Effects of global charge conservation on time evolution of cumulants of conserved charges in relativistic heavy ion collisions

We investigate the effect of the global charge conservation on the cumulants of conserved charges observed in relativistic heavy ion collisions in a finite rapidity window, $\Delta \eta$, with a special emphasis on the time evolution of fluctuations in the hadronic medium. It is argued that the experimental result of the net-electric-charge fluctuation observed by the ALICE Collaboration does not receive effects from global charge conservation because of the finite diffusion distance of charged particles in the hadronic stage. We emphasize that the magnitude of the effect of global charge conservation can be estimated experimentally by combining the information on the $\Delta \eta$ dependencies of various cumulants of conserved charges, similarly to other dynamical properties of the hot medium.

Figure 1

Second-order cumulants of conserved charges without initial fluctuation as a function of $\Delta \eta /d\left(\tau \right)$ with five finite values of the parameter $L$ and infinite $L$.

Figure 2

Second-order cumulants of conserved charges without initial fluctuation as a function of $\Delta \eta /{\eta }_{\mathrm{tot}}$ with five values of the parameter $T$. The corresponding results in an infinite volume are also plotted for several values of $T$.

Figure 3

Fourth-order cumulants of conserved charges without initial fluctuation as a function of $\Delta \eta /{\eta }_{\mathrm{tot}}$ with five values of $T$.

Figure 4

Fourth-order cumulants of conserved charges under the initial condition (41) with five values of $T$.

Figure 5

Second-order cumulants of conserved charges under the initial condition (42) with five values of $T$. The experimental results from Ref. [17] with ${\eta }_{\mathrm{tot}}=8$ are also plotted by squares for comparison; see Sec. 3c for a detailed discussion.

Figure 6

Fourth-order cumulants of conserved charges under the initial condition (42) with five values of $T$.