Impact of nuclear structure on the background in the chiral magnetic effect in ${}_{44}{}^{96}\mathrm{Ru}+{}_{44}{}^{96}\mathrm{Ru}$ and ${}_{40}{}^{96}\mathrm{Zr}+{}_{40}{}^{96}\mathrm{Zr}$ collisions at $\sqrt{s_{NN}}=7.7–200 \mathrm{GeV}$ from a multiphase transport model

Impacts of nuclear structure on multiplicity $\left(N_{\mathrm{ch}}\right)$ and anisotropic flows $(v_2$ and $v_3)$ in the isobaric collisions of ${}_{44}{}^{96}\mathrm{Ru}+{}_{44}{}^{96}\mathrm{Ru}$ and ${}_{40}{}^{96}\mathrm{Zr}+{}_{40}{}^{96}\mathrm{Zr}$ at $\sqrt{s_{NN}}$ = 7.7, 27, 62.4, and 200 GeV are investigated by using the string melting version of a multiphase transport (AMPT) model. In comparison with the experimental data released recently by the STAR Collaboration, it is found that the impact of quadrupole deformation ${\beta }_2$ on the $v_2$ difference is mainly manifested in the most central collisions, while the octupole deformation ${\beta }_3$ is in the near-central collisions, and the neutron skin effect dominates in the mid-central collisions. Viewing from the energy dependence, these effects are magnified at lower energies.

Figure 1

Upper panels: Distributions of the number of charged hadrons from the simulation by AMPT in the pseudorapidity window $\left|\eta \right|<$ 0.5 in $\mathrm{Ru}+\mathrm{Ru}$ and $\mathrm{Zr}+\mathrm{Zr}$ collisions at $\sqrt{s_{NN}}$ = 200 GeV for five sets of Woods-Saxon parameters: (a) Case 1, (b) Case 2, (c) Case 3, (d) Case 4, and (e) Case 5. More details on definition of cases can be found in the text. The STAR data [4] for isobar collisions at $\sqrt{s_{NN}}$ = 200 GeV are also shown for comparisons. Middle panels: The $\mathrm{Ru}+\mathrm{Ru}$ to $\mathrm{Zr}+\mathrm{Zr}$ ratios for five sets of Woods-Saxon parameters at $\sqrt{s_{NN}}$ = 200 GeV, as well as the STAR data are shown, respectively. Lower panels: The $\mathrm{Ru}+\mathrm{Ru}$ to $\mathrm{Zr}+\mathrm{Zr}$ ratios for five sets of Woods-Saxon parameters at $\sqrt{s_{NN}}$ = 7.7, 27, and 62.4 GeV, respectively. Notice that the horizontal axis is zoomed in for clarity in the lower panels.

Figure 2

Upper panels: The mean charge multiplicity $N_{\mathrm{ch}}$ within $\left|\eta \right|<$ 0.5 as a function of centrality in $\mathrm{Ru}+\mathrm{Ru}$ and $\mathrm{Zr}+\mathrm{Zr}$ collisions at $\sqrt{s_{NN}}$ = 7.7, 27, 62.4, and 200 GeV. The STAR data [4] for isobar collisions at $\sqrt{s_{NN}}$ = 200 GeV are also shown for comparison. The centrality bins are slighted shifted for clarity. Lower panels: The ratio of the mean charge multiplicity in $\mathrm{Ru}+\mathrm{Ru}$ collisions to that in $\mathrm{Zr}+\mathrm{Zr}$ collisions with matching centrality and energy. The above data include statistical uncertainty.

Figure 3

(Upper panels) Elliptic flow $v_2\left\{2\right\}$ measurements for five cases in isobar collisions at $\sqrt{s_{NN}}$ = 7.7, 27, 62.4 and 200 GeV as a function of centrality by using two-particle correlations. The solid and open symbols represent measurements for $\mathrm{Ru}+\mathrm{Ru}$ and $\mathrm{Zr}+\mathrm{Zr}$ collisions, respectively. The STAR data [4] for isobar collisions at $\sqrt{s_{NN}}$ = 200 GeV are also shown for comparison. The data points are shifted along the $x$ axis for clarity. (Lower panels) The ratios of $v_2$ in $\mathrm{Ru}+\mathrm{Ru}$ over $\mathrm{Zr}+\mathrm{Zr}$ collisions. The statistical uncertainties are represented by lines.

Figure 4

(a) Elliptic flow $v_2\left\{2\right\}$ measurements for five cases in the most central isobar collisions as a function of energy by using two-particle correlations. (b) The ratios of $v_2\left\{2\right\}$ in $\mathrm{Ru}+\mathrm{Ru}$ over $\mathrm{Zr}+\mathrm{Zr}$ collisions in the most central collisions. (c) Elliptic flow $v_2\left\{2\right\}$ measurements for five cases in mid-central isobar collisions as a function of energy by using two-particle correlations. (d) The ratios of $v_2\left\{2\right\}$ in $\mathrm{Ru}+\mathrm{Ru}$ over $\mathrm{Zr}+\mathrm{Zr}$ collisions in mid-central collisions. For (a) and (b), the STAR data [4] for isobar collisions at $\sqrt{s_{NN}}$ = 200 GeV are also shown for comparison. The data points are shifted along the $x$ axis for clarity, and the statistical uncertainties are represented by lines.

Figure 5

Upper panels: Triangular flow $v_3${2} for five cases in isobar collisions at $\sqrt{s_{NN}}$ = 200 GeV as a function of centrality by using two-particle correlations. The STAR data [4] for isobar collisions at $\sqrt{s_{NN}}$ = 200 GeV are also shown for comparison. The data points are shifted along the $x$ axis for clarity. Lower panels: The ratios of $v_2$ in $\mathrm{Ru}+\mathrm{Ru}$ over $\mathrm{Zr}+\mathrm{Zr}$ collisions. The statistical uncertainties are represented by the bars on dots.

Figure 6

Upper panels: Eccentricity ${\varepsilon }_2$ for three cases in isobar collisions at $\sqrt{s_{NN}}$ = 7.7, 27, 62.4, and 200 GeV as a function of centrality. The solid and open symbols represent measurements for $\mathrm{Ru}+\mathrm{Ru}$ and $\mathrm{Zr}+\mathrm{Zr}$ collisions, respectively. The data points are shifted along the $x$ axis for clarity. Lower panels: The ratios of ${\varepsilon }_2$ in $\mathrm{Ru}+\mathrm{Ru}$ over $\mathrm{Zr}+\mathrm{Zr}$ collisions. The statistical uncertainties are represented by bars on dots.

Figure 7

Upper panels: The ratios of $\sqrt{\langle {\varepsilon }_2^2\rangle }$ in $\mathrm{Ru}+\mathrm{Ru}$ over $\mathrm{Zr}+\mathrm{Zr}$ collisions in the most central collisions. Lower panels: The ratios of $\sqrt{\langle {\varepsilon }_2^2\rangle }$ in $\mathrm{Ru}+\mathrm{Ru}$ over $\mathrm{Zr}+\mathrm{Zr}$ collisions in mid-central collisions. The statistical uncertainties are represented by bars on dots.