Characterizing the initial- and final-state effects in isobaric collisions at energies available at the BNL Relativistic Heavy Ion Collider

A multiphase transport model (AMPT) is employed to predict symmetric correlations (SC), asymmetric correlations (ASC), normalized symmetric correlations (NSC), and normalized asymmetric correlations (NASC) in ${}^{96}\mathrm{Ru}+{}^{96}\mathrm{Ru}$ and ${}^{96}\mathrm{Zr}+{}^{96}\mathrm{Zr}$ collisions at 200 GeV. This study offers insights into the behavior of SC, ASC, NSC, and NASC, considering various nuclear structure scenarios to account for differences between the two isobars. Additionally, I emphasize the importance of detailed experimental measurements as they will serve as a critical constraint for refining the predictions of theoretical models.

Figure 1

Comparisons of the centrality dependence of the two-particle flow harmonics $v_n^2=SC(n,-n$) using the two-subevents method for $\mathrm{Ru}+\mathrm{Ru}$ and $\mathrm{Zr}+\mathrm{Zr}$ at $\sqrt{{\mathit{s}}_{NN}}=200$ GeV from the AMPT model with various parameters given in Table 1.

Figure 2

Same as in Fig. 1 but for the four-particle $SC(1,1,-1,-1$) (a), $SC(2,2,-2,-2$) (b), and $SC(3,3,-3,-3$) (c) using the two-subevents method.

Figure 3

Same as in Fig. 1 but for the six-particle $SC(1,1,1,-1,-1,-2$) (a), $SC(2,2,2,-2,-2,-2$) (b), and $SC(3,3,3,-3,-3,-3$) (c), using the one-subevent method.

Figure 4

Same as in Fig. 1 but for the four-particle $SC(1,2,-1,-2$) (a) and $SC(1,3,-1,-3$) (b), using the two-subevent method.

Figure 5

Same as in Fig. 1 but for the four-particle $SC(2,3,-2,-3$) (a), $SC(2,4,-2,-4$) (b), $SC(2,4,-2,-4$) (c), and $SC(3,4,-3,-4$) (d), using the two-subevent method.

Figure 6

Same as in Fig. 1 but for the six-particle symmetric correlations $SC(2,2,3,-2,-2,-3$) (a), $SC(2,2,4,-2,-2,-4$) (b), $SC(3,3,2,-3,-3,-2$) (c), and $SC(4,4,2,-4,-4,-2$) (d), using the one-subevent method.

Figure 7

Same as in Fig. 1 but for the six-particle symmetric correlations $SC(2,3,4,-2,-3,-4$) (a) and $SC(2,3,5,-2,-3,-5$) (b), using the one-subevent method.

Figure 8

Comparisons of the centrality dependence of the three-particle asymmetric correlations $ASC(1,1,-2$) (a), $ASC(1,2,-3$) (b), and $ASC(1,3,-4$) (c), using the two-subevents method for $\mathrm{Ru}+\mathrm{Ru}$ and $\mathrm{Zr}+\mathrm{Zr}$ at $\sqrt{{\mathit{s}}_{NN}}=200$ GeV from the AMPT model with various parameters given in Table 1.

Figure 9

Same as in Fig. 8 but for the three-particle asymmetric correlations $ASC(2,2,-4$) (a), $ASC(2,3,-5$) (b), and $ASC(2,4,-5$) (c), using two-subevents method.

Figure 10

Same as in Fig. 8 but for the four-particle asymmetric correlations $ASC(3,3,-2,-4$) (a), $ASC(2,5,-3,-4$) (b), and $ASC(2,2,2,-6$) (c), using two-subevents method.

Figure 11

Same as in Fig. 8 but for the five-particle asymmetric correlations $ASC(1,1,1,-1,-2$) (a), $ASC(2,2,2,-3,-3$) (b), $ASC(2,2,2,-2,-4$) (c), and $ASC(2,2,3,-3,-4$) (d), using one-subevent method.

Figure 12

Comparisons of the centrality dependence of the same harmonic normalized symmetric correlations ${\gamma }_{1,1,-1,-1}$ (a), ${\gamma }_{2,2,-2,-2}$ (b), and ${\gamma }_{3,3,-3,-3}$ (c), for $\mathrm{Ru}+\mathrm{Ru}$ and $\mathrm{Zr}+\mathrm{Zr}$ at $\sqrt{{\mathit{s}}_{NN}}=200$ GeV from the AMPT model Case-1 and Case-2 parameters given in Table 1. The curves represent the initial state eccentricity fluctuations.

Figure 13

Same as in Fig. 12 but for the mixed harmonic normalized symmetric correlations ${\beta }_{1,2,-1,-2}$ (a), ${\beta }_{1,3,-1,-3}$ (b), ${\beta }_{2,3,-2,-3}$ (c), ${\beta }_{2,4,-2,-4}$ (d), ${\beta }_{2,5,-2,-5}$ (e), and ${\beta }_{3,4,-3,-4}$ (f).

Figure 14

Comparisons of the centrality dependence of the normalized asymmetric correlations ${\rho }_{1,1,-2}$ and ${\rho }_{1,1,1,-1,2}$ (a), ${\rho }_{2,2,2,-3,-3}$ (b), ${\rho }_{2,2,-4}$, ${\rho }_{2,2,2,-2,-4}$, and ${\rho }_{2,2,3,-3,-4}$ (c), and ${\rho }_{2,4,-6}$ (d), for $\mathrm{Ru}+\mathrm{Ru}$ and $\mathrm{Zr}+\mathrm{Zr}$ at $\sqrt{{\mathit{s}}_{NN}}=200$ GeV from the AMPT model Case-1 and Case-2 parameters given in Table 1. The curves represent the initial state eccentricity fluctuations.

Figure 15

Same as in Fig. 14 but for ${\rho }_{1,2,-3}$ (a), ${\rho }_{1,3,-4}$ (b), ${\rho }_{2,3,-5}$, ${\rho }_{2,3,2,-2,-5}$, and ${\rho }_{2,3,3,-3,-5}$ (c), and ${\rho }_{3,3,-2,-4}$ and ${\rho }_{2,3,3,-4,-4}$ (d).