Allowed through a t-channel W boson. Along one fermion line the up quark becomes a down quark by emitting a virtual ; along the other the charm antiquark absorbs it and becomes a strange antiquark. The middle panel shows this weak charged current exchange. Both electric charge and baryon number are conserved at each vertex, and the relevant CKM matrix entries are nonzero.
This is the unique physical-particle tree-level Feynman diagram. A neutral exchange would require a flavor-changing neutral current on each line, absent at tree level in the Standard Model. An annihilation into a neutral boson would likewise require an off-diagonal up-type neutral current. The different generations do not forbid the charged-current graph.
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.
A leading short-distance Standard Model contribution to neutral D-meson mixing is a box Feynman diagram with two W bosons and two internal down-type quark lines:
Figure 1.
Short-distance box contribution to neutral D-meson mixing
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The incoming pair becomes ; the internal labels run over the down quark, strange quark and bottom quark. Each corner is a weak charged current vertex. Four such vertices make the contribution of order . Summing the internal flavours produces Cabibbo-Kobayashi-Maskawa matrix factors and the Glashow-Iliopoulos-Maiani mechanism: the flavour-independent term cancels by . This box Feynman diagram is one contribution; long-distance intermediate hadron states can also contribute to neutral D-meson mixing.