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

We argue that the transverse shape of the fireball created in the heavy-ion collision could be strongly influenced by event-by-event fluctuations of the eccentricity vectors for the forward-going and backward-going wounded nucleons: PεₙF≡εₙFe^inΦₙ*F and PεₙB≡εₙBe^inΦₙ*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 PεₙF and PεₙB along the pseudorapidity, and hence exhibits sizable forward-backward (FB) asymmetry (εₙB≠εₙF) and/or FB twist (Φₙ*F≠Φₙ*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 event-by-event 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.