Importance of Isobar Density Distributions on the Chiral Magnetic Effect Search

Under the approximate chiral symmetry restoration, quark interactions with topological gluon fields in quantum chromodynamics can induce a chirality imbalance and parity violation in local domains. An electric charge separation (CS) could be generated along the direction of a strong magnetic field ($\mathbf{B}$), a phenomenon called the chiral magnetic effect (CME). CS measurements by azimuthal correlators are contaminated by major backgrounds from elliptic flow anisotropy ($v_2$). Isobaric ${}_{44}{}^{96}\mathrm{Ru}+{}_{44}{}^{96}\mathrm{Ru}$ and ${}_{40}{}^{96}\mathrm{Zr}+{}_{40}{}^{96}\mathrm{Zr}$ collisions have been proposed to identify the CME (expected to differ between the two systems) out of the backgrounds (to be almost the same). We show, by using the density functional theory calculations of the proton and neutron distributions, that these expectations may not hold as originally anticipated because the two systems may have sizable differences in eccentricity and $v_2$.

Figure 1

Proton and neutron density distributions of the ${}_{44}{}^{96}\mathrm{Ru}$ and ${}_{40}{}^{96}\mathrm{Zr}$ nuclei, assumed spherical, calculated by the DFT method.

Figure 2

(a) ${\epsilon }_2\{\psi \}$ and (b) $\overline{B_{\mathrm{sq}}}\{\psi \}$ with respect to $\psi ={\psi }_{\mathrm{RP}}$ and ${\psi }_{\mathrm{PP}}$ as functions of $b$ in RuRu and ZrZr collisions, calculated by MCG with the DFT densities in Fig. 1.

Figure 3

Relative differences between RuRu and ZrZr collisions in ${\epsilon }_2\{\psi \}$ and $\overline{B_{\mathrm{sq}}}\{\psi \}$ with respect to (a) $\psi ={\psi }_{\mathrm{RP}}$ and (b) $\psi ={\psi }_{\mathrm{PP}}$, using the DFT densities in Fig. 1. The shaded areas correspond to DFT density uncertainties from Ru and Zr deformities; the hatched areas show the corresponding results using WS of Eq. (1).

Figure 4

Relative differences between RuRu and ZrZr collisions as functions of centrality in $v_2\{\psi \}$ (of charged particles in $|\eta |<1$) and $\overline{B_{\mathrm{sq}}}\{\psi \}$ with respect to $\psi ={\psi }_{\mathrm{RP}}$ and ${\psi }_{\mathrm{EP}}$, simulated by AMPT with the DFT densities in Fig. 1.