Possible observables for the chiral electric separation effect in Cu + Au collisions

The quark-gluon plasma (QGP) generated in relativistic heavy-ion collisions could be locally parity-odd. In parity-odd QGP, the electric field may induce a chiral current which is called the chiral electric separation effect (CESE). We propose two possible observables for CESE in Cu + Au collisions: The first one is the correlation ${\zeta }_{\alpha \beta }=\langle cos\left[2({\varphi }_{\alpha }+{\varphi }_{\beta }-2{\Psi }_{\mathrm{RP}})\right]\rangle$; the second one is the charge-dependent event-plane angle ${\Psi }_2^q$ with $q=\pm$ being charge. Nonzero $\Delta \zeta ={\zeta }_{\mathrm{opp}}-{\zeta }_{\mathrm{same}}$ and $\Delta \Psi =\langle |{\Psi }_2^{+}-{\Psi }_2^{-}|\rangle$ may signal the CESE in Cu + Au collisions. Within a multiphase transport model, we study how the final state interaction affects these observables. We find that the correlation ${\gamma }_{\alpha \beta }=\langle cos({\varphi }_{\alpha }+{\varphi }_{\beta }-{\Psi }_{\mathrm{RP}})\rangle$ is sensitive to the out-of-plane charge separation caused by the chiral magnetic effect and to the in-plane charge separation caused by the in-plane electric field, but it is not sensitive to the CESE. On the other hand, $\Delta \zeta$ and $\Delta \Psi$ are sensitive to the CESE. Therefore, we suggest that future experiments measure the above observables in Cu + Au collisions in order to disentangle different chiral and charge separation mechanisms.

Figure 1

Centrality dependence of $\langle cos({\varphi }_{\alpha }+{\varphi }_{\beta })\rangle$ in Cu + Cu collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV. The open symbols represent the results from the normal AMPT model without anomalous effects and the AMPT model with an initial CME-like charge separation, and the solid symbols represent the experimental data [14].

Figure 2

Net electric charge distributions in the transverse momentum plane in the initial partonic states for different settings of AMPT models for centrality bin of 30–40% in Cu + Au collisions $\sqrt{s_{{}_{NN}}}=200$ GeV. (a) Normal setting without any anomalous effect. (b) AMPT with out-of-plane charge separation which mimic the CME. (c) AMPT with in-plane CSE caused by the in-plane electric field. (d) AMPT with in-plane CSE plus a quadrupolar distribution due to the CESE and CME. (e) The same as (d) but with the strength of CME doubled. (f) The same as (d) but with the strength of the in-plane CSE doubled.

Figure 3

Charge configuration of CME plus CESE plus in-plane CSE in Cu + Au collisions.

Figure 4

Centrality dependence of ${\gamma }_{\alpha \beta }=\langle cos({\varphi }_{\alpha }+{\varphi }_{\beta })\rangle$ from different initial settings of AMPT models (open symbols) in Cu + Au collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV. Also shown are the experimental data for Cu + Cu collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV (solid symbols) [14]. Different panels are in one-to-one correspondence with Fig. 2.

Figure 5

Centrality dependence of the difference between opposite-charge $\left({\zeta }_{\mathrm{opp}}\right)$ and same-charge $\left({\zeta }_{\mathrm{same}}\right)$ correlations of ${\zeta }_{\alpha \beta }=\langle cos\left[2({\varphi }_{\alpha }+{\varphi }_{\beta })\right]\rangle$ for three different initial settings of AMPT models in Cu + Au collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV. Some points are slightly shifted along the horizonal axis for clearer representation.

Figure 6

Centrality dependence of the difference between event plane angles reconstructed from the positively charged hadrons and negatively charged hadrons, $\langle |{\Psi }_2^{+}-{\Psi }_2^{-}|\rangle$, for six initial settings of AMPT models in Cu + Au collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV.