Conserved charge fluctuations using the $D$ measure in heavy-ion collisions

We study the net-charge fluctuation $D$-measure variable, in high-energy heavy-ion collisions in heavy-ion jet interaction generator (HIJING), ultrarelativistic quantum molecular dynamics (UrQMD), and hadron resonance gas (HRG) models for various center-of-mass energies ($\sqrt{s_{{}_{NN}}}$). The effects of kinematic acceptance and resonance decay, in the pseudorapidity acceptance interval ($\mathrm{\Delta }\eta$) and lower transverse momentum ($p_T^{\text{min}}$) threshold, on fluctuation measures are discussed. A strong dependence of $D$ with the $\mathrm{\Delta }\eta$ in HIJING and UrQMD models is observed as opposed to results obtained from the HRG model. The dissipation of fluctuation signal is estimated by fitting the $D$ measure as a function of the $\mathrm{\Delta }\eta$. An extrapolated function for higher $\mathrm{\Delta }\eta$ values at lower $\sqrt{s_{{}_{NN}}}$ is different from the results obtained from models. Particle species dependence of $D$ and the effect of the $p_T^{\text{min}}$ selection threshold are discussed in HIJING and HRG models. The comparison of $D$, at midrapidity, of net-charge fluctuations at various $\sqrt{s_{{}_{NN}}}$ obtained from the models with the data from the A Large Ion Collider Experiment (ALICE) experiment is discussed. The results from the present paper as a function of $\mathrm{\Delta }\eta$ and $\sqrt{s_{{}_{NN}}}$ will provide a baseline for comparison to experimental measurements.

Figure 1

Fluctuation, $D$, for net charge as a function of $\mathrm{\Delta }\eta$ for (0–5%) centrality in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV with HIJING and UrQMD models. The $D$ from HRG calculations for net charge without resonance decay (solid line), with resonance decay (dashed line), and with net pion (dash-dotted line) are also shown.

Figure 2

The $D$ values for net-charge fluctuations as a function of $\mathrm{\Delta }\eta$ for (0–5%) centrality in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=19.6$, 200, and 2760 GeV with the HIJING model. The $D$ from HRG, with and without resonance decay contribution, compared with model calculations at different $\sqrt{s_{{}_{NN}}}$ energies.

Figure 3

The $\langle N_{\text{ch}}\rangle {\nu }_{(\pm ,\mathrm{dyn})}^{\text{corr}}$ (left axis) and $D$ (right axis) as a function of $\mathrm{\Delta }\eta$ intervals for (0–5%) centrality in $\mathrm{Au}+\mathrm{Au}$ collisions at different $\sqrt{s_{{}_{NN}}}$. The data points are fitted with the $\text{Erf}(\mathrm{\Delta }\eta /\sqrt{8}\sigma )$ up to $\mathrm{\Delta }\eta =2.0$ shown in solid line and extrapolation up to higher $\mathrm{\Delta }\eta$ intervals is shown in dashed line.

Figure 4

The $\langle N_{\text{ch}}\rangle {\nu }_{(\pm ,\mathrm{dyn})}^{\text{corr}}$ (left axis) and $D$ (right axis) as a function of $\mathrm{\Delta }\eta$ intervals for (0–5%) centrality in $\mathrm{Pb}+\mathrm{Pb}$ collisions at different $\sqrt{s_{{}_{NN}}}$. The data points are fitted with the $\text{Erf}(\mathrm{\Delta }\eta /\sqrt{8}\sigma )$ up to $\mathrm{\Delta }\eta =2.0$ shown in solid line and extrapolation up to higher $\mathrm{\Delta }\eta$ intervals is shown in dashed line. The $D$ from HRG, with and without resonance decay contribution, compared with the experimental data and HIJING model calculation.

Figure 5

Collision energy dependence of $\sigma$ (upper panel) which characterizes the diffusion at the freeze-out are calculated using HIJING and UrQMD models for (0–5%) centrality in $\mathrm{Au}+\mathrm{Au}$ collisions. The $D$ values as a function of $\sqrt{s_{{}_{NN}}}$ are shown in the lower panel. The solid symbols are values extracted from the simulated data at $\mathrm{\Delta }\eta =5.0$ and the open symbols are extrapolated values of $D$ using the functional form at the same $\mathrm{\Delta }\eta$ interval.

Figure 6

The $D$ values for net-charge, net-pion, net-kaon, and net-proton fluctuations as a function of $\mathrm{\Delta }\eta$ for (0–5%) centrality in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV with the HIJING model. The $D$ from HRG calculations for net charge and net baryon without and with inclusion of resonance decay are compared with model calculations.

Figure 7

The lower $p_T$ selection range dependence of the $D$ for net-charge, net-pion, net-kaon, and net-proton fluctuations calculated for (0–5%) centrality in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV with the HIJING model. The $D$ from HRG calculations is compared with HIJING model calculations.

Figure 8

Collision energy dependence of $D$ for the net-charge fluctuations measured at midrapidity in central (0–5%) heavy-ion collisions at SPS [22], RHIC [23], and LHC [20] energies. The model calculations (HIJING, UrQMD, and HRG) for different energies are also shown.