I would be less interested in scattering amplitude of all particle physics concepts as a test case because the scattering amplitudes because it is one of the concisest definition and its solution is straightforward (not easy of course). So once you have a good grasp of the QM and the scattering then it is a matter of applying your knowledge of math to solve the problem. Usually the real problem is to actually define your parameters from your model and define the tree level calculations. Then for LLM to solve these it is impressive but the researchers defined everything and came up with the workflow.

So I would read this (with more information available) with less emphasize on LLM discovering new result. The title is a little bit misleading but actually "derives" being the operative word here so it would be technically correct for people in the field.