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. 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 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. The net charge, Q, and charge ratio, R, are defined by Q = n + - n - R = n + / n - n + and n - are the numbers of reconstructed positive and negative particles in the event. The normalized variances for these quantities are v(Q) = V(Q) / n ch v(R) = V(R) * n ch where V(Q) and V(R) are the variances. In the different scenarios described below, the behavior of v(Q) and v(R) is studied as a function of detector acceptance. A detector with 4π coverage is used and the acceptance is varied by cuts in the azimuth ( p = Δφ/2п) events with charged particles each were generated for each scenario. Using two different measures below, the influences of charge asymmetries, global charge conservation, backgrounds from secondary sources, detector efficiency and neutral resonances are studied. A simple model of the quark-gluon plasma is also studied. 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 2 Random emission with charge asymmetry 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 was used and the influence on v(R) is huge. SCENARIO 1 Random emission with charge symmetry 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 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 and the acceptance is varied by cuts in the azimuth ( p = Δφ/2п) events with charged particles each were generated for each scenario. where n + and n - are the numbers of reconstructed positive and negative particles in the event. 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 SCENARIO 3 Random emission with charge symmetry and global charge conservation v(Q) = 1 – ε 2 and v(R) = ε + O(ε 2 ) asymptotically. In the figure above ε = 0.1 was used and the influence on v(R) is huge.