Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-305/3/e/solution

The invariant interaction is
because has charge while the fermion pair has charge . Once has a vacuum expectation value, it generates a Majorana-type fermion mass and can split the two Majorana components of the original Dirac field.
The operator has dimension
so its coupling is classically marginal in four dimensions. By comparison, has dimension three and its coefficient is a relevant mass parameter.

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