CCAST,WORLD LAB,CTR THEORET PHYS,BEIJING 100080,PEOPLES R CHINA
; ACAD SINICA,INST THEORET PHYS,BEIJING 100080,PEOPLES R CHINA
; ACAD SINICA,INST HIGH ENERGY PHYS,BEIJING 100039,PEOPLES R CHINA
; UNIV HAWAII MANOA,DEPT PHYS,HONOLULU,HI 96822
We discuss the search for a 1(--) gluonium state, O, in connection with a possible solution for the so-called p pi, K* (K) over bar puzzle in the J/psi and psi' decays. Some issues are examined. In particular, we argue that the expected most favorable process psi' --> pi pi O can have an appreciable branching ratio (say 10(-3) similar to 10(-4)) only if the O has a very narrow partial decay width to p pi (say 1 similar to 10 MeV) For the 0(-+) system we deduce a relation that BR(eta(c)' --> h) approximate to BR (eta(c) --> h), where h denotes an exclusive light hadronic channel. This relation may be useful for the experimental search of the yet to be confirmed eta(c)' state, for which the branching ratios of psi' --> gamma eta(c)' --> gamma KK pi, gamma eta pi pi, gamma eta'pi pi are estimated to be about 1 x 10(-4) if the mass of eta(c)' is around 3600 MeV, and this relation may also serve as a criterion to determine whether there exist anomalous decays in eta(c) and eta(c)' system, in particular in the VV decay channels, which might be related to the 0(-+) glueball-charmonium mixing. We emphasize that the bigluonium and the trigluonium may have very different effects on these decays.