On The Origin of the OZI Rule in QCD

TL;DR

This paper investigates the origin of the OZI rule in QCD, confirming its suppression in vector and axial vector mesons through lattice calculations, and revealing significant violations in scalar mesons, linking to the U_A(1) anomaly.

Contribution

The study provides lattice QCD evidence that the OZI rule's suppression is consistent with quark model predictions and identifies large violations in scalar mesons, offering insights into the (1) anomaly.

Findings

OZI rule holds in vector and axial vector mesons as observed in lattice QCD.

Large OZI violation is found in scalar mesons, consistent with quark model expectations.

Results favor the large N_c interpretation over instanton-based explanations for the (1) anomaly.

Abstract

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.