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The neutral flavour states $d\bar{s}$ and $s\bar{d}$ can mix through second-order weak interactions. Box diagrams with W bosons and internal up-type quarks induce a strangeness-changing-by-two four-quark operator. The GIM mechanism removes its flavour-independent part.

Allowed through second-order weak interactions, not a tree-level neutral-current vertex. This is the flavour-changing transition responsible for neutral kaon mixing, with change of strangeness by two. Box Feynman diagrams contain two W bosons and internal up-type quarks. Their vertices come from the weak charged current and contain CKM matrix factors. At low energy they generate an operator $({\bar{s}}_L{\gamma }_{\mu }{d}_L)({\bar{s}}_L{\gamma }^{\mu }{d}_L)$ plus its conjugate. The GIM mechanism cancels the flavour-independent part of the internal-quark sum; unequal quark masses leave a nonzero loop amplitude.