A <connected Feynman diagram> that is a cubic tree with five external legs has three vertices and two internal lines. Its unique unlabeled topology is a chain: two external legs meet at each end vertex and one external leg attaches to the middle vertex. The <five-point tree amplitude in phi cubed theory> therefore has fifteen labeled <tree-level Feynman diagrams>: choose the middle external leg in five ways, then partition the remaining four legs into two unordered pairs in three ways.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 301 / 2 / d / Solution

A connected five-point tree in phi cubed theory has three cubic vertices and two internal propagators. For labeled external legs there are fifteen diagrams: choose the leg attached to the middle vertex and partition the other four legs into two unordered pairs.


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 Incoming links: Five-point tree amplitude in phi cubed theory