The Ground State Of 4 (+ +) Meson Nonet And The Glueball,

The existence of glueballs is an important prediction of the Quantum Chromodynamics(QCD) theory. The experimental discovery of these glueballs would give further support to the QCD theory. In the case of explicitly exotic quantumnumbers, glueballs can be identified without a comparative study of the qq spectrum. However, models of glueballs predict that the majority of the light glueballs will have nonexotic quantum numbers, and therefore must be identified against abackground of conventional qq quark model mesons.It is widely accepted that the a₄ (2040), K₄^* (2045) and f₄(2050) belong to theground 4⁺⁺ q(q|-) nonet. However, the ninth member of the ground 4⁺⁺ q(q|-) nonet is not yet determined experimentally. Also, in contrast to the ground scalar and tensor glueballs, the information on the ground 4⁺⁺ glueball predicted by lattice QCD and other approaches is rather limited. Therefore, the estimation of masses of the ground4⁺⁺ glueball and conventional q(q|-) states remains an interesting task. This couldprovide some calibration for more realistic models of glueballs and a template against which to interpret the nature of new observed resonances.In the framework of meson-meson mixing, in the presence of thea₄ (2040), K₄^* (2045) and f₄(2050) being the 1³F₄ q(q|-) states, we suggest that the f'₄, the ninth member of the 1³F₄ meson nonet, has a mass of about 2084 MeV, andsome predictions on the f₄ and f'₄ decaying into two photons and pseudoscalar mesons are presented. Also, the mass of the lowest lying 4⁺⁺ glueball is predicted to be about 3.15 GeV by using the meson-glueball mass relation derived from the glueball dominance picture, which is in agreement with 3.42GeV, the average value of the recent predicted results was given by lattice QCD, potential model, semi-relativistic potential model and quasi-particle model.