Glueball theory of theξ(2.22)

We consider the possibility that the ξ(2.22) is a bound state of two TM (transverse magnetic) constituent gluons in the general context of the MIT bag theory. Only orbital angular momentum quantum number l=1 TM gluons are considered. The ξ(2.22) is analyzed both as a $0^{++}$ state and as a $2^{++}$ state. The method of effective Lagrangians is used to compute the processes V→ξ+γ and ξ→m+m¯, for V=ψ/J,Υ and m=K,π, where in the latter computations, contact is made with the theory of Lepage and Brodsky for exclusive processes in QCD. When compared to our results, the limited data which now exist on ψ/J→ξ+γ are not obviously inconsistent with either the $0^{++}$ or the $2^{++}$ assignment for the ξ. Observation of a ξ signal in Υ→ξγ, ξ→$K^{+}$ $K^{\mathrm{-}}$, with the branching-ratio product B(Υ→ξγ)B(ξ→$K^{+}$ $K^{\mathrm{-}}$)∼1.4×10 ${}_{}{}^{\mathrm{-}5}{}_{}{}^{}$ would strongly favor the $0^{++}$ assignment. The finding of the relation of widths Γ(ξ→${\pi }^{+}$ ${\pi }^{\mathrm{-}}$)≪Γ(ξ→$K^{+}$ $K^{\mathrm{-}}$ ) would do likewise.