Removing the influence of centrality fluctuations in the analysis of forward-backward multiplicity correlations in heavy-ion collisions

In high-energy heavy-ion collisions, forward-backward multiplicity (FB) correlation strengths are affected greatly by centrality fluctuation and centrality window width. A method called ${\mathrm{FB}}_{\mathrm{relative}}$ is raised to reduce or remove the influence. This method is tested by a Monte Carlo simulation and is compared with the ${\mathrm{FB}}_{\mathrm{average}}$ and ${\mathrm{FB}}_{\mathrm{profile}}$ methods. The ${\mathrm{FB}}_{\mathrm{relative}}$ method is also used for the hijing event generator of Au+Au collisions, and comparisons between the correlation strengths of different collision energies $\sqrt{s_{NN}}$ from 7.7 to 200 GeV are shown. As a result, the correlation strengths are all very weak, and the similarities of correlation strengths $b$ of different centrality windows within 0%–50% are obvious, and it is observed that the correlation strengths decrease with the increasing pseudorapidity gap at $\left|\eta \right|<2$.

Figure 1

ISets of forward and backward $\eta$ windows for different separation $\mathrm{\Delta }\eta$.

Figure 2

FB correlation strengths $b$ of different centrality windows of the MC source without additional FB correlations ($\alpha =0$) for the ${\mathrm{FB}}_{\mathrm{average}}$, ${\mathrm{FB}}_{\mathrm{profile}}$, and ${\mathrm{FB}}_{\mathrm{relative}}$ methods.

Figure 3

Averages of $b$ over $\mathrm{\Delta }\eta$ from 0 to 2 for the ${\mathrm{FB}}_{\mathrm{average}}$, ${\mathrm{FB}}_{\mathrm{profile}}$, and ${\mathrm{FB}}_{\mathrm{relative}}$ methods. $\langle b\rangle$ is plotted as a function of correlation parameter $\alpha$. The results of Eq. (13) are denoted by “Deduced.”

Figure 4

FB correlation strengths $b$ of different centrality windows of hijing event generator of Au+Au collisions at $\sqrt{s_{NN}}=7.7$ to 200 GeV for the ${\mathrm{FB}}_{\mathrm{relative}}$ method.

Figure 5

FB correlation strengths $b$ of different pseudorapidity gaps $\mathrm{\Delta }\eta$ as a function of collision energy $\sqrt{s_{NN}}$ from 7.7 to 200 GeV for the ${\mathrm{FB}}_{\mathrm{relative}}$ method.

Figure 6

FB correlation strengths $b$ of different reference windows for hijing event generator at $\sqrt{s_{NN}}=200\mathrm{GeV}$ by using the ${\mathrm{FB}}_{\mathrm{profile}}$ method. The sums of reference-window widths are denoted by $\mathrm{\Delta }{\eta }_{\mathrm{ref}}$.

Figure 7

Sensitivity of the FB correlation strengths $b$ to the fitting range for the ${\mathrm{FB}}_{\mathrm{profile}}$ method. (a) Full range fitting. (b) Fitting near the centrality windows. (c) Results of piecewise fitting. (d) Averages of $b$ of the reference bins within the centrality windows. The centrality windows and corresponding fitting ranges are shown in the right column.

Figure 8

On the bottom graph, the probability distribution function (PDF) of ${\mu }_{\varepsilon }$ is set to an even function $H\left({\mu }_{\varepsilon }\right)$, and the PDF of $N_{\mathrm{ref}}$ is equal to $\int H\left({\mu }_{\varepsilon }\right)exp\left[-\frac{{\left(N_{\mathrm{ref}}-{\mu }_{\varepsilon }\right)}^2}{2{\mu }_{\varepsilon }}\right]d{\mu }_{\varepsilon }$. On the top graph, for different $N_{\mathrm{ref}}$, PDFs of ${\mu }_{\varepsilon }$ are calculated as $g\left({\mu }_{\varepsilon }\right)$ [Eq. (9)] and $F\left({\mu }_{\varepsilon }\right)$ [Eq. (B1)].

Figure 9

By using Eq. (C2), the FB correlation strengths $b$ of different centrality windows for Au+Au collisions of the hijing event generator at $\sqrt{s_{NN}}=7.7–200$ GeV are shown, and are denoted by “o MDF” short for “no modification”. The results calculated with Eq. (12) are denoted by “MDF”.