# Eikonal approximation in QFT

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.

In asymptotic region (high energy $s\rightarrow \infty$ and small momentum transfer $t$), the eikonal approximation means we drop out any diagram that has connections between internal lines; or it is corresponding to taking infinite ladder and cross-ladder Feynman's diagrams (including tree-level diagrams) in calculation of scattering amplitude and differential cross section. So, we will obtain leading contribution to the scattering process, and, by this reason, this is a good approximation.