  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.
