On The Origin of the OZI Rule in QCD

The 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 ^3P_0 pair creation operator for hadronic decays by flux tube breaking, the quark model respects the OZI rule at 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 ^3P_0 pair creation model, scalar mesons, and the U_A(1) anomaly responsible for the large OZI violation which drives the \eta' mass. In particular, we note that our result favors the large N_c and not the instanton interpretation of the solution to the \eta' mass problem.