Methods of Studying Net Charge Fluctuations in Nucleus-Nucleus Collisions Event-by-event fluctuations of the net charge in local regions of phase space have been proposed as a probe of the multiplicity of resonances (mainly ρ and ω) in a hadron gas, and may – according to some models – be sensitive to a quark-gluon plasma phase transition. In a quark-gluon plasma, where the quarks carry ± 2/3 and ± 1/3 unit charges, the corresponding value for v(Q) is 5/18. So if the charge distribution in the plasma survives the transition to ordinary matter, a 72% reduction of the fluctuations would be seen. In a real experiment there are also a lot of other factors influencing the values of v(Q) and v(R). The effects of such factors are simulated in different scenarios below. The behavior of v(Q) and v(R) is studied as a function of detector acceptance. A detector with 4π coverage is used (except for scenario 7) and the acceptance is varied by cuts in the azimuth ( p = Δφ/2п) events with charged particles each were generated for each scenario. Consider a scenario, where each particle is assigned a random charge of +1 or –1 with equal probability. With a fixed number of charged particles within the acceptance, the variance of Q is V(Q) = - 2 = n ch. The variance of R approaches the value 4/ n ch. It is therefore useful to define normalized variances. They are A lot of variables for measuring the fluctuations have been proposed. Two of them are addressed here. The net charge, Q, and charge ratio, R, are defined by where n + and n - are the numbers of reconstructed positive and negative particles in the event. In a hadron gas the values of v(Q) and v(R) are expected to be near 1 and 4 respectively. Henrik Tydesjö Evert Stenlund Joakim Nystrand SCENARIO 5 Random emission with charge symmetry, global charge conservation and a non- negligible background This sample includes a background, b = 20%, of uncorrelated particles. The fluctuations from scenario 1 are reduced by a factor (1- p (1- b )). If scenario 4 and scenario 5 are combined the general expression of the reduction is 1- p (1- b ) E. SCENARIO 2 Random emission with charge asymmetry With a charge asymmetry defined by v(Q) = 1 – ε 2 and v(R) = ε + O(ε 2 ) asymptotically. In the figure above ε = 0.1 is used and the influence on v(R) is huge. As expected, v(Q) = 1 and v(R) approaches 4 asymptotically. v(R) rises for low values of p, because events with n + = 0 or n - = 0 have to be excluded. SCENARIO 1 Random emission with charge symmetry SCENARIO 3 Random emission with charge symmetry and global charge conservation With global charge conservation the fluctuations seen in scenario 1 are reduced by a factor (1- p ). With an acceptance of 1 there are of course no fluctuations. SCENARIO 4 Random emission with charge symmetry, global charge conservation and less than 100% detection efficiency In this simulation the detection efficiency, E, is 80%. The fluctuations from scenario 1 are reduced by a factor (1- pE ). A simple model of the hadronization of the quark-gluon plasma is used. The combinations hadronize with the same probability and create 2 pions in 60% of the cases and 3 pions in 40% of the cases. In this simulation the opening angle between the pions has σ φ = π/18. SCENARIO 8 Random emission of pions from a quark- gluon plasma SCENARIO 6 Random emission of (π + π - )-resonances In this scenario resonances with random azimuthal angle φ are decaying into a π + and a π -. The azimuthal angles of the pions are φ+dφ and φ-dφ, where dφ is randomly chosen from a Gaussian with width σ φ. In the figures below σ φ = π/3, π/6 and π/18. There is a stronger reduction of the fluctuations with smaller opening angles of the pions. Here two detectors are used, each covering 25% of the acceptance and placed opposite to each other. When trying to combine the information from both detectors, this strange behavior is seen. The separation between the detectors is greatly influencing the shapes seen in scenario 6. In this simulation an opening angle between the pions with width σ φ = π/6 was used. SCENARIO 7 Random emission of (π + π - )-resonances at two detectors separated in azimuth