: From 3.5 and 5.0 cm/ns, depending on detectors Finite angular resolution and multihit events considered

12. It is important to compare the response of a perfect detector to that of the real detector Example: the charged particle multiplicity distribution, as measured: In a 4 π detector In the real MEDEA detector (with or w/o Hodoscope)

13. To perform a centrality analysis, a preliminary selection of the events is made (well measured events), in order to ensure they carry enough information to extract global variables. For instance, in a perfect particle detector, the total parallel momentum in each event should be constant and equal to the projectile momentum. Any real detector gives however a broad distribution of the total parallel momentum, due to undetected or misidentified particles. Example: MEDEA detector + Hodoscope With MEDEA only a large fraction of momentum is lost and almost all events are badly measured

14. One can also look at the correlation between two global variables. Examples: In this case a good correlation is observed between multiplicity and total detected charge.

15. By means of one global variable (choose the best!) values of the true and reconstructed impact parameters may be compared. Example of a realistic correlation between true and reconstructed impact parameter, according to the average parallel velocity 3 centrality regions (central, intermediate and peripheral) may be extracted MEDEA + HodMEDEA only

16. As before, for the total multiplicity as a global variable

17. An example of multiplicity analysis at SPS energies: the NA57 experiment Ref. The NA57 Collaboration, J.Phys. G31(2005)321 Multiplicity is important not only for classification of events according to centrality, but also beacuse it is related to the entropy of the system and to the initial energy density. In NA57 the production of strange and multistrange hyperons is studied as a function of the centrality

18. The experimental set-up includes two planes of microstrip detectors for centrality evaluation Each plane has 3 arms with 200 strips/arm (pitches from 100 to 400 μm) At 158 AGeV/c (central rapidity y cm = 2.9) the two planes cover 1.9 < η < 3.0 3.0 < η < 4.0

21. Reconstruction of multiplicity The detector provides analogue signals roughly proportional to the energy lost by particles in the strips. Strip signals are equalized during calibration runs and noisy strips removed from the analysis From contiguous strips, the number of clusters is determined The hit multiplicity is then evaluated considering also the energy deposited, to account for clusters produced by the passage of more than one particle.

22. The contribution of the empty target (interaction of the beam with air or other materials along the beam line) is measured in a special run and subtracted. This amount to about 6 %, mostly at low multiplicity. Decrease at low multiplicity is due to the trigger efficiency, which is mainly optimized for central collisions. Hit multiplicity distribution @160 AGeV/c

23. Hit multiplicity distribution @40 AGeV/c

24. Correlation between the number of hits and the charged particle multiplicity, according to theoretical models filtered by the detector response. To obtain the total multiplicity over the full azimuthal range, a comparison is made between the data and a simulation of the collision according to some model (here VENUS and RQMD), filtered by the GEANT response of the detector.

25. Comparison between the charged particle multiplicity experimental and theoretical model distributions. The distribution of charged particle multiplicity, evaluated as described, is used to determine the centrality of the collision and to evaluate the number of wounded nucleons N wound (nucleons which suffered at least one inelastic collision in the process). N wound is determined by a geometrical (Glauber) model and N ch = const x (N wound ) α

26. For such study, 9 centrality classes were identified, according to the fraction of the total inelastic cross section (evaluated by the Glauber model for this case as 7.26 barn).

27. For further studies of the centrality dependence of the strangeness production however, more stringent selection criteria have been used, and only 5 centrality classes have been used: 5% most central collisions

28. Since each experiment may use a different centrality definition, it is sometimes important to compare reasults from different experiments Comparison between the number of wounded nucleons for each of the (same) five centrality classes in experiments NA57 and NA50

29. For the value of dN/dη a disagreement is observed especially in central collisions between the different SPS experiments.

30. Determination of the reaction plane Several methods exist to determine the reaction plane Sphericity tensor method (Gyulassy et al., Phys.Lett.110B(82)185) Transverse momentum analysis (Danielewicz et al., Phys.Lett.157B(85)146) Azimuthal correlation method (Wilson et al., Phys.Rev. C45(92)738)

31. The applicability of any method to determine the reaction plane relies on two points i)The events are well measured, i.e. they are complete events with the momenta of all particles well determined ii)The problem has a solution, i.e. the impact parameter differs from zero

32. An example: determination of the reaction plane to study pion shadowing effects in heavy ion collisions at 100 MeV/A (F.Riggi et al., Phys. Rev. C55(1997)2506) Geometrical picture of the pion production process Dynamical picture of the process

33. Selection of well measured events Only about 1% of the inclusive events were selected!

34. Chosen method: transverse momentum analysis The reaction plane is determined by the vector Q in the XY-plane This is calculated event-by-event, by a weighted vectorial sum over all the detected fragments M= total proj+target mass ν = multiplicity w = appropriate weight of the event

35. A widely used technique to estimate the resolution of the method is to split the event into two subevents and calculate the reaction planes for the two subevents. Comparing the two gives the resolution

36. Result: pions are emitted mainly perpendicular to the reaction plane … whereas for photons the distribution is flat

37. Microscopic BNV calculations predict this squeeze-out effect when pion reabsorption is included