Origin of the Okubo-Zweig-Iizuka rule in QCD

Abstract

The Okubo-Zweig-Iizuka (OZI) rule is prominent in hadronic phenomena only because OZI violation is typically an order of magnitude smaller than expected from large ${N}_{c}$ arguments. With its standard ${}^{3}{P}_{0}$ pair creation operator for hadronic decays by flux tube breaking, the quark model respects the OZI rule at the tree level and exhibits the cancellations between OZI-violating meson loop diagrams required for this dramatic suppression. However, if the quark model explanation for these cancellations is correct, then OZI violation would be expected to be large in the nonet with the same quantum numbers as the pair creation operator: the ${0}^{++}$ mesons. Experiment is currently unable to identify these mesons, but we report here on a lattice QCD calculation which confirms that the OZI rule arises from QCD in the vector and axial vector mesons as observed, and finds a large violation of the rule in the scalar mesons as anticipated by the quark model. In view of this result, we make some remarks on possible connections between the ${}^{3}{P}_{0}$ pair creation model, scalar mesons, and the ${U}_{A}(1)$ anomaly responsible for the large OZI violation which drives the ${\ensuremath{\eta}}^{\ensuremath{'}}$ mass.