Comment on "When can hadronic loops scuttle the Okubo-Zweig-Iizuka rule?"

Abstract

Previous calculations by Geiger and Isgur showed that systematic cancellations among hadronic loops occur for $u\overline{u}\ensuremath{\leftrightarrow}s\overline{s}$ mixing in all the low-lying nonets except ${0}^{++}$. They suggested it is due to $^{3}P_{0}$ dominance of the effective quark-antiquark ($q\overline{q}$) pair creation operator. Here we give a general argument that there should be a large mixing for ${0}^{++}$ nonet from hadronic loops no matter what kind of model is assumed for $q\overline{q}$ creation. By the same argument we show that the Okubo-Zweig-Iizuka (OZI) rule should be best obeyed in the ${1}^{\ensuremath{-}\ensuremath{-}}$, ${2}^{++}$, and ${3}^{\ensuremath{-}\ensuremath{-}}$ nonets, but not very well obeyed in the ${0}^{\ensuremath{-}+}$, ${1}^{+\ensuremath{-}}$, and ${1}^{++}$ nonets. All these model independent expectations are compatible with calculations by Geiger and Isgur using the $^{3}P_{0}$ model as well as experimental data. A similar argument also suggests a large hadronic loop contribution for the $p\overline{p}\ensuremath{\rightarrow}\ensuremath{\varphi}\ensuremath{\varphi}$ reaction.