Complications in the interpretation of the charge-asymmetry-dependent π flow for the chiral magnetic wave
The charge asymmetry ($A_ch$) dependence of the $π^₋$ and $π^+$ elliptic flow difference, $Δv_2(A_{\text{ch}})$, has been regarded as a sensitive observable for the possible chiral magnetic wave (CMW) in relativistic heavy ion collisions. In this work, we first demonstrate that, due to nonflow backgrounds, the flow measurements by the Q-cumulant method using all charged particles as reference introduce a trivial linear term to $Δv_2(A_{\text{ch}})$. The trivial contribution to the slope of triangle flow difference $Δv_3( A_{\text{ch}})$ can be negative if the nonflow is dominated by back-to-back pairs. After eliminating the trivial term, we find that the nonflow between like-sign pairs gives rise to an additional positive slope to $Δv_2(A_{\text{ch}})$ because of the larger multiplicity dilution to $π^+$ ($π^₋$) at positive (negative) $A_{\text{ch}}$. We further find that the competition between different π sources can introduce another nontrivial linear-$A_{\text{ch}}$ term due to their different multiplicity fluctuations and anisotropic flows. We then study the effect of neutral cluster (resonance) decays as a mechanism for local charge conservation on the slope parameter of $Δv_2(A_{\text{ch}})$. We find that the slope parameter is sensitive to the kinematics of those neutral clusters. Light resonances give positive slopes while heavy resonances give negative slopes. Local charge conservation from continuum cluster mass distribution can give a positive slope parameter comparable to experimental data. Our studies indicate that many non-CMW physics mechanisms can give rise to a $A_{\text{ch}}$-dependent $Δv_2(A_{\text{ch}})$ and the interpretation of $Δv_2(A_{\text{ch}})$ in terms of the CMW is delicate.