Problem of theη-meson mass

In quark-gluon theory a conventional assumption is that the surprisingly large mass of the $\eta$ meson is caused by virtual annihilation and re-creation of a $q\overline{q}$ pair, the intermediate states being gluon states. The simplest component of the gluon states consists of two gluons. The virtual-annihilation mechanism is usally defined in terms of transitions through states containing gluons but no quarks. It is shown that if this definition is accepted, the virtual-annihilation mechanism is of the wrong sign to explain the large $\eta$ mass, unless the theory is more pathological than is commonly supposed. An alternate, diagrammatic definition of virtual annihilation is discussed briefly.