Left-right splitting of elliptic flow due to directed flow in heavy ion collisions

Abstract

Recently the splitting of elliptic flow ${v}_{2}$ at finite rapidities has been proposed as a result of the global vorticity in noncentral relativistic heavy ion collisions. In this study, we find that this left-right (i.e., on opposite sides of the impact parameter axis) splitting of the elliptic flow at finite rapidities is a result of the nonzero directed flow ${v}_{1}$, with the splitting magnitude $\ensuremath{\approx}8{v}_{1}(1\ensuremath{-}3{v}_{2})/(3\ensuremath{\pi})$. We also use a multiphase transport model, which automatically includes the vorticity field and flow fluctuations, to confirm the ${v}_{2}$ splitting. In addition, we find that the analytical expectations for the ${v}_{2}$ splitting work for the raw ${v}_{2}$ and ${v}_{1}$ (i.e., before event plane resolutions are applied) measured relative to either the first- or second-order event plane. Since the ${v}_{2}$ splitting is mostly driven by ${v}_{1}$, it vanishes at zero transverse momentum $({p}_{\mathrm{T}})$, and its magnitude and sign may have nontrivial dependencies on ${p}_{\mathrm{T}}$, centrality, collision energy, and hadron species.