Allowed through an s-channel W boson. The initial up quark and down antiquark annihilate into a virtual , which produces the final charm quark and strange antiquark. The two weak charged current vertices contain the nonzero CKM matrix elements and , with complex conjugations determined by fermion-flow conventions.
The left panel shows the unique physical-particle tree-level Feynman diagram. A neutral exchanged gauge boson cannot connect these charged annihilation currents, and flavour-diagonal neutral vertices cannot turn an up quark into a charm quark. There is no additional elementary charged scalar in the minimal Standard Model.
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.