The OZI rule is related to asymptotic freedom, in the following sense: In an OZI-suppressed diagram the gluons must be "hard" (high energy), since they carry the energy necessary to make the hadrons into which they fragment. But asymptotic freedom says that gluons couple weakly at high energies (short ranges). By contrast, in OZI-allowed processes the gluons are typically "soft" (low energy), and in this regime the coupling is strong.
The OZI (Okubo-Zweig-Iizuka) rule is a principle in particle physics that states that the decay of a particle into two other particles can be suppressed if the intermediate particle is a flavor singlet. This means that the intermediate particle has no flavor, such as the gluon in the strong nuclear force.
The OZI rule helps to explain the behavior of hadrons (particles made up of quarks) and their decays. It also helps to determine the structure of strong interactions between particles, which is an important aspect of the Standard Model of particle physics.
The OZI rule was first proposed by physicists Murray Gell-Mann, Yoichiro Nambu, and George Zweig in the 1960s based on experimental observations. It was later confirmed through various experiments, including the discovery of the J/psi particle in 1974 by the SLAC and Brookhaven National Laboratory collaborations.
While the OZI rule holds true in most cases, there are some exceptions. For example, the decay of the eta particle into two pi mesons violates the OZI rule. These exceptions can be explained by the effects of quark mixing and the non-zero masses of the quarks.
The OZI rule is closely related to the concept of quark confinement, which is the theory that quarks cannot exist as free particles. The OZI rule helps to explain why certain combinations of quarks, such as three quarks in a baryon, are more stable than others. This stability is a result of the strong nuclear force, which binds the quarks together and prevents them from existing as isolated particles.