Impact of event activity variable on the ratio observables in isobar collisions

The STAR isobar data of ⁹⁶Ru+⁹⁶Ru and ⁹⁶Zr+⁹⁶Zr collisions at s_NN=200 GeV show that ratios of observables (R_O) such as the multiplicity distribution, p(N_ch), and the harmonic flow, v_n, deviate from unity, when presented as a function of centrality, c [1]. These deviations have been attributed to the differences in the shape and radial profiles between ⁹⁶Ru and ⁹⁶Zr nuclei. In addition, the ratios R_O(x) depend on the choice of the event activity variable x, which could be either N_ch or centrality. We estimate the difference ΔR between these two choices, based on the published p(N_ch), as well as those from a multiphase transport (AMPT) model with varied nuclear structure parameters: nuclear radius (R₀), surface diffuseness (a₀), quadrupole deformation (β₂), and octupole deformation (β₃). In contrary to R_vn(c), R_vn(N_ch) is nearly independent of the analysis approaches, suggesting that nonflow effects are better controlled by N_ch than c. The ratios of observables sensitive to the chiral magnetic effect (CME) are also much closer to unity for x=N_ch than x=c, indicating that the ratios calculated at the same N_ch provide a better baseline for the non-CME background. According to the AMPT results, the dominant parameter for ΔR is a₀, while R₀ and β_n are only important in central collisions. The published p(N_ch) is also used to estimate ΔR_〈pT〉 for mean transverse momentum, which is non-negligible compared with R_〈pT〉−1.