Cumulants of multiplicity distributions in most-central heavy-ion collisions

I investigate the volume corrections on cumulants of total charge distributions and net proton distributions. The required volume information is generated by an optical Glauber model. I find that the corrected statistical expectations of multiplicity distributions mimic the negative binomial distributions at noncentral collisions, and they tend to approach the Poisson ones at most-central collisions due to the “boundary effects,” which suppress the volume corrections. However, net proton distributions and reference multiplicity distributions are sensitive to the external volume fluctuations at most-central collisions, which imply that one has to consider the details of volume distributions in event-by-event multiplicity fluctuation studies.

Figure 1

(a) Probability distribution of the Poisson parameter $\lambda$ (black dashed line) and the reference multiplicity (red solid line). (b) Mean value ($M$) and variance (${\sigma }^2$) of total charge distributions. (c) Skewness ($S$) and kurtosis ($\kappa$) of total charge fluctuations. (d) The scale variance ($\omega ={\sigma }^2/M$) of total charge distributions. The notation $\overline{P_A}\left(k\right)$ in panel (a) stands for ${\mathcal{P}}_A\left(k\right)$ in the text. The bands in panels (b), (c), and (d) represent the corresponding NBD expectations from Eq. (20).

Figure 2

(a) Distributions of reference multiplicity and cumulant products, (b) $\omega =c_2/c_1$, (c) $S\sigma =c_3/c_2$, and (d) $\kappa {\sigma }^2=c_4/c_2$ of net proton distributions with various strengths of Gaussian-type external volume fluctuations: $a=0.01$ (black solid lines), $a=0.10$ (blue dashed lines), and $a=0.50$ (red dotted lines).