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 $W^{+}$ and becomes a down quark through the nonzero CKM matrix element $V_{cd}$. 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 $-1/3+1=2/3$, equal to the initial charge, and its final lepton number is $-1+1=0$. 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.