Strongly Intensive Measures for Transverse Momentum and Particle Number Fluctuations

The strongly intensive measures $\Delta[P_T,N]$ and $\Sigma[P_T,N]$ are used to study the event-by-event fluctuations of the transverse momentum $P_T$ and particle multiplicity $N$ in nucleus-nucleus collisions. A special normalization for these fluctuation measures ensures that they are dimensionless and yields a common scale required for a quantitative comparison of fluctuations. In this paper basic properties of the $\Delta[P_T, N]$ and $\Sigma[P_T, N]$ measures are tested within different phenomenological models using the Monte Carlo simulations (the so-called fast generators) and analytical solutions. The obtained results are helpful to elucidate the properties of $\Delta[P_T,N]$ and $\Sigma[P_T,N]$ measures.