The OZI rule states that a QCD diagram is suppressed if it can be cut into two by only cutting gluon lines (the precise wording is addressed in the question What is the precise statement of the OZI Rule?). Famously, the OZI rule is responsible for the $\phi$ meson decaying primarily to kaons rather than pions, even though the latter is kinematically preferred.
I've seen two different explanations for the OZI rule, one based on asymptotic freedom and one based on large $N$.
The asymptotic freedom explanation (as described in, for instance, Griffiths' Elementary Particles $\S2$) goes as follows: the internal gluons in an OZI-forbidden diagram are typically hard because they carry the entire energy of the process. Since the QCD coupling is smaller at higher energy, the diagram is suppressed. Conversely, the gluons in an OZI-allowed diagram are typically softer, and therefore they couple more strongly.
The large $N$ explanation (which I've seen in Coleman's Aspects of Symmetry and David Tong's gauge theory lecture notes) says that OZI-forbidden diagrams are suppressed by additional powers of $1/N$, where $N$ is the number of colours, relative to OZI-allowed diagrams. Quoting Coleman: "Graphs for [OZI]-forbidden processes must involve at least two quark loops, and thus are down in amplitude by at least one factor of $1/N$".
Now it seems a few situations are possible (of which #1 and #2 seem the most likely to me):
- Both explanations are correct, and if this is the case then either
- the asymptotic freedom and large $N$ effects are of roughly equal importance in explaining OZI suppression;
- or one effect typically dominates over the other.
- One of the explanations is correct and the other is incorrect, for some reason I don't know.
- Neither is correct and there is some other explanation, but again I don't see anything wrong with either explanation.
- These two explanations are somehow equivalent.
Which explanation is correct?
