Forward-backward eccentricity and participant-plane angle fluctuations and their influences on longitudinal dynamics of collective flow

Abstract

We argue that the transverse shape of the fireball created in heavy ion collision is controlled by event-by-event fluctuations of the eccentricity vectors for the forward-going and backward-going wounded nucleons: $\vec{\epsilon}_n^{\mathrm{F}}\equiv \epsilon_n^{\mathrm{F}} e^{i n\Phi_n^{\mathrm{*F}}}$ and $\vec{\epsilon}_n^{\mathrm{B}}\equiv \epsilon_n^{\mathrm{B}} e^{i n\Phi_n^{\mathrm{*B}}}$. Due to the asymmetric energy deposition of each wounded nucleon along its direction of motion, the eccentricity vector of the produced fireball is expected to interpolate between $\vec{\epsilon}_n^{\mathrm{F}}$ and $\vec{\epsilon}_n^{\mathrm{B}}$ along the pseudorapidity, and hence exhibits sizable forward-backward(FB) asymmetry ($\epsilon_n^{\rm B}\neq\epsilon_n^{\rm F}$) and/or FB-twist ($\Phi_n^{\mathrm{*F}}\neq\Phi_n^{\mathrm{*B}}$). A transport model calculation shows that these initial state longitudinal fluctuations for $n=2$ and 3 survive the collective expansion, and result in similar FB asymmetry and/or a twist in the final state event-plane angles. These novel EbyE longitudinal flow fluctuations should be accessible at RHIC and the LHC using the event-shape selection technique proposed in earlier papers. If these effects are observed experimentally, it could improve our understanding of the initial state fluctuations, particle production and collective expansion dynamics of the heavy ion collision.