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Does the eikonal approximation for calculating a scattering amplitude in QFT provide the exact result in the limit of $s\rightarrow\infty$ at finite $t=0$ ($s$ and $t$ are the usual Mandelstam variables)?
If so, does it match the answer obtained in the Born approximation in the same limit?
See e.g. Eq. (15-16) of http://arxiv.org/abs/hep-ph/0112161 for an explicit expression of the eikonal approximation.
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