Contributions to the event-by-event charge asymmetry dependence for the elliptic flow of pi^{+} and pi^{-} in heavy-ion collisions

We discuss various contributions to the event-by-event charge-asymmetry dependence of ${\pi }^{+}$ and ${\pi }^{-}$ elliptic flow, recently measured by the STAR Collaboration at RHIC. It is shown that under general assumptions, the difference between $v_2^{+}$ and $v_2^{-}$ at a given fluctuating value of an asymmetry parameter, $A$, is a linear function of $A$, as observed in the preliminary data. We discuss two mechanisms that are qualitatively consistent with the experimental data and result in a signal of the correct order of magnitude. Our subsequent hydrodynamic calculations, assuming local charge conservation at freeze-out, yield a qualitative and partial quantitative understanding of the observed signal, so offering a detailed test of the hydrodynamic model in heavy-ion collisions.