Can (1440) Be a Pseudoscalar Glueball Which Appreciably Mixes with '(958)?

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Abstract
We have studied the η- η′- ι mixing by using the Gell-Mann-Oakes-Renner type approach to the chiral U(3) ×U(3) and also U(4) ×U(4) algebras involving anomaly and found that η′- ι mixing could be appreciable. The model also predicted (by using PCAC and also sometimes a simple quark counting argument) that while the rate of ι→γγ is relatively small, Γ(ι→ργ) will be rather large ≃1 MeV. The η- η′-ι mixing has also been studied by us using the method of “asymptotic flavor SU(3) symmetry plus the constraint algebras involving the generators of underlying symmetry groups of QCD”. Essentially the same conclusion as derived in the first approach has been obtained for the structures of η- η′-ι mixing. In this paper, we study the ι→γγ and ι→ργ decays in the second approach without using quark counting argument. We find a result which is compatible (at least in flavor SU(3) symmetry studied) with that of the first approach. We conclude that a part of the present experimental situation can be understood with the presence of pseudoscalar glueball ι(1440) which mixes rather appreciably with the η′. Critical experiments for the model are also discussed.

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