Dynamical evolution of critical fluctuations and its observation in heavy ion collisions

We study time evolution of critical fluctuations of conserved charges near the QCD critical point in the context of relativistic heavy ion collisions. A stochastic diffusion equation is employed in order to describe the diffusion property of the critical fluctuation arising from the coupling of the order parameter field to conserved charges. We show that the diffusion property gives rise to a possibility of probing the early time fluctuations through the rapidity window dependence of the second-order cumulant and correlation function of conserved charges. It is pointed out that their nonmonotonic behaviors as functions of the rapidity interval are robust experimental signals for the existence of the critical enhancement around the QCD critical point.

Figure 1

Function $F\left(X\right)$ defined in Eq. (16).

Figure 2

Susceptibility in rapidity space $\chi \left(T\right)$ (upper) and diffusion coefficient in the Cartesian coordinates $D_{\mathrm{C}}$ in units of fm (lower) as a function of $T$ for several values of $r$ and $c_{\mathrm{c}}$. The regular parts of the susceptibility ${\chi }^{\mathrm{reg}}\left(T\right)$ and of the diffusion coefficient $D_{\mathrm{C}}^{\mathrm{reg}}\left(T\right)$, labeled “reg,” are also shown. The thin dashed lines show the initial and final values.

Figure 3

Time slices of second-order cumulant (upper) and correlation function (lower) for a noncritical trajectory.

Figure 4

Second-order cumulant (upper) and correlation function (lower) for a trajectory passing through the critical point with $r=0$ and $c_{\mathrm{c}}=4$.

Figure 5

Same as Fig. 4 but with weaker criticality with $c_{\mathrm{c}}=1$.

Figure 6

Second-order cumulant (upper) and correlation function (lower) for a trajectory in the crossover region with $r=1$ and $c_{\mathrm{c}}=4$.