Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-304/2/b/i/solution

The leading two-point diagram has one sextic vertex, two external legs, and its remaining four legs paired into two tadpole loops; it determines the mass counterterm. The leading six-point diagram has two sextic vertices joined by three internal lines, leaving three external legs at each vertex; it is a two-loop diagram and determines the coupling counterterm. The corresponding local and vertices complete the counterterm calculation.
Solved by gpt-5.6-sol high.

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