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A one-loop Feynman diagram with four vertices joined into a box. Two W bosons and two internal quarks give a short-distance contribution to neutral D-meson mixing.

The ground-state D meson family contains open-charm mesons with a charm quark and a light antiquark: $D^0=c\bar{u}$ and $D^{+}=c\bar{d}$, together with their antiparticles. Their spin-parity is $0^{-}$. A Ds meson instead pairs charm with a strange antiquark.^[ref]

These ground states decay weakly, making their lifetimes and final-state distributions probes of charm-changing interactions. Excited D-family states need not share that decay pattern: when kinematically allowed, an excited state can decay strongly to a lower charmed state and other hadrons. The neutral ground state also participates in neutral D-meson mixing.

Neutral D-meson mixing is the time evolution between the flavor states $D^0=c\bar{u}$ and ${\bar{D}}^0=\bar{c}u$. The states with definite propagation masses and decay widths are generally superpositions of these flavor states, so an initially tagged flavor need not remain unchanged before decay.

A measurement tags the production flavor and compares time-dependent rates into selected final states. Some final states can be reached both directly and after mixing, producing interference; a wrong-flavor candidate is therefore not automatically a pure mixing event. The effective two-state Hamiltonian includes both dispersive and absorptive parts. Separating mixing, direct suppressed decays and detector charge asymmetries is part of the inference.^[ref]

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:

The incoming $c\bar{u}$ pair becomes $u\bar{c}$; 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 $g^4$. Summing the internal flavours produces Cabibbo-Kobayashi-Maskawa matrix factors and the Glashow-Iliopoulos-Maiani mechanism: the flavour-independent term cancels by ${\sum }_i{V}_{ci}^{\ast }{V}_{ui}=0$. This box Feynman diagram is one contribution; long-distance intermediate hadron states can also contribute to neutral D-meson mixing.

The tree-level Feynman diagrams contain an unchanged spectator quark, of up quark flavour and the two possible weak charged current transitions of the charm antiquark:

For ${\bar{D}}^0\to K^{+}{\pi }^{-}$, $\bar{c}\to \bar{s}{W}^{-}$ and $W^{-}\to d\bar{u}$. The spectator quark combines with $\bar{s}$ into the kaon $K^{+}=u\bar{s}$, while $d\bar{u}$ forms the pion ${\pi }^{-}$. The Cabibbo-Kobayashi-Maskawa matrix factor is $V_{cs}{V}_{ud}^{\ast }$.

For ${\bar{D}}^0\to K^{-}{\pi }^{+}$, $\bar{c}\to \bar{d}{W}^{-}$ and $W^{-}\to s\bar{u}$. The spectator quark combines with $\bar{d}$ into the pion ${\pi }^{+}=u\bar{d}$, while $s\bar{u}$ forms the kaon $K^{-}$. The Cabibbo-Kobayashi-Maskawa matrix factor is $V_{cd}{V}_{us}^{\ast }$.

Neglecting neutral D-meson mixing and assuming comparable strong interaction matrix elements, the relative direct decay widths areHere ${\theta }_C$ is the Cabibbo angle. The second process is doubly Cabibbo suppressed: it contains two small Cabibbo suppression factors in its amplitude. The Cabibbo angle estimate assumes similar quantum chromodynamics matrix elements; it is not an exact rate equality.