Past exam of the particle and nuclear physics course of the University of Cambridge / 2022 / Section A / 3 / a / Solution

Use the usual Feynman rule convention in which the diagonal quadratic terms of the free Lagrangian, including the physical W boson and Z boson masses, are incorporated into their propagators. Then there areA line joining two ends is a propagator, not an interaction vertex. Gauge boson self-interactions begin with cubic terms in the Yang-Mills theory Lagrangian. The question's $g,W,Z,\gamma$ name four families: they include eight gluon colour components and the two charged W bosons $W^{\pm }$.

There is a convention to distinguish here: if a calculation expands around massless free fields, quadratic $m_W^2{W}_{\mu }^{+}{W}^{-\mu }$ and $m_Z^2{Z}_{\mu }{Z}^{\mu }/2$ terms may be drawn as two-leg mass insertions. Those two insertion types belong to that bookkeeping convention. Similarly, two-point self-energy corrections occur in loop diagrams. Neither is an additional fundamental interaction in the standard physical-mass, tree-level rules used for the count above.