The information of the event-by-event fluctuations is extracted from flow harmonic distributions and cumulants, which can be done experimentally. In this work, I employ the standard method of Gram-Charlier series with the normal kernel to find such distribution, which is the generalization of recently introduced flow distributions for the studies of the event-by-event fluctuations. Also, I introduce a new set of cumulants $j_n\{2k\}$ which have more information about the fluctuations compared with other known cumulants.
The experimental data imply that not only all of the information about the event-by-event fluctuations of collision zone properties and different stages of the heavy-ion process are not encoded in the radial flow distribution $p(v_n)$, but aThe information of the event-by-event fluctuations is extracted from flow harmonic distributions and cumulants, which can be done experimentally. In this work, I employ the standard method of Gram-Charlier series with the normal kernel to find such distribution, which is the generalization of recently introduced flow distributions for the studies of the event-by-event fluctuations. Also, I introduce a new set of cumulants $j_n\{2k\}$ which have more information about the fluctuations compared with other known cumulants.
The experimental data imply that not only all of the information about the event-by-event fluctuations of collision zone properties and different stages of the heavy-ion process are not encoded in the radial flow distribution $p(v_n)$, but also the observables describing harmonic flows can generally be given by the joint distribution $\mathcal{P}(v_1,v_2,...)$. In such a way, I first introduce a set of joint cumulants $\K_{nm}$, and then I find the flow joint distribution using these joint cumulants. Finally, I show that the Symmetric Cumulants $SC(2,3)$ and $SC(2,4)$ obtained from ALICE data are explained by the combinations $\K_{22}+\frac{1}{2}\K_{04}-\K_{31}$ and $\K_{22}+4\K_{11}^2$.lso the observables describing harmonic flows can generally be given by the joint distribution $\mathcal{P}(v_1,v_2,...)$. In such a way, I first introduce a set of joint cumulants $\K_{nm}$, and then I find the flow joint distribution using these joint cumulants. Finally, I show that the Symmetric Cumulants $SC(2,3)$ and $SC(2,4)$ obtained from ALICE data are explained by the combinations $\K_{22}+\frac{1}{2}\K_{04}-\K_{31}$ and $\K_{22}+4\K_{11}^2$.
