I am really confused about the difference between the eikonal and soft limits. I am trying to understand how collinear divergences cancel in gravitational scattering amplitudes.
Let me first define the soft limit as the low energy limit, i.e., a soft particle is defined as a particle with energy $E \rightarrow 0$. In Weinberg's paper from 1965 where he derives the soft photon and graviton theorems, he computes the IR divergence from virtual soft exchanges for an amplitude with gravitons coupled to massive scalars. He then shows that in the massless limit, the IR divergent factor contains collinear divergences which cancel in the case of gravity but not in QED. Essentially, his result proves that collinear divergences that arise between a soft graviton and other massless particles cancel.
My confusion now is that several papers that refer to this result from Weinberg's paper say that collinear divergences cancel in the eikonal limit. For example, 1207.4926. But isn't the eikonal approximation related to the center of mass energy being very large? More specifically, taking $t/s \rightarrow 0$ where $t$ and $s$ are the Mandelstam variables. This does not need to have anything to do with soft particles of any kind, if I understand correctly. Are there two different definitions of what the eikonal approximation means? Or are the seemingly different definitions here somehow related?
