Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2017/iii/paper-305/3/a/iv/solution

Allowed through a virtual W boson. The charm quark emits a and becomes a down quark through the nonzero CKM matrix element . The virtual W boson produces a positive muon and a muon neutrino through the leptonic weak charged current. The right panel is the unique physical-particle tree-level Feynman diagram.
Its total electric charge is , equal to the initial charge, and its final lepton number is . The decay is Cabibbo suppressed, rather than forbidden. These diagram counts use unitary gauge: in covariant gauges charged unphysical Goldstone bosons can supply gauge-dependent pieces of the same physical amplitudes, not additional physical channels.

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