= Solution
<Feynman diagrams> organize the perturbative calculation of the <matrix element> in <Fermi's golden rule>. Each external line labels an incoming or outgoing particle state; each internal line contributes a <propagator> for a generally off-shell intermediate field; and each <interaction vertex> contributes a coupling and the appropriate <spin>, <momentum> and internal-symmetry structure. All indistinguishable allowed diagrams must be summed as <probability amplitudes> before taking the absolute square, so their <interference> contributes to the rate.
In the <radiative pion decay> diagram in part (b), solid arrowed lines are <fermions>; the wavy line joining the hadronic and leptonic vertices is a <W boson> <propagator>; and the wavy outgoing line is an external <photon>. Arrows track fermion number, so an outgoing <antimuon> has an arrow towards its production vertex. Each vertex conserves <four-momentum>; an internal <propagator> need not satisfy the on-shell <energy–momentum relation>. A closed <loop Feynman diagram> additionally requires an integration over an internal <four-momentum>.
The final <Lorentz-invariant phase space>, conservation <Dirac delta functions>, and the initial-state normalization or incident <flux> turn the squared <scattering amplitude> into a <decay rate> or <cross section>. A diagram supplies the dynamics; it is not itself the final <density of states>.
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