Flavor-changing neutral current

A flavor-changing neutral current changes fermion flavor without changing electric charge. Such currents are absent at tree level in the Standard Model and are strongly suppressed at loop level by the Glashow-Iliopoulos-Maiani mechanism.

A penguin diagram is a loop topology in which a neutral gauge boson is emitted during a flavour-changing transition. A representative electroweak top-quark diagram contains a charged vector and a down-type quark loop. Individual attachments need not be gauge invariant; the physical amplitude includes the required companion graphs and flavour sums.

Unitarity of the CKM matrix cancels flavour-independent contributions to weak flavour-changing neutral amplitudes. In a quark loop, equal internal masses would give a common contribution whose off-diagonal CKM sum vanishes; unequal masses leave a suppressed nonzero amplitude. This explains why neutral kaon mixing occurs through loops rather than a tree neutral-current vertex.

For $q=u,c$ and a neutral photon or Z boson, the loop runs over down-type quarks. CKM unitarity cancels a common mass-independent loop contribution. The large bottom mass relative to down and strange masses normally makes the surviving bottom contribution largest, and $|V_{cb}|>|V_{ub}|$ favours final charm. Adding a resolved photon to a $qZ$ final state introduces another electromagnetic coupling and three-body phase space without removing the flavour cancellation. Some diagrams use the quartic gauge vertex, so the number of vertices need not increase.

The Glashow-Iliopoulos-Maiani mechanism uses the unitarity of the quark mixing matrix to cancel flavor-changing neutral-current amplitudes when equal-charge quark masses are degenerate. The remaining loop amplitudes are suppressed by quark-mass differences.